laplace experiment zeichnen

Laplace Experiment

In diesem Artikel dreht sich alles um Laplace . Von der Laplace Wahrscheinlichkeit bis hin zum Laplace Würfel wird dir alles zu Laplace Experimenten erklärt.

Du möchtest wissen:  Was ist ein Laplace Experiment ? In unsrem Video erfährst du bequem und einfach was genau es bedeutet, wenn einem Zufallsexperiment die Laplace Bedingung zugrunde liegt.

Laplace Experiment Definition

Laplace wahrscheinlichkeit, laplace experiment aufgaben, laplace experiment — häufigste fragen, wahrscheinlichkeitsrechnung.

Ein Laplace Experiment ist ein Zufallsexperiment, bei dem alle elementaren Ergebnisse die selbe Wahrscheinlichkeit haben. Die dazugehörige Laplace Wahrscheinlichkeit wird mit der Laplace Formel berechnet, welche sich durch die Division der Anzahl des Ereignisses durch alle möglichen Ergebnisse ergibt.

Laplace Experiment Erklärung

Generell unterscheidet man in der Statistik unterscheidet verschiedene Spezialfälle von Wahrscheinlichkeiten. Einer dieser Sonderfälle ist die Laplace Wahrscheinlichkeit . Diese liegt den dazugehörigen Laplace Experimenten zugrunde und setzt voraus, dass alle elementaren Ergebnisse des Zufallsexperimentes die gleiche Wahrscheinlichkeit haben. Einfach gesagt, muss jedes mögliches Szenario gleich wahrscheinlich sein, damit von Laplace die Rede sein kann.

Laplace Experiment Beispiele

Das gängigste Beispiel für einen Laplace Versuch ist das Werfen eines ungezinkten Würfels. Ungezinkt bedeutet, dass dieser nicht manipuliert ist und, dass alle sechs Seiten mit gleicher Wahrscheinlichkeit gewürfelt werden. Bei einem Laplace Würfel fällt die 1 also genau gleich oft wie die 6, wenn man unendlich oft würfeln würde. Weitere Beispiele sind das Werfen einer Münze oder das drehen an einem Glücksrad. Die Wahrscheinlichkeit Kopf oder Zahl zu werfen beträgt dann nämlich jeweils genau 50%. Bei dem letzteren Beispiel muss zusätzlich beachten werden, dass alle möglichen Felder gleich häufig vorkommen müssen, damit die Laplace Bedingung erfüllt ist.

Du weist jetzt, dass jedem Laplace Experiment die Laplace Wahrscheinlichkeit zugrunde liegt. Die Bedingung, dass alle Versuchsausgänge gleich wahrscheinlich sind muss also erfüllt sein. Aber woher weiß man, ob diese Grundbedingung gegeben ist oder nicht?

Kein Laplace Experiment?

Wenn du also die Wahrscheinlichkeit für ein Ereignis bestimmen sollst, prüfe zunächst ob es sich bei dem Zufallsexperiment überhaupt um einen Laplace Versuch handelt oder nicht. Hier spricht man auch vom sogenannten Elementarereignis ω , also einem Ereignis, für das die Eintrittswahrscheinlichkeit immer gleich hoch ist. Es gilt:

Laplace Formel

Allgemein ist die Wahrscheinlichkeit in einem Laplace Experiment für ein Ereignis A durch die Laplace Formel wie folgt definiert:

Abschließend schauen wir uns noch zwei praktische Beispiele von Laplace Experimenten an. So wird deutlich wie man die Wahrscheinlichkeit dieser Zufallsexperimente einfach mit der Laplace Formel berechnen kann.

Laplace Würfel

Laplace Experiment Beispiel: Roulette

Die Wahrscheinlichkeit eine rote Zahl zu würfeln liegt also bei ungefähr 49%.

Das war auch schon alles Wichtige ! Zur Wiederholung hier nochmal die zentrale Formel:

• Was ist ein Laplace Experiment? Ein Laplace Experiment ist ein Zufallsexperiment, bei dem alle Ergebnisse dieselbe Wahrscheinlichkeit haben, einzutreffen. Ein typisches Beispiel hierfür ist der Wurf eines Würfels. Jede Augenzahl hat dieselbe Wahrscheinlichkeit gewürfelt zu werden, nämlich 1/6.   
• Was ist die Laplace Formel? Die Laplace Formel bestimmt die Wahrscheinlichkeit eines Ereignisses (E) im Laplace Experiment. Wenn die Gesamtzahl aller möglichen Ergebnisse n ist, berechnet sich die Wahrscheinlichkeit mit P(E) = 1/n.  
• Wie läuft ein Laplace Versuch ab? In einem Laplace Versuch (Experiment) müssen alle möglichen Ereignisse mit gleicher Wahrscheinlichkeit stattfinden. Das heißt, dass jedes zufällige Ergebnis gleich hohe Chancen hat, einzutreffen. Ein typisches Beispiel für ein Laplace Versuch ist der Wurf eines fairen Würfels.

Neben dem Laplace Experiment gibt es noch andere Zufallsexperimente. Wie du dann die Wahrscheinlichkeit berechnest , erfährst du hier!

Beliebte Inhalte aus dem Bereich Wahrscheinlichkeitsrechnung

• Bedingte Wahrscheinlichkeit Dauer: 02:16
• Vierfeldertafel Dauer: 04:46
• Satz der totalen Wahrscheinlichkeit Dauer: 01:58

Weitere Inhalte: Wahrscheinlichkeitsrechnung

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Laplace-Experiment & Laplace-Wahrscheinlichkeit

Hast du dich schon einmal gefragt, wie du die Wahrscheinlichkeit von bestimmten Ereignissen berechnest? Die Laplace-Wahrscheinlichkeit bietet eine der wichtigsten Möglichkeiten, um solche Wahrscheinlichkeiten zu bestimmen.

Aber welche Voraussetzungen müssen erfüllt sein, damit du mit der Laplace-Wahrscheinlichkeit rechnen darfst?

simpleclub zeigt dir alles, was du über Laplace-Experimente und Laplace-Wahrscheinlichkeiten wissen musst.

Laplace-Experiment einfach erklärt

Ein prototypisches Beispiel für ein Laplace-Experiment ist das einmalige Werfen mit einem Würfel.

Ein Laplace-Experiment ist einfach ein Zufallsexperiment mit der Zusatzbedingung, dass alle Ergebnisse die gleiche Wahrscheinlichkeit haben.

Das Würfeln ist zum Beispiel ein Laplace-Experiment , da es ein normales Zufallsexperiment ist und zusätzlich alle Zahlen mit der gleichen Wahrscheinlichkeit auftreten.

Laplace-Wahrscheinlichkeit

Mit der Laplace-Wahrscheinlichkeit berechnest du die Wahrscheinlichkeit eines beliebigen Ereignisses A A A A bei einem Laplace-Experiment .

Dabei teilst du die Anzahl der Elemente , die zu diesem Ereignis führen, durch die Gesamtanzahl an Möglichkeiten.

Laplace-Experiment Definition

Ein Laplace Experiment ist ein Zufallsexperiment, bei dem alle Ergebnisse dieselbe Wahrscheinlichkeit haben.

Laplace-Wahrscheinlichkeit Definition

Die Laplace-Wahrscheinlichkeit berechnet die Wahrscheinlichkeit eines bestimmten Ereignisses A A A A durch:

Laplace-Experiment

Ein Laplace Experiment ist also nichts anderes als ein normales Zufallsexperiment mit zusätzlicher Einschränkung.

Bei einem Zufallsexperiment sind immer drei Merkmale erfüllt:

• Der Ausgang des Zufallsexperiments ist nicht vorhersagbar .
• Das Zufallsexperiment hat mehrere Ausgänge (sogenannte Ergebnisse).
• Das Zufallsexperiment kann beliebig oft wiederholt werden.

Für ein Laplace-Experiment muss zusätzlich gegeben sein:

Dies vereinfacht das Rechnen mit Wahrscheinlichkeiten erheblich. Deshalb werden dir Laplace Experimente in der Schule häufig begegnen.

Typische Alltagsbeispiele sind das Werfen eines normalen Würfels, das Ziehen einer bestimmten Karte aus einem Kartendeck oder andere Situationen, in denen der Ausgang aller Ergebnisse genau gleich wahrscheinlich ist.

Alle Zufallsexperimente, bei denen nicht alle Ergebnisse die gleiche Wahrscheinlichkeit haben, sind keine Laplace Experimente !

Zum Beispiel ist das Drehen des folgenden Glücksrads kein Laplace-Experiment, da nicht alle Ergebnisse die gleiche Wahrscheinlichkeit haben.

Berechnung der Laplace-Wahrscheinlichkeit

Du kannst die Wahrscheinlichkeit eines Laplace-Experiments berechnen, wenn du die Anzahl der Ergebnisse zu einem Ereignis durch die Gesamtanzahl an Möglichkeiten teilst.

Beim einmaligen Werfen eines handelsüblichen Würfels gehören zu dem Ereignis G G G G : Es wird eine gerade Zahl gewürfelt die Ergebnisse 2 2 2 2 , 4 4 4 4 und 6 6 6 6 . Die Anzahl an Möglichkeiten zu dem Ereignis G G G G sind also 3 3 3 3 .

Mathematisch ausgedrückt ist das die Mächtigkeit des Ereignisses G G G G . Du sagst also Ereignis G G G G besitzt die Mächtigkeit 3 3 3 3 .

Das schreibst du dann mit Betragsstrichen um das Ereignis:

Es können insgesamt die Zahlen 1 1 1 1 bis 6 6 6 6 gewürfelt werden.

Die Anzahl aller Ergebnisse im Ergebnisraum ist die Mächtigkeit des Ergebnisraum .

Du kannst die Wahrscheinlichkeit des Ereignisses G G G G , also P(G) P ( G ) P(G) P ( G ) , nun durch die Laplace-Wahrscheinlichkeit berechnen. Dazu teilst du die Mächtigkeit des Ereignisses durch die Mächtigkeit des Ergebnisraums .

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Pasch würfeln

Jan und ein Freund würfeln in einem Café mit zwei Würfeln darum, wer von ihnen den nächsten Kaffee bezahlen muss.

Bei einem Pasch (beide Würfel zeigen dieselbe Augenzahl) ist Jan an der Reihe, bei allen anderen Würfen muss sein Freund bezahlen.

Berechne die Wahrscheinlichkeit , dass Jan den nächsten Kaffee bezahlen muss.

Es handelt sich um ein Laplace Experiment , da alle möglichen Würfe gleich wahrscheinlich sind.

Es gibt 6 Möglichkeiten , einen Pasch zu würfeln (also 6 gewünschte Ergebnisse ):

Insgesamt gibt es 36 mögliche Ergebnisse , da mit zwei Würfeln 36 verschiedene Kombinationen möglich sind:

Du berechnest nun die Wahrscheinlichkeit dafür, dass Jan Kaffee holen muss, indem du die Anzahl der gewünschten Ergebnisse (einen Pasch) durch die Anzahl aller möglichen Ergebnisse teilst:

Karte ziehen

In einem gewöhnlichen Skatdeck befinden sich insgesamt 32 Karten .

Wie hoch ist die Wahrscheinlichkeit bei einmaligem Ziehen einen Buben aus dem Deck zu ziehen?

Wieder handelt es sich um ein Laplace Experiment , da die Wahrscheinlichkeit eine bestimmte Karte zu ziehen bei jeder Karte genau gleich groß ist.

Es gibt vier Buben in dem Kartendeck, also ist dies auch die Anzahl der gewünschten Ergebnisse :

Insgesamt sind 32 Karten im Kartendeck, also können auch 32 verschiedene Karten gezogen werden. Somit gibt es 32 mögliche Ergebnisse :

Nun berechnest du die Gesamtwahrscheinlichkeit einen Buben zu ziehen , indem du die Anzahl der gewünschten Ergebnisse (ein Bube wird gezogen) durch die Anzahl aller möglichen Ergebnisse teilst:

Zusammenfassung

Ein Laplace-Experiment ist ein Zufallsexperiment , bei dem zusätzlich alle Ergebnisse die gleiche Wahrscheinlichkeit besitzen.

Bei der Laplace-Wahrscheinlichkeit berechnest du die Wahrscheinlichkeit eines Ereignis A A A A , indem du die Anzahl der günstigen Möglichkeiten durch die Gesamtmöglichkeiten teilst.

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Laplace Experiment

„Lasst uns eine Münze werfen.“ Hättet ihr vielleicht nicht gedacht, dass man die Wahrscheinlichkeit berechnen kann, ob im nächsten Moment Zahl oder Kopf erscheint? Dann solltet ihr unbedingt einen Blick auf das Laplace Experiment werfen.

Was ist die Laplace Regel

• Der französische Mathmatiker Pierre-Simon Laplace (1749 – 1827) machte Entdeckungen in der Wahrscheinlichkeitsrechnung, die in der modernen Mathematik heute unverzichtbar sind. Er hat herausgefunden, dass bei manchen Zufallsexperimenten alle Ergebnisse gleichwahrscheinlich sind. Bei einem Münzwurf ist es zum Beispiel gleichwahrscheinlich, auf welcher Seite die Münze landet – Kopf oder Zahl. Zufallsexperimente wie diese nennt man daher nach dem französischen Mathematiker Laplace-Zufallsexperimente

Laplace Wahrscheinlichkeit berechnen

Vorgehensweise

• Anzahl aller überhaupt möglichen Elementarereignisse berechnen
•  Anzahl der Elementarereignisse berechnen, bei denen E eintritt
• Laplace-Wahrscheinlichkeit berechnen

Formel Laplace Experiment

Einführung in das Laplace Experiment

Natürlich gehen wir davon aus, dass in Wirklichkeit die Karten gezinkt und Münzen und Würfel manipuliert sein können. Dennoch brauchen wir für die Berechnung und den Versuch eine exaktere Form der Wirklichkeit.

Einen Laplace Versuch gibt es nur in der Theorie. Wir betrachten das Münzbeispiel.

Wenn Du eine reale Münze wirfst, kann sie auf die eine oder andere Seite fallen. Da aber eine Münze mechanisch hergestellt ist, kann sie Unregelmäßigkeiten aufweisen, die dazu führen, dass sie öfter auf die eine Seite fällt als auf die andere. Außerdem kann eine Münze auch in sehr seltenen Fällen auf der Kante stehenbleiben.

Laplace hat sich für seine Wahrscheinlichkeitsrechnung eine Münze vorgestellt, die wirklich genau zu 50% auf der einen oder anderen Seite zu liegen kommt. Außerdem fällt die Laplace Münze nie auf die Kante. Es handelt sich also um das theoretische Idealbild einer Münze.

Dementsprechend gibt es dann auch andere Lapalace-Zufallsgeräte (z.B. Würfel).

Wird ein Zufallsexperiment mit einer endlichen Ergebnismenge E hinreichend oft wiederholt und zeigt sich dabei, daß keines der Elementarereignisse gegenüber einem anderen bevorzugt auftritt, so werden alle Ereignisse stets näherungsweise gleich häufig auftreten und wir sprechen von einem Laplace-Experiment

Wann die Laplace-Formel nicht gilt

Beim Münz- und Würfelwurf funktioniert die Anwendung der Laplace-Formel prima. Bei vielen anderen Zufallsexperimenten allerdings nicht. Sie kann nur dann angewendet werden, wenn alle Elementarereignisse die selbe Eintrittswahrscheinlichkeit haben. Bei der Münze und beim Würfel ist das gegeben: Per Zufall erscheint eine der Seiten und keine hat eine höhere Wahrscheinlichkeit als irgendeine andere Seite. Bereits bei einem gezinkten Würfel, der z. B. in 50% aller Fälle eine 6 ergibt und in 50% aller Fälle eine Augenzahl zwischen 1 und 5 versagt die Laplace-Formel.

Wieso kann die Formel nun nicht auf solche Zufallsexperimente angewendet werden?

Das liegt daran, dass in der Formel nur die Anzahlen eine Rolle spielen: Die Anzahl aller gesuchten Elementarereignisse wird durch die Anzahl aller möglichen Elementarereignisse geteilt. Verwendet man nur die Anzahlswerte, dann setzt man voraus, dass die Eintrittswahrscheinlichkeit jedes einzelnen Elementarereignisses gleich ist — andernfalls müssten auch die Eintrittswahrscheinlichkeiten der Elementarereignisse in der Formel auftauchen. ⇒ Die Laplace-Formel darf nur dann verwendet werden, wenn jedes Elementarereignis die selbe Eintrittswahrscheinlichkeit hat (siehe z. B. Würfel oder Münzwurf)

Bei den folgenden Experimenten und Ereignissen handelt es sich um das Laplace Experiment:

• Münze werfen
• Karte ziehen
• Glücksrad drehen
• Gameshow Prinzip – Tür, Box oder Durchgang wählen

Ω = {1, 2, 3}

Beim Drehen des Glücksrades kannst du als Ergebnis also entweder die 1, die 2 oder die 3 erhalten.

Da die Flächen der jeweiligen Zahlen gleich groß sind, besitzt jedes Ergebnis die gleiche Wahrscheinlichkeit beim Drehen angezeigt zu werden.

Kein Laplace Experiment

Auch bei diesem Glücksrad ergibt sich beim Drehen wieder die Ergebnismenge:

Ω = {1, 2, 3}.

Da die Fläche der Zahl 3 jedoch größer ist, als die Flächen der Zahlen 1 und 2, besitzen die drei Zahlen nicht mehr die gleiche Wahrscheinlichkeit. Die Wahrscheinlichkeit von Zahl 3 ist höher als die der Zahlen 1 und 2.

Wir werfen einen sechsseitigen Würfel und möchten verschiedene Wahrscheinlichkeiten bei dem Versuch berechnen:

• Wie groß ist die Wahrscheinlichkeit, die Zahl 3 zu Würfeln?
• Wie groß ist die Wahrscheinlichkeit, entweder eine 1 oder 4 zu Würfeln

Wir wissen, dass der Würfel sechs gleiche Seiten hat. Somit können als Ergebnis beim Würfeln die Zahlen 1, 2, 3, 4, 5 oder 6 geworfen werden. Die Anzahl der möglichen Ergebnisse beträgt somit „6“. Kommen wir nun zu den drei Teilaufgaben:

• P({3}) = 1 : 6 = 0,1666…
• P({1, 4}) = 2 : 6 = 0,33333…

Historische Bemerkungen

Statistik : „Ich würfle n mal und berechne….“ Verfahren, um empirische Daten zu gewinnen, darzustellen, zu verarbeiten, zu analysieren, ..

Wahrscheinlichkeitstheorie : „Ich sage für die Zukunft voraus….“ Bestimmung eines Maßes für den Grad der Möglichkeit des Eintreffens noch unverwirklichter Ereignisse.

Stochastik : „Mathematik des Zufalls“, Sammelbegriff für die Gebiete Statistik und Wahrscheinlichkeitstheorie

Die häufigsten Fehler beim LaPlace Experiment

Haben wir es also tatsächlich mit einem LaPlace Experiment zu tun, können alle Ergebnisse mit der gleichen Wahrscheinlichkeit folgen. Dabei spielt uns vor allen Dingen die menschliche Intuition ein Schnippchen. Wirfst du zum Beispiel eine Münze, entspricht die Menge der Ergebnisse Omega: KK, KZ, ZK, ZZ. Diese Ereignisse besitzen die gleiche Wahrscheinlichkeit.

Ist einem Spieler die Reihenfolge herzlich egal, verändert sich auch die Menge der Ergebnisse zu: KK KZ ZZ – das Ergebnis KZ trifft mit doppelter Wahrscheinlichkeit zu? Werfen wir also eine Münze 2 Mal, können wir dies noch recht schnell erkennen. Bei anderen Experimenten ist das gar nicht mehr so übersichtlich.

Vollkommen durcheinander gerät unsere Logik, wenn eine Familie mit zwei Kindern in das Münzexperiment einsteigt und damit beginnt, jeweils die Münzen zu werfen. Klar, es steht 50 zu 50, ob nun das erste oder zweite Kind beginnt die Münze zu werfen. Dabei ist aber die Wahrscheinlichkeit für Mädchen und Junge doppelt so hoch zu berechnen.

Aus diesem Grund solltest du von Anfang an genauestens nachdenken, ob die Ergebnisse mit der gleichen Wahrscheinlichkeit auftreten. Bei berechtigten Zweifeln kann ein Baumdiagramm weiterhelfen.

Fazit zum LaPlace Experiment

Im Prinzip müssen wir davon ausgehen, dass es in der Realität eigentlich keines der LaPlace Experimente gibt, da die Wirklichkeit immer von der Theorie abweicht. Wir haben es hier mit reinen Zufallsexperimenten zu tun, bei denen alle Ergebnisse mit der gleichen Wahrscheinlichkeit auftreten. So ist davon auszugehen, dass es sich bei der Münze und dem Würfel, um den Willen einer Person im Raum und um ein  LaPlace Experiment handelt.

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• Varianz berechnen →

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A Student's Guide to Laplace Transforms

An introduction from the author:

Hello, and welcome to the website for A Student's Guide to Laplace Transforms. On this site, you'll find resources designed to help you understand the Laplace transform and how it can be used to solve problems in physics and engineering. Those resources include:

Complete solutions to every problem in the book

From this page, you'll be able to get a series of hints to help you solve each of the chapter-end problems in the text, or you can see the full solution to each problem straight away. To access this material, just click on "Interactive Problems" and then pick the chapter and problem number you'd like to work through.

Video podcasts

For each of the five chapters of A Student's Guide to Laplace Transforms I've recorded a series of video podcasts in which I explain the most significant principles, equations, and figures contained within that chapter. Just click on "Video Tutorials" and then pick the chapter and section of the video you'd like to view.

Supplemental documents and links

In the Supplemental Materials section, you can access tutorials and links to helpful resources for the following topics:

• Vectors and Functions (tutorial)
• Regions of Convergence (tutorial)
• Convolution (tutorial)
• Derivatives (slopes of sinusoidal and real exponential functions) (tutorial)
• Partial Fractions (tutorial)
• Analytic Continuation (references and links)
• Contour Integration (references and links)
• Synthesis of t f(t) from -dF(s)/ds (MATLAB video demonstration)

Book Corrections

After the book went to print, several errors were identified in the printing. A list of those corrections are listed in here:

• Corrections

I hope you find the material on this site useful, and I’m interested any comments you may have as to how this site and the text could be more useful to you. Thanks for your time.

To contact Dan Fleisch, send an e-mail to [email protected]

Laplace Experiment: Regel, Beispiele, Aufgaben

Laplace experiment - definition, beispiele für laplace experimente, was sind keine laplace-aufgaben.

In diesem Lerntext erklären wir dir alles zum Thema Laplace-Experimente , eine Art von Zufallsexperimenten, die du aus deinem Mathematikunterricht schon kennen wirst. Du wirst schnell verstehen, wie du bei dieser Art von Zufallsversuchen rechnest. Am Ende kannst du dein erlerntes Wissen zu Laplace und Wahrscheinlichkeiten in Aufgaben weiter vertiefen und kontrollieren.

Ein Laplace Experiment ist eigentlich nichts anderes als das, was du in deinem Matheunterricht als Zufallsversuch kennenlernst - mit einer kleinen Einschränkung: Ein Laplace Experiment ist ein Zufallsversuch, bei dem die Wahrscheinlichkeiten aller möglichen Ergebnisse gleich sind . Typische Beispiele bei Laplace sind in der Regel das Werfen einer Münze oder eines gewöhnlichen Würfels. Das Besondere an diesen Versuchen ist, dass sie uns das Rechnen mit Wahrscheinlichkeiten vereinfachen. In Laplace-Experimenten gilt die Regel:

$P (E) = \frac {Anzahl\ der\ gewünschten\ Ergebnisse}{Anzahl\ der\ möglichen\ Ergebnisse}$

Wir müssen also einfach die Anzahl der Ergebnisse, die gewünscht sind, durch die Anzahl aller Ergebnisse dividieren.

Ein Laplace Experiment ist ein Zufallsversuch, bei dem die Wahrscheinlichkeiten aller möglichen Ergebnisse gleich sind.

Wie du siehst, ist die Rechnung für dich nicht neu. Und das ist nicht verwunderlich, da die allermeisten Zufallsexperimente, die du bis jetzt kennengelernt hast, Laplace-Experimente sind. Im Lerntext Zufallsversuche - Wahrscheinlichkeit von Ergebnissen berechnen kannst du nochmal alles Weitere dazu nachlesen.

Gut zu wissen

Pierre-Simon Laplace war ein französischer Mathematiker und Physiker, der um 1800 zu den Themen Wahrscheinlichkeitsrechnung und Differentialgleichungen forschte. Der Name Laplace kann dir in deinem Mathematikunterricht noch öfter begegnen.

Betrachten wir nun einige Beispiele, um den Unterschied zwischen Laplace-Experimenten und anderen Zufallsversuchen zu verstehen.

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Das erste "Laplace-Beispiel" ist ein wirklicher Klassiker in der Wahrscheinlichkeitsrechnung: das einmalige Werfen eines Würfels. Ein normaler Würfel hat sechs Seiten, die mit den Zahlen 1 bis 6 beschriftet sind. Jede Zahl hat die gleiche Wahrscheinlichkeit, gewürfelt zu werden.

Jede Zahl wird mit einer Wahrscheinlichkeit von

$P(E) = \frac {1}{6} \approx 16,7 \%$

gewürfelt.

Betrachten wir die Wahrscheinlichkeit für das Ereignis "eine gerade Zahl würfeln":

Ereignis: "eine gerade Zahl würfeln"

Ereignismenge: $E= \{2, 4, 6\}$

$P (E) = \frac {3}{6} = \frac {1}{2}~~\widehat{=}~~50 \%$

Weitere Beispiele

Im folgenden Beispielkasten siehst du noch zwei weitere Beispiele, die dir beim Thema Laplace in Wahrscheinlichkeitsrechnung in Mathe begegnen können:

• Das Werfen einer Münze: Die Wahrscheinlichkeit für Kopf und Zahl liegt jeweils bei $50 \%$
• Das Drehen dieses Glücksrades: Jedes Feld hat eine Wahrscheinlichkeit von $ \frac {1}{6} \approx 16,7 \%$

Schauen wir uns einmal an, welche Art von Zufallsversuch kein Laplace-Experiment ist. Es gibt einige Zufallsversuche, bei denen nicht alle möglichen Ergebnisse die gleiche Wahrscheinlichkeit haben.

Dazu gehören beispielsweise Würfel, bei denen eine bestimmte Zahl auf mehr als einer Seite abgebildet ist oder das Werfen einer Reißzwecke, die auf Grund ihrer Form nicht auf jeder Seite gleich wahrscheinlich liegen bleibt.

Nun weißt du, was ein Laplace-Experiment in Mathe ist, welche Regeln bei Laplace gelten und wie du die jeweiligen Wahrscheinlichkeiten bestimmen kannst. Vertiefe dein Wissen zu Laplace und Wahrscheinlichkeit in unseren Aufgaben . Dabei wünschen wir dir viel Spaß und Erfolg!

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Was ist ein Laplace-Experiment?

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Ein Los aus einem Topf ziehen mit 8 Gewinnen und 20 Nieten

Schreiben einer Klassenarbeit

Welche Rechenregel gilt bei einem Laplace-Versuch?

$P (E) = \frac {Anzahl\ der\ gewünschten\ Ergebnisse}{Anzahl\ der\ möglichen\ Ergebnisse}$

$P (E) = \frac {Anzahl\ der\ möglichen\ Ergebnisse}{Anzahl\ der\ gewünschten\ Ergebnisse}$

$P (E) = \frac {Anzahl\ der\ möglichen\ Ergebnisse}{Anzahl\ der\ gewünschten\ Ergebnisse} \cdot 100\ %$

Markiere die richtigen Aussagen!

Die Wahrscheinlichkeit eine 3 zu treffen liegt bei 25%.

Es handelt sich bei dem Versuch um kein Laplace Experiment.

Das Werfen einer Münze ist ein Laplace Experiment.

Was ist kein Laplace-Experiment?

Wahl zum Klassensprecher

Werfen eines Würfels

Ziehen einer Karte aus einem Kartenspiel

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Laplace method

of asymptotic estimation

A method for determining the asymptotic behaviour as $ 0 < \lambda \rightarrow + \infty $ of Laplace integrals

$$ \tag{1 } F ( \lambda ) = \int\limits _ \Omega f ( x) e ^ {\lambda S ( x) } d x , $$

where $ \Omega = [ a , b ] $ is a finite interval, $ S $ is a real-valued function and $ f $ is a complex-valued function, both sufficiently smooth for $ x \in \Omega $. The asymptotic behaviour of $ F ( \lambda ) $ is the sum of the contributions from points at which $ \max _ {x \in \Omega } S ( x) $ is attained, if the number of these points is assumed to be finite.

1) If a maximum is attained at $ x = a $ and if $ S ^ { \prime } ( a) \neq 0 $, then the contribution $ V _ {a} ( \lambda ) $ from the point $ a $ in the asymptotic behaviour of the integral (1) is equal to

$$ V _ {a} ( \lambda ) = - \frac{f ( a) + O ( \lambda ^ {-} 1 ) }{\lambda S ^ { \prime } ( a) } e ^ {\lambda S ( a) } . $$

2) If a maximum is attained at an interior point $ x ^ {0} $ of the interval $ \Omega $ and $ S ^ { \prime\prime } ( x ^ {0} ) \neq 0 $, then its contribution equals

$$ V _ {x ^ {0} } ( \lambda ) = \ \sqrt {- \frac{2 \pi }{\lambda S ^ { \prime\prime } ( x ^ {0} ) } } [ f ( x ^ {0} ) + O ( \lambda ^ {-} 1 ) ] e ^ {\lambda S ( x ^ {0} ) } . $$

This formula was obtained by P.S. Laplace [1] . The case when $ f ( x) $ and $ S ^ { \prime } ( x) $ have zeros of finite multiplicity at maximum points of $ S $ has been completely investigated, and asymptotic expansions have been obtained (see [2] – [8] ). The Laplace method can also be extended to the case of a contour $ \Omega $ in the complex plane (see Saddle point method ).

Let $ \Omega $ be a bounded domain in $ \mathbf R _ {x} ^ {n} $ and suppose that the maximal $ m $ of $ S ( x) $ in the closure of $ \Omega $ is attained only at an interior point $ x ^ {0} $, where $ x ^ {0} $ is a non-degenerate stationary point of $ S $. Then

$$ F ( \lambda ) = \left ( \frac{2 \pi } \lambda \right ) ^ {n/2} | \mathop{\rm det} S _ {xx} ^ { \prime\prime } ( x ^ {0} ) | ^ {-} 1/2 [ f ( x ^ {0} ) + O ( \lambda ^ {-} 1 ) ] e ^ {\lambda S ( x ^ {0} ) } . $$

In this case, asymptotic expansions for $ F ( \lambda ) $ have also been obtained. All the formulas given above hold for complex $ \lambda $, $ | \lambda | \rightarrow \infty $, $ | \mathop{\rm arg} \lambda | \leq \pi / 2 - \epsilon $. There are also modifications of the Laplace method for the case when the dependence on the parameter is more complicated (see [4] , [8] ):

$$ F ( \lambda ) = \int\limits _ {\Omega ( \lambda ) } f ( x , \lambda ) e ^ {S ( x , \lambda ) } d x . $$

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The Beauty of Laplace’s Equation, Mathematical Key to … Everything

Physics has its own Rosetta Stones. They’re ciphers, used to translate seemingly disparate regimes of the universe. They tie pure math to any branch of physics your heart might desire. And this is one of them:

It’s in electricity. It’s in magnetism. It’s in fluid mechanics. It’s in gravity. It’s in heat. It’s in soap films. It’s called Laplace’s equation. It’s everywhere.

Laplace’s equation is named for Pierre-Simon Laplace, a French mathematician prolific enough to get a Wikipedia page with several eponymous entries. In 1799, he proved that the the solar system was stable over astronomical timescales---contrary to what Newton had thought a century earlier. In the course of proving Newton wrong, Laplace investigated the equation that bears his name.

It has just five symbols. There’s an upside-down triangle called a nabla that’s being squared, the squiggly Greek letter phi (other people use psi or V or even an A with an arrow above it), an equals sign, and a zero. And with just those five symbols, Laplace read the universe.

Phi is the thing you’re interested in. It’s usually a potential (something physics majors confidently pretend to understand), but it can be plenty of other things. For now, though, let’s say that it represents the height above sea level of every point on a landscape. On a hilltop, phi is large. In a valley, it’s low. The nabla-squared is a set of operations collectively called the Laplacian, which measures the balance between increasing and decreasing values of phi (heights) as you move around the landscape.

From the top of a hill, you descend no matter which direction you walk. This is what makes it the top of the hill, but it also makes the Laplacian negative: the going-down options entirely outweigh the going-up. It’s positive in a valley for the same reason: you can’t go anywhere but up. Somewhere between these two, there’s going to be a place where a step can take you uphill as much as it can down. At that point, where up and down are exactly balanced, the Laplacian is zero.

In Laplace’s equation, the Laplacian is zero everywhere on the landscape. That has two related consequences. First, from anywhere on the land, you have to be able to go up as much as you can go down. Second, the highest and lowest values of phi are restricted to the edges of the landscape. This is simply a result of the first part: If there’s any variation in phi, it has to happen before the crest of the hill or the trough of the valley. So you have to stop looking where land starts to level out.

Real places are too bumpy to satisfy Laplace’s equation. But soap is more cooperative. Dunk a contorted wire hanger into soapy water and you’ll notice that the film doesn't have any bumps. Play around a bit and you’ll see that you can never position the hanger so that the soap seems to go higher than the hanger’s highest point or lower than its lowest point. From any perspective, the highest and lowest parts are on the wire boundaries.

The shape of that film is caused by surface tension. But it’s perfectly described and predicted by Laplace’s equation---reminder, an equation that he studied because it described the solar system.

Or imagine a charged piece of metal out in empty space. Usually, space has no voltage, but in this case the space very close to the metal is going to have a voltage very similar to the metal itself. Far away, the voltage will be small---but only infinitely far away will it truly be zero. As you move away from the metal, there won’t be any sharp peaks or troughs because no other charges are around to cause voltage spikes, so the voltage will gradually drop off.

And that brings us back to Laplace. To find the voltage anywhere in space due to this piece of metal, you just need to solve Laplace’s equation.

Actually, no you don’t. That’s the beauty of the Rosetta Stones of physics: When you solve Laplace’s equation for soap films, you only specify anything about wire hangers at the last step. Everything before that is completely independent of the soap, so it’s perfectly applicable here to the voltage. You don’t need to change a thing.

That same solution can be applied all over the place, and all you ever need to do is change the last step. Gravity is large at a mass and asymptotically approaches zero---and you’re back to Laplace. Water’s velocity is zero where something’s in its way and unperturbed far away---and you’re back to Laplace. The head of a drum tightly fits its rim and the surface tension keeps it taut and flat---and you’re back to Laplace. So it goes throughout the universe, through classes and research alike. Laplace pops up wherever you look, and you only ever have to solve it the one time.

Until someone decides to hit the drum, as people are wont to do. But that’s a perturbation for another time.

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Laplace probability

Experiments in which all results are equally likely are called Laplace experiments .

The probability of an event is calculated in a Laplace experiment with the formula:

$|E| ...$ Number of results where $E$ occurs $|\Omega| ...$ Total number of results

Examples of Laplace experiments are the throwing of a coin, a dice or the turning of a wheel of fortune with fields of equal size.

A dice is thrown. Your are interested in the probability of an even number.

Sample space : $\Omega=\{1,2,3,4,5,6\}$ Event : $E=\{2, 4, 6\}$ Probability: $P(E) = \frac{|E|}{|\Omega|}$ $=\frac{3}{6}$

Non-Laplace experiment

In non-Laplace experiments , the probabilities for each possible outcome can not be determined by e.g. symmetry considerations or the like. However, after many experiments have been carried out, estimates of the probabilities can be determined.

Examples of non-Laplace experiments are the throwing of thumbtacks, a LEGO stone or a crown cork. It is not exactly possible to say which event occurs with which probability.

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Sakhalin: Your Essential Guide to Russia’s Enigmatic Eastern Island

• January 14, 2024

A Journey Through Giant Burdocks, Wild Bears, and the Echoes of Ancient Japanese Temples

From the most dreaded place of exile in the Russian Empire to a Japanese industrial base and one of the most attractive and inaccessible places for domestic tourism in Russia.

Table of Contents

An island that was Russian, then Japanese, and then Russian again

From the 17th to the mid-19th century, it was believed that Sakhalin was a peninsula. This misconception firmly established itself on the maps of the time, as navigators failed to circumnavigate the island. The proximity of Sakhalin’s southern tip to the mainland created a false impression of being impassable for ships. An additional complexity arose from the fact that the route taken by ships from the Russian Empire involved passing through a narrow strait, which Nevelskoy managed to navigate only in 1849.

For a long time, people did not believe Nevelskoy, but he insisted that he had discovered a route through the strait, for which he became something of a hero in Primorye. Monuments and plaques dedicated to him can be found in Yuzhno-Sakhalinsk, Vladivostok, and Khabarovsk. The H4H creative association created a graphic novel based on this story, which won a cultural initiatives contest and became part of the interior of the Khabarovsk Airport. By the way, the Sakhalin region is the only Russian entity entirely located on islands.

The remote and isolated location of the island during the Russian Empire was used as a natural barrier, and it became the site of penal colonies for hard labor prisoners. Its geographical position led to Sakhalin’s hard labor being regarded as particularly cruel.

During the period of the island’s development, Russian ships followed the Amur River and reached the island from the north, where the oldest port, Alexandrovsk, was founded. The Japanese attempted to develop the island from the south, entering through the Kuril Islands (part of the Sakhalin region) and Aniva Bay. For a long time, the Kurils were inhabited by the Ainu, representatives of a small indigenous people. The very word “Kurils” comes from the Ainu: “kuru” means “man.”

In the 17th century, Japan conducted its first expeditions towards the islands and began their development. Russia reached them later. The first mentions of the islands in Russian language date back to the late 17th century. For a long time, Russian, Dutch, Japanese, and Anglo-French navigators studied the islands, landed on them, and disputed their territorial ownership. However, only Russia and Japan managed to establish a foothold. To end the territorial disputes, the governments of the two countries signed an agreement under which the Kuril Islands went to Japan, and Sakhalin to Russia, which continued to develop the island mainly from the north. After the Russo-Japanese War of 1904-1905, which ended in Russia’s defeat, the southern part of Sakhalin became part of Japan as the Karafuto Prefecture.

Until the second half of the 20th century, the island was owned by Japan and was quite successful in developing its resources. A huge number of mines were opened, several cities and lighthouses were built. In particular, the current regional center, Yuzhno-Sakhalinsk, was the former Japanese city of Toyohara. The famous Aniva lighthouse, now considered a symbol of Sakhalin, was built by Japanese engineers. After Japan’s defeat in World War II, the island passed to the Soviet Union. Contrary to history, the main life of the island moved from the north to the south. Alexandrovsk, which was convenient to reach by water, lost to Yuzhno-Sakhalinsk with its infrastructure built by the Japanese, connections to neighboring cities, and airport. Interestingly, before leaving, the Japanese buried and hid the mining sites, and locals say that not all the old mines have been found yet, and they are sometimes stumbled upon during walks.

Because the island belonged to three different countries in just over a hundred years, it did not have time to develop any significant urban infrastructure. The cities lack outstanding architectural monuments and unique museums. However, some unusual Japanese architecture has remained. Meanwhile, Sakhalin compactly houses incredible natural attractions. Here, one can climb through forests and bamboo thickets to breathtakingly beautiful mountains as if outlined in graphite, and through a mountain pass reach the sea, into which clear mountain rivers flow with fish splashing in them.

The Ainu and Nivkh: Inhabitants of Sakhalin

For a long time, the island was mainly inhabited by the Ainu and Nivkh peoples. These ethnic groups are very different, making their coexistence as unusual as the neighboring of birch and bamboo on the slopes of Sakhalin’s mountains. Both are isolate peoples . However, the Ainu belong to the Australoid race, while the Nivkh are Mongoloids (the main population of Asian territories). It’s fascinating how representatives of different races have coexisted for ages on a small piece of land at the edge of the world.

There is no single version regarding the origin of the Ainu, leading to a multitude of theories — both scientific and conspiratorial. One theory suggests that the Ainu are the ancestors of the indigenous population of Australia, remaining in the north after continental migration. Some researchers write that the Ainu are the forebears of the Japanese. This theory is supported by the fact that before Japanese expansion, the Ainu mainly inhabited the Japanese island of Hokkaido. However, the Ainu suffered greatly from Japanese imperialism, and their culture and language were almost completely destroyed in the 19th and early 20th centuries. Now, there are just over two thousand Ainu living on Sakhalin.

The Nivkh are among the indigenous small-numbered peoples of the north. They suffered less from Japanese rule. However, during the Soviet era, they experienced a difficult phase of literacy development, destruction of tribal communities, and relocation to cities. About 2,200 Nivkh live in the Sakhalin region and another approximately two thousand in Khabarovsk.

During the Karafuto period, Japan brought captured Koreans to Sakhalin for hard labor. By the mid-20th century, the Korean population of the island was about 45,000 people. For comparison, the current population of Yuzhno-Sakhalinsk is 180,000. This large number of people, deprived of their homeland, was forced to adapt to life first under Japanese and then Soviet rule. In the USSR, Koreans were issued passports, and there were national kindergartens and schools. However, Sakhalin Koreans did not feel part of the larger community of Soviet Koreans (Koryo-saram) and struggled to integrate. Moreover, they were considered members of an ‘unreliable nation’ because they had lived in the Japanese Empire.

In the late 1990s, three countries – Russia, South Korea, and Japan – began a repatriation campaign for the first generation of Sakhalin Koreans (born before August 15, 1945) to their historical homeland. Now, about 3,500 repatriates from Russia live in South Korea. Under the program, the Korean government provides medical insurance and a monthly allowance to the repatriates. The Japanese government, in turn, buys housing (apartments up to 40 m²) and covers transportation costs. Additionally, every two years, Sakhalin Koreans who have moved to their homeland have the right to visit Sakhalin for free, funded by the Japanese government. Most Sakhalin Koreans settled in the city of Ansan , where 500 apartments were specially built for them.

Korean influence is weakly traced on Sakhalin: many Sakhalin Koreans no longer know the language and do not associate themselves with Korea. However, there are several authentic restaurants (for example, “Koba” ) on the island where you can try traditional dishes.

Yuzhno-Sakhalinsk — the capital and base for exploring the island

The city is predominantly characterized by typical Soviet architecture, with almost no remaining Japanese buildings. This is because during the Soviet period, the city was radically rebuilt after being liberated from ‘imperialist Japanese rule.’ Many buildings were demolished, and from the few that remained, some were turned into museums. Perhaps the main thing that has been preserved from the Japanese period is the layout. The city was founded from scratch near the Russian village of Vladimirovka, and Chicago was chosen as the model for its layout. Toyohara was divided into four parts by two main streets, O-dori (now Lenin) and Maoka-dori (Sakhalinskaya).

Japan established itself thoroughly on the island. In Toyohara, trade routes converged, new bays were developed, and roads were built. The city’s population grew steadily. Initially due to the military garrison, and later due to a paper mill, a sugar and distillery plant. Now, the buildings of the former Japanese factories are abandoned. Many of them can only be accessed with rare tours, while others are completely closed. However, their presence is still recalled by street names, such as Paper Street.

Another building in the Neo-Japanese style is the Karafuto Governorate Museum built in the 1930s (29 Communist Avenue). It now houses the Sakhalin Regional Museum . And in the former bank of colonial development, there is the Art Museum (137 Lenin Street).

Several other iconic buildings constructed by the Japanese have been preserved: the central hospital of Toyohara (41 Chekhov Street), the conference hall of the Karafuto Governorate (30 Dzerzhinsky Street), and the Toyohara City Hall (41 Communist Avenue). The Sakhalin Railway Museum in Yuzhno-Sakhalinsk is distinct from many similar museums in Russia due to its exhibits. This is because the island long maintained the Japanese standard of railway gauge, which differs from the Russian standard. Accordingly, the rolling stock was entirely different.

If in Vladivostok everything is named after the Far Eastern explorer and writer Vladimir Arsenyev, then in Yuzhno-Sakhalinsk, mentions of Chekhov are everywhere. At the end of the 19th century, Sakhalin was both the most dreaded place for exile to hard labor and one of the most tempting corners of Russia, which was not so easy to access. Chekhov received an editorial assignment and embarked on a ship along with prisoners, military personnel, and sailors to the most remote point of the empire. In his notes, which Chekhov compiled under the title ‘The Island of Sakhalin,’ the writer talked about many things: the geography and climate of the island, the life of the convicts, and ordinary residents. This book caused a great resonance at the time, and even now it was very interesting to read it while traveling to Sakhalin: some things have changed drastically, while others have remained the same. Now in Yuzhno-Sakhalinsk, there is even a museum dedicated to this one book, which turned out to be so significant for the island.

GoSakhalin is the website of the Sakhalin Tourist and Information Center. And in their official Telegram channel , you can find announcements of affordable excursions shortly before they start.

In any case, for travelers, Yuzhno-Sakhalinsk remains primarily a hub and a place of rest. Here they return for the night and dinner, and it seems that real adventures begin outside the doorstep.

Surrounding Area

10–20 kilometers from Yuzhno-Sakhalinsk

The main reason people visit Sakhalin is for its unique nature. Mountains, forests, rivers, lakes, and the sea, all on a small piece of land. In one day, you can travel from the Sea of Okhotsk to the Sea of Japan, cross several climate zones, see bamboo groves, birches, and spruces in one place, spot a running fox and a swimming orca. The island’s landscapes can boldly compete in Instagram appeal with Iceland or Norway.

Within Yuzhno-Sakhalinsk alone, there are about 30 kilometers of marked ecotrails, with brief descriptions and routes available on the official tourism portal. I also found an ecotrail in Nevelsk, which is not mentioned on the official website.

The ecotrails in Yuzhno-Sakhalinsk start from the ‘Mountain Air’ ski center on the sopka (a term for mountains in the Far East) Bolshevik. There are five in total: ‘Children’s’ (2.7 kilometers), ‘Eight’ (8 kilometers), ‘Northern Ring’ (9 kilometers), ‘Russian’ (3.2 kilometers), and ‘Yelanka’ (5 kilometers). You can take a cable car to the start of the trails and then slowly descend through the forest and park to the city. However, the lift does not operate in rainy and windy weather.

Hiking the ‘Eight’ trail took me no more than three hours, including stops to catch my breath and take photos. Every kilometer and a half along the route, there are benches. From the top of the mountain, there is a view of Yuzhno-Sakhalinsk, and it seems you can see a piece of the Sea of Okhotsk.

Chekhov Peak

The route to Chekhov Peak is a high-mountain trekking path that requires a certain level of physical fitness. Chekhov Peak has an elevation of 1045 meters, with an absolute altitude gain of 752 meters. The trail is narrow and slippery in places, hardly suitable for children or people with limited mobility.

Chekhov Peak is part of the Susunai Range, which supports Yuzhno-Sakhalinsk from the southeast. You can exit from Gagarin city park to the foothills in about half an hour. The ascent to the peak itself cannot be missed: a marked trail and informational signs lead to it. On particularly steep ascents, ropes are hung for safety, but it is possible to walk up the slope without them.

In late spring, the forest trail has many streams, as well as May primroses and butterflies. The foothills are scattered with rare, incredibly large, and wonderfully fragrant marsh callas. Halfway to the peak, bamboo thickets are encountered, through which birches break through. This is also a kind of magic because, as a biologist friend explained to me, birch and bamboo are not supposed to coexist in the natural environment, but somehow they manage to do so. Occasionally, spruces are encountered — not tall, but very fluffy. Closer to the top, the vegetation becomes sparser, and the impressive views of the sea, mountains, and lakes open up from the height.

• The entire hike takes five to six hours.
• Even in summer, there is snow on the summit. In the afternoon, it starts to melt, making it more difficult to walk.
• Don’t forget to bring food and water.
• Wear boots with covered ankles, a jacket, and a head covering.
• Inform your family and friends, and someone living in Sakhalin, before setting out on the route. If you’re traveling alone, you could notify, for example, the hotel receptionist or roommates in a hostel.
• Snakes and bears are found around the trail. Watch your feet and try to make as much noise as possible. For example, play music on your phone and sing along occasionally.
• The ascent to Chekhov Peak can be the start of a journey to the village of Lesnoye on the shore of the Sea of Okhotsk. The distance to the village is 27 kilometers. With good preparation and an early start from Yuzhno-Sakhalinsk, this distance can be covered in one day.

Mud Volcano in Klyuchi

A mud volcano is an eruption on the earth’s surface of clay masses, mineralized waters, and gases. The mechanism of formation of these volcanoes is not fully understood. According to the existing theory, such volcanoes are formed near oil fields.

The mud volcano in Klyuchi consists of a mud field about 200 meters in diameter. There, you can see about 20 points of activity, resembling miniature volcano craters. This mud volcano became active in 1959, 1979, 2001, and 2011 (the last time due to a strong earthquake in Japan). During these eruptions, mud columns reached several tens of meters in height. Bus 189 goes to Klyuchi from Yuzhno-Sakhalinsk. The distance from the village to the top of the volcano is nine kilometers and takes about two and a half hours to walk.

Ecopark in the Vestochka area: Frog Rock, Aikhor Waterfall, ‘Sunny Glade’ Recreation Park

Not far from Yuzhno-Sakhalinsk, there is a fairly large ecopark, known primarily for the Frog Rock outcrop. An outcrop is a remnant of harder rock around which softer rock has eroded over time. Outcrops are often known for their unusual shapes and are natural monuments. Frog Rock is part of a series of rocks standing one behind the other. This was once the seabed of an ancient sea, and fossilized shells can be found in its vicinity. From the top of the rock, amazing views of the Aniva Bay, Tunaycha and Changeable Lakes open up. This place was sacred to the Ainu, the indigenous inhabitants of the island.

The trail to the ‘Sunny Glade’ ecopark begins behind the ‘Electron’ culture house. Despite its name, it is not a city park, but a full-fledged forest with laid-out paths. There are houses, glades with tables for rest where you can cook barbecues, and wooden walkways leading to various attractions. These are all paid services.

The path to Frog Rock outcrop goes along the Komissarovka River. In areas of spring flooding, callas bloom and bamboo grows. The outcrop is located on a hill, with a total elevation gain of about 300 meters. The road is quite challenging, usually taking from an hour to an hour and a half. The higher you climb, the more you can see: the sea, the mountain gorge, the road to Vestochka. In the same park is the Aikhor Waterfall, which is also a short climb away, but along a less well-maintained trail. You can plan a whole day to visit Vestochka and even spend the night, without returning to Yuzhno-Sakhalinsk.

Vestochka is three high-rise buildings on one side of the road and a cottage settlement on the other. It is part of Yuzhno-Sakhalinsk, though located 15 kilometers from the main part of the city. A taxi there costs about 1000 rubles and takes 40 minutes. About a kilometer after turning off the main road, the asphalt ends and a terribly dusty dirt road begins. If you’re lucky, you can catch a bus that runs three times a day.

What else to see on the island

40 kilometers from Yuzhno-Sakhalinsk

The oldest city in the south of Sakhalin, founded by Nevelskoy’s expedition. Here you can find a huge number of monuments dedicated to sailors, naval battles, and ships. The most significant monument in the city in recent decades has become the stele dedicated to ‘Koreans interned by the Japanese in Sakhalin, who never returned to their homeland,’ located on Mount Sorrow, created through the efforts of three countries’ governments (Russia, Japan, and Korea).

In Korsakov, some Japanese heritage has been preserved: the former building of the Hokkaido Takushoku Bank, a colonial development bank (Sovetskaya Street, 3), trade warehouses in the port, a document storage facility ‘Bunsyoko’ (Krasnoflotskaya Street, 1), a couple of rusty fire hydrants, and remnants of Shinto temples in the form of pillars with hieroglyphs. One of the local nighttime entertainments is watching the lights of the gas processing plant.

How to get there. Three electric trains a day, the journey takes just over an hour, and the ticket costs 75 rubles (0.75 euros).

Bird and Giant Capes

90 kilometers from Yuzhno-Sakhalinsk

Two capes, recognized as natural monuments in 1990, along whose coasts are many wind and wave-carved grottoes, caves, arches, and columns of various sizes and whimsical shapes, among which colonies of sea birds reside.

The place is not very close, but it’s very picturesque at any time of the year. In the area of one of the rocks, there is a pool where, during the salmon spawning period, you can observe a fascinating spectacle — a huge gathering of pink salmon.

Many tourists stay on the coast overnight to witness the sunset and sunrise. Near Cape Giant, there is a toilet, parking, and a rest area with benches.

How to get there. The journey from Yuzhno-Sakhalinsk goes through the village of Okhotskoe, where you can buy fresh crabs, and takes about three hours one way. The road is fully passable only by high vehicles like Mitsubishi Pajero, Suzuki Jimny, as the last ten kilometers of the route have deep puddles, potholes, small cliffs, and rivers.

Nevelsk and Steller Sea Lions

Nevelsk is nestled between mountains and sea. The rocky mountains and the coast, which consists of small stone needles and shells, in every way explain why Chekhov so often mentioned in ‘The Island of Sakhalin’ how harsh the land of Sakhalin is.

Steller sea lions are the largest of the eared seals. One of their habitats is the breakwater in Nevelsk. As soon as you arrive in the town, the smell from the Steller sea lions’ haul-out site hits you. ‘They eat there, live, give birth to their young – that’s why it smells,’ the locals explain. Another feature is the noise. Steller sea lions are very loud!

You can view the sea lions from the central square, where binoculars are installed. However, tourists usually hire a boat and approach the haul-out site to get a closer look at the seals. You can see how the Steller sea lions bark, lie in the sun, jump into the sea and, most interestingly, try to jump back. The views from the square through binoculars are not as detailed and impressive. A place on the boat will cost 1000–1500 rubles (9.99 – (14.98 euros). You can also buy a tour from Yuzhno-Sakhalinsk for 3500 rubles (34.96 euros). The most animals are present in spring and early summer. In autumn, there may be a couple of dozen individuals left.

From the embankment, you can observe the huge kelp laminaria floating in the sea. Some travelers catch them themselves and eat them. Although dishes made from seaweed are found in cafes and also sold in stores. Signs are installed on the shore indicating where to run in case of a tsunami. The last major earthquake with waves was recorded in 2007. Many houses were destroyed and two people died. The most famous Sakhalin tsunami was the 1952 tragedy , when the aftermath of the earthquake almost completely destroyed Severo-Kurilsk.

How to get there. From the bus station (Karl Marx Street, 51b) in Yuzhno-Sakhalinsk, buses go to Nevelsk, the ticket costs 300 rubles (3.00 euros), and the journey takes about an hour. Tickets can be purchased at the bus station ticket office or from the driver (cash or transfer). It’s not possible to board the bus somewhere in the city, as the bus does not make stops. It’s better to buy a return ticket immediately upon arrival in Nevelsk at the Nevelsk bus station ticket office (Lenina Street, 1). The bus is popular with locals, and there may simply be no seats left.

Remnants of structures from the Karafuto period include the Maoka-Jinja temple with a Japanese-style garden and an abandoned railway built by the Japanese. It used to connect Kholmsk with Yuzhno-Sakhalinsk. Tourists usually come to see two photogenic bridges – Devil’s and Witch’s – and a tunnel in the mountain that makes a full circle inside it. The trail passes along the old rails, and there are many vipers, so one needs to watch their step.

How to get there. The bus to Kholmsk takes two hours, the ticket costs 450 rubles (4.49 euros), with 14 trips a day.

Slepikovsky Cape and Lighthouse

120 kilometers from Yuzhno-Sakhalinsk

At Slepikovsky Cape, there is the only relic grove of Korean cedar on Sakhalin. Also located here is the functioning Slepikovsky Lighthouse, which is a 27-meter tall round tower, connected by corridors to utility and residential buildings.

The cape and lighthouse are named after the commander of the Russian partisan detachment Bronislav Grotto-Slepikovsky, who operated in Southern Sakhalin during the 1904–1905 war. The route to the lighthouse goes through the villages of Yablochnoe and Sadovniki, where some of the best beaches on Sakhalin are located — with the cleanest water and white sand.

How to get there. The cape is located 29 kilometers north of Kholmsk. From Kholmsk to the turn towards the lighthouse, there is asphalt with dirt sections. From the turn to the lighthouse, there is first a dirt road, then beach sand, which is recommended to be driven on with deflated tires. Visiting time is from spring to autumn, as the road to the cape is not cleared in winter.

110 kilometers from Yuzhno-Sakhalinsk

In 1891, when the island had a penal colony, this was the Russian village of Siraroko, named after a nearby Ainu settlement. In 1905, the south of Sakhalin was given to the Japanese, and the village was renamed Higashi Shiraura. Here there were a railway station, a brick factory, and a coal mine. 40 years later, the settlement was renamed Vzmorye.

During the Japanese times, there was the Shinto shrine Higashi Shiraura Inari-Jinja. Only the torii gates remain — P-shaped gates without doors that are placed on the path to a Shinto shrine. These are the only torii on Sakhalin. On the torii, there is an inscription ‘In honor of the 2600th anniversary of the foundation of Great Japan’ — this mythological date was widely celebrated in 1940.

On the way to the torii, you can see the famous giant burdocks and bear’s garlic. Vzmorye is also known as a place where poached crabs are sold along the highway.

How to get there. Two electric trains and one train that start from Yuzhno-Sakhalinsk stop in Vzmorye. Unfortunately, all three are in the evening. You can also get there on passing buses that go to the north of the island.

Tikhaya Bay

140 kilometers from Yuzhno-Sakhalinsk

On one side, the bay is framed by Mount Smely, and on the other side, the majestic Zhdanko Ridge begins. To the left in the bay itself is an island-kekur, which can be reached during low tide, as well as the epic cliffs of Tikhaya Cape. By the way, behind this cape, there are waterfalls that become icefalls in winter. At the base of the bay is the mouth of the Tikhaya River, where during the season you can see the spawning of pink salmon and chum salmon. Bears are aware of this, so they are often encountered here.

How to get there. Buses going to Poronaysk stop in the village of Tikhoye, near which the bay is located. There are four trips a day.

Aniva Lighthouse

The lighthouse has a complex history: there were attempts to maintain it under Soviet rule, but Aniva was so remote from inhabited areas that it was not profitable. Eventually, the lighthouse was switched to autonomous mode, bringing in a radioactive isotope to sustain its operation, and then it was completely closed. To this day, you can find signs on the walls reading ‘Caution, radioactive’. But now this warning is outdated, as the radioactive isotope was removed when the lighthouse was decommissioned. The lighthouse is very beautiful, offering views of the island and sea, and inside you can explore the remnants of rooms and working areas.

On the return trip, tourists are also taken to Mramornaya Bay, where you can also climb a mountain and view the jagged coast of Sakhalin from above. Orcas and whales are often encountered in these areas, most frequently in summer. I would also recommend taking a combined tour in summer to Aniva Lighthouse, the Blue Lakes, and Busse Lagoon, where you can see the amazingly blue waters and try sea urchins.

A kilometer from Novikov is Cape Tri Kamnya (46.320342 143.373006), which can even be reached by car. Four kilometers from the cape is the small Strelka waterfall , which requires a walk. If you stay in the village overnight, you can take a hike to the Blue (turquoise) Lakes (46.359603, 143.471909). On the way, there’s an abandoned Japanese power station. You can extend your route by another 15 kilometers and reach the opposite shore of the peninsula – to Cape Evstafiya. The road from Novikov to Cape Evstafyeva through the Blue Lakes can be driven in a jeep, if there hasn’t been prolonged rain before. But it’s better to ask in advance those who have recently been there, and get the phone number of a local tractor driver in Novikov, so that if something happens, he can pull you out.

How to get there. Getting there independently is almost impossible. The lighthouse is located on a rocky outcrop in the sea, and the nearest land is a high cliff. However, some people do reach Novikovo (the nearest village) by bus or car, and then walk 44 kilometers on foot to Aniva (the name of both the lighthouse and the bay). It takes about one and a half hours to drive from Yuzhno-Sakhalinsk to Novikovo. And then another two hours of rough dirt road to the boat dock. A tour from the company ‘Friends-Hikers’ costs 6000 rubles (59.93 euros) in May (in summer – 7000 rubles (69.92 euros)).

Klokovsky Waterfall

190 kilometers from Yuzhno-Sakhalinsk

Klokovsky Waterfall is one of the highest waterfalls on Sakhalin Island. Its height is variously reported to be 48–49 meters, with a width of up to nine meters. The waterfall is accessible year-round, but is most full in late spring and early summer.

Alexandrovsk-Sakhalinsky

The ‘Tri Brata’ (Three Brothers) rocks are definitely a symbol of Alexandrovsk-Sakhalinsky, and perhaps of the entire island. They are located in the Alexandrovsk Gulf almost opposite Cape Zhonkiyor. From the cape, there is a stunning view of the vast Tatar Strait and the Three Brothers. At low tide, it’s possible to calmly explore all the attractions of the gulf, collect seaweed and shells, see hermit crabs scuttling along the seabed with their shells on their backs, or watch the leaves of laminaria sway. At the strongest low tide, you can even walk to the Three Brothers through the water.

In the 19th century, convicts carved a 90-meter tunnel through Cape Zhonkiyor to service the lighthouse. To reach the tunnel by land, you need to come at low tide. Otherwise, you’ll have to climb the rocks. The tunnel is lined with logs, but there is almost always water at the bottom and a strong wind howls through it. If you pass through the tunnel, you will see the ‘Tri Sestry’ (Three Sisters) rocks and an old lighthouse from the end of the 19th century. All these places are described by Chekhov in ‘The Island of Sakhalin’: ‘Most often we went to the lighthouse, which stands high above the valley, on Cape Zhonkiyor. During the day, the lighthouse, if looked at from below, is a modest white house with a mast and lantern, but at night it shines brightly in the darkness, and then it seems that the penal colony looks at the world with its red eye. The road to the house climbs steeply, winding around the mountain, past old larches and firs. The higher you climb, the freer you breathe; the sea spreads before your eyes, thoughts gradually come, having nothing to do with the prison, the penal colony, or the exile settlement, and only then do you realize how dull and difficult life is down below.’

How to get there. From Yuzhno-Sakhalinsk, there is one bus trip per day – at 12:10. The ticket costs 2200 rubles (21.97 euros), and the journey takes nine hours.

600 kilometers from Yuzhno-Sakhalinsk

The main transit point on the way to the oil refineries. The village might be of interest to those curious to see a harsh northern town living off production: low-rise buildings made of siding and unexpectedly bright murals on the walls of five-story buildings. There is a local history museum in the village (Sovetskaya Street, 3) – it is praised for its excellent exhibition of the Nivkh culture and a monument to Nevelskoy. Also, one of the longest rivers of Sakhalin, the Tym (which translates from Nivkh as ‘spawning river’), flows through the town.

How to get there. A night train goes to Nogliki every day, taking almost 12 hours. The cheapest ticket in a seated carriage costs 1100 rubles (10.99 euros), a compartment – 4100 (40.95 euros). There is even a luxury (SV) carriage for 12600 rubles (125.85 euros).

Where to Stay

Hostels in the Far East are divided into work and tourist types. The former will also accommodate tourists, but the atmosphere there is like a dormitory where their own rules are already established, and you may feel like an uninvited guest. To avoid such a hostel, it’s important to carefully read the reviews, not book the cheapest hostels, not stay on the outskirts or near airports and train stations.

In the Islander hostel , mainly travelers stay, it’s very cozy, with convenient kitchen and showers with toilets. A double room costs 3000 rubles per day, and dorms – from 900 rubles (8.99 euros) per night. If you book directly through the website and for a long term, you can get a good discount.

The ‘Moneron’ hotel is located near the railway and bus stations. It’s a classic budget hotel with small clean rooms. The ‘comfort’ class rooms have a bath, and the hotel provides a complete set with slippers, towels, and a hairdryer. Prices start from 2800 rubles (27.97 euros) per night for a single economy room, while ‘comfort’ costs 4900 rubles (48.94 euros). Breakfast is included in the price.

The ‘Belka’ hotel building is made using Finnish technology in a wooden style from milled timber. The cost of large rooms with wooden walls and huge beds starts from 5800 rubles (57.93 euros). Breakfast is also included in the price. The hotel complex includes a sauna, spa, tavern, and gym.

Near Bussé Bay is the island’s only dome-shaped glamping site. A night for two costs 8000-10,000 rubles (79.90 – 99.88 euros). An extra bed is 2000 (19.98 euros). Each dome has a shower, toilet, and electricity. On cooler days, you can light the stove and sit by the fire with a cup of hot cocoa.

In other towns, apart from Yuzhno-Sakhalinsk, the choice of hotels is quite modest and usually limited to one or two hotels, which cannot always be booked online. They have to be found on the map and booked by phone.

Transport on the Island

Car. If you’re only traveling between cities, there won’t be any problems – the roads between them are mostly paved, and the dirt roads are of more or less good quality. It gets more complicated with natural attractions. Almost all of them are accessed by dirt roads, which not every car can navigate.

In Yuzhno-Sakhalinsk, ‘Yandex.Taxi’ and ‘Maxim’ operate (also in Korsakov and Kholmsk). A trip within the city limits will cost a maximum of 300 rubles (3.00 euros).

Railway. From Yuzhno-Sakhalinsk, about 30 electric trains depart daily. Most of them go to nearby areas like Dalnyaya, Khristoforovka, and Novoaleksandrovka stations – 8–23 minutes travel time.

To other cities, there’s only one electric train per day. It takes an hour to Korsakov and the ticket costs 80 rubles (0.80 euro). To Tomari, it’s four hours and 300 rubles (3.00 euros). To Poronaysk, it’s five hours of travel and 500 rubles (4.99 euros) for a ticket. Long-distance electric trains depart in the evening, as these routes are used by residents of the province who return from work in Yuzhno-Sakhalinsk to their homes.

There is also one train on the island – Yuzhno-Sakhalinsk to Nogliki, 12 hours of travel and 1100 rubles (10.99 euros) for a ticket in a sitting carriage.

Buses. It seems you can reach even the most remote settlements by bus. Often there’s only one trip per day, but at least it exists. To Kholmsk, Nevelsk, and Korsakov, the journey takes about an hour and a half, with tickets costing around 300 rubles (3.00 euros); to Poronaysk and Uglegorsk, it’s four to five hours and 1200 rubles (11.99 euros) for a ticket. You can check the current schedule on avtovokzaly.ru . But it’s always better to double-check by phone: +7 (4242) 72-25-53. The address of the bus station is Karl Marx Street, 51b.

Airplane. Sakhalin has a quite extensive network of airports, and you can fly from Yuzhno-Sakhalinsk to Okha, Zonalnoye, Shakhtyorsk, Poronaysk, Smirnykh, Yuzhno-Kurilsk, and Iturup. Flights are operated by the Far Eastern airlines ‘Aurora’ and ‘Taiga’ . These routes are served by small propeller planes Bombardier and Mi-8 helicopters. Such a flight is an interesting experience in itself. Moreover, some flights are quite inexpensive. For example, to Zonalnoye, Shakhtyorsk, and Poronaysk, tickets cost 2000–3000 rubles (19.98 – 29.96 euros) one way. To Okha and the Kurils – from 6000 rubles (59.93 euros).

Ferry. From Korsakov, ferries run to different settlements in the Kurils every three to four days. The ferry to Kurilsk takes about 22 hours, to Yuzhno-Kurilsk – 22–30 hours, and to Malokurilskoye – about 40 hours. Interestingly, a ticket to any of these settlements costs from 2800 rubles (27.97 euros), available on the website of the ferry company.

How to get there

By plain. To travel to Yuzhno-Sakhalinsk from Europe, passengers typically fly through major transit hubs. Common routes involve flying from a European city to one of the major Russian airports offering direct flights to Yuzhno-Sakhalinsk, such as Moscow’s Sheremetyevo or Domodedovo airports. In 2023 it is only possible to fly to Moscow from major transit hubs such as Istanbul or Erevan. From there, travelers can catch one of the direct flights to the island. Some routes might also include stops or transfers in other large cities in Russia or Asia, depending on the airline and the flight itinerary, for instance, Novosibirsk, Krasnoyarsk, Irkutsk, Ulan-Ude, Chita, Blagoveshchensk, Vladivostok, Khabarovsk, Komsomolsk-on-Amur, Sovetskaya Gavan, and Petropavlovsk-Kamchatsky. There is even one international flight from Harbin, China.

In good weather, on approach to Yuzhno-Sakhalinsk, you can see the Tatar Strait, the Western Ridge, and the city itself. The airport is located within the city limits, and from there, you can easily reach any point by public transport (buses 63 and 3) or taxi.

Ferry. Vanino (Khabarovsk Krai) to Kholmsk (Sakhalin) . Passenger tickets for the ferry are sold at the Vanino railway station or at the ticket office in Kholmsk (Lenin Square, 5). They can also be reserved by phone: +7 (42137) 74088 (Vanino), +7 (42433) 50880 (Kholmsk). The ferries run daily, with a journey time of 18–20 hours. A seat costs 650 rubles (6.49 euros), while the cheapest cabin spot is 1400 rubles (13.98 euros). There is a dining room on board.

I was on the island in early May, and this has its pros and cons. On one hand, it’s already not very cold in Sakhalin at this time, and you can walk around in a light jacket or sweatshirt, and sometimes even just in a T-shirt. At the end of spring, you can catch the largest number of Steller sea lions in Nevelsk (closer to summer they migrate towards Avacha Bay). Also at this time, you can see the forest awakening: streams penetrate it from all sides, in their floodplains swamp callas bloom, meadows fill with primroses, and the hills are covered with bright green bamboo shoots. On the other hand, there is still snow in the mountains, in which you can get stuck while climbing, and the sea, which is not very warm in these areas, is completely unsuitable for swimming.

In summer, Sakhalin is not very hot, the coast blooms with wild roses, the sea warms up a bit, and there is less chance of bad weather when visiting remote attractions. Also, it’s precisely at this time you can see orcas (June – July) and whales (July – August), as well as the salmon spawning.

In winter, snowboarders and skiers come to Sakhalin. The mountains on the island are not high, so they are suitable even for beginners.

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Sakhalin, Russia

Tours, Attractions and Things To Do in Sakhalin

Sakhalin is the largest island of the Russian Federation. It is located in the Pacific Ocean and is famous for seafood and picturesque places. And in the Sakhalin region there is the cutest island in the world - Tuleniy, a favorite place of seals and fur seals.

History of Sakhalin

Scientists confirm that the island was completely inhabited already 2.5 thousand years ago. People led a settled lifestyle and fished.

The first mention of Sakhalin dates back to 1640. At the same time, Russian Cossacks came here for the first time.

In 1855, the Treaty of Shimoda recognized Sakhalin as a joint possession of Japan and the Russian Empire. But already in 1875 Sakhalin was ceded to Russia, which, in turn, gave part of the Kuril Islands to Japan.

In the XIX century Sakhalin was a place of exile.

The largest city on the island is Yuzhno-Sakhalinsk. It was founded in 1882.

About half a million people live on Sakhalin.

Sakhalin Sights

The Sakhalin State Regional Museum of Local Lore is located in a building that was built in 1937 in the teikan-zukuri style designed by a Japanese architect. Here you will get acquainted with the times when Japan owned the island and see how people lived on Sakhalin: what they wore, what they ate, what they produced.

Also in Yuzhno-Sakhalinsk there is a museum of railway equipment, the Sakhalin Regional Art Museum, the Chekhov Museum, the exhibition hall of the Union of Artists of Russia, the Bear Museum, geological and archaeological museums.

The Victory Museum and Memorial Complex is dedicated to the Russian-Japanese and World War II wars. This museum is different from the usual museums of this subject. Here you will learn about the Portsmouth Peace Treaty, about the fighting in the Far East and much more.

The Resurrection Cathedral of Yuzhno-Sakhalinsk is young, it was built in 1995. People come here to bow to the deceased leaders of the Sakhalin Region, headed by Governor Igor Farkhutdinov.

Tikhaya Bay is one of the most famous attractions of Sakhalin. It is so called because it is always quiet and peaceful here. This beautiful place will not leave anyone indifferent. Next to the bay is the Zhdanko ridge, which looks like a dragon.

Cape Giant is considered the most picturesque on Sakhalin. Nature has created columns, arches and peculiar sculptures here - stones that have been polished by water for centuries.

Cape Columnar is also very beautiful. After the eruption of the volcano, basalt pillars appeared here. They look so neat, as if they were created by man.

Take a look at Cape Crillon with its old lighthouse, weather station and border outpost.

The “Mountain Air” resort, located on Bolshevik Mountain, is considered the pride of the island. It is also recognized as the best in the Far East. If you come here in winter, be sure to ski or snowboard, if in summer - look at the city from a height of 600 meters.

The Poronai State Nature Reserve is home to animals and birds listed in the Red Book. Red Book animals also live in the Noglika Nature Reserve.

The “Vostochny” State Nature Reserve, which occupies 66 thousand hectares, is known for the dark coniferous taiga and animals that are listed in the Red Book. Please note that visiting the reserve is possible only after receiving a special pass.

If you love mountains, then climb Chekhov Peak. It's not difficult to reach the top, and the stunning views will more than pay for a two-hour climb. Also go to the mountain called Frog. It is so named because the outlines of one of the mountain ranges resemble a sitting frog. Once this place was considered a temple of wisdom and a place of power. Do not ignore the Ostraya Mountain. Tourists climb to the top to see the wreckage of the IL-114 plane, which crashed in 1976.

The lighthouse on Cape Slepikovsky, built by the Japanese, looks very picturesque. You can climb to a 28-meter height and take beautiful photos.

The 30-meter lighthouse at Cape Aniva was also built by the Japanese in the 1930s. In the 1990s, it was converted into a nuclear one, and now it is abandoned. You can get to the lighthouse only by sea.

The rocks of the Three Brothers will surprise you with their panorama. It is said that once three brothers stole the sorcerer's treasures, and for this he turned them into stones. By the way, Chekhov wrote about these rocks.

The beaches in Okhotsk, Yablochny and Starodubsky will appeal to lovers of lazy recreation. For example, the beach near the village of Yablochnoye is considered one of the best on Sakhalin. There is fine sand and a warm sea. And on the beach of the village of Starodubskoye, you can find reddish Sakhalin amber.

Lake Busse is worth a visit, if only to collect oysters that appear on the shore at low tide. We also advise you to go to the lakes Gorachee, Kipyashee, Tunaycha and Vavay lakes, Bird waterfalls, Cheremshansky, Ilya Muromets and Klokovsky.

The port of Korsakov is one of the largest ports in the Far East. People come here to admire the panorama and see the big ships, because the port has the status of an international one.

The seaside thoriums of the Higashi Shirauda Jinzda Temple - the gate left over from the Shinto temple – is one of the most photographed points of Sakhalin. There are also remains of the Temple of the Sun on the island.

Pugachevsky mud volcano is not a classic volcano. It is a perfectly round clay desert with a diameter of 4 kilometers. There is a swamp around the perimeter. Every few years, the volcano spews thousands of tons of mud, and the fountain can reach 50 meters in height. Another mud volcano is located near the Novoderevenskoye station. There are several constantly bubbling craters here.

If active recreation is not enough, you can go to the caves of Mount Vida. Pay attention to the cave of Bear tragedies, it is considered the most interesting.

Moneron Island is very small, but very beautiful. There are amazing views here. You can only get here with an excursion group.

The Tuleniy island is one of the cutest islands of the Sakhalin region. Seals and sea lions (big-eared seals) like to lie on a small island with a length of 636 meters.

Dagin thermal springs are almost 60 hot springs that gush out of the ground at a rate of three liters per second. The springs are considered healing and attract the attention of not only tourists, but also local residents.

Sinegorsky mineral springs are located near Yuzhno-Sakhalinsk. They are famous for the fact that the water contains arsenic. This mineral water cures many diseases. Therefore, two health resorts were built on the springs, where people come not only from Russia.

Be sure to visit the Kuril Islands. The state Nature Reserve "Small Kuriles" includes the islands of Zeleny, Storozhevoy, Shikotan, Rifovy, Anuchin, Signalny, Polonsky and Tanfilyev. Here are the famous Tyatya volcano, the Kuril Reserve and much more.

What to bring from a trip to Sakhalin?

Take a bigger suitcase with you because you will not leave without gifts and souvenirs. Be sure to bring seafood from the trip: fish, caviar, Sakhalin crabs, seafood. Grab the national unts as well. Girls will love the jewelry of indigenous peoples. Music lovers will be pleased with the musical instrument harp. Also take syrup from a local berry called klopovka, chocolate with squid and algae and traditional amulets.