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I'll have to watch it for my own one

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It is amazing to see how nothing is new under the sun and the discovery of something might have already been done by someone else. Moreover, it just shows how math links to other subjects such as Physics.

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the topic in this video is explained very simple. It was understandable knowledge for calculus.The approaches are similar to the things we have already learned

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1. Watch the video on the history of calculus. (TOK)

2. Watch the second video and take notes while watching it.
https://www.youtube.com/watch?v=3JwB06oDpT4

3. How to use TI to find the limits?
https://www.youtube.com/watch?v=W1QxQ5qsSeM

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Newton vs. Leibniz - The Controversy Over the Discovery of the Calculus

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I think it is really interesting how two scientists/mathematicians discovered an extremely similar concept individually. I also feel as if their conflict was over exaggerated by Germany and the UK, as it is very possible that two people can reach the same conclusions independently.

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It is a paradox about a coin flip in which you have a chance of winning infinite times.

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No one has the infinite resources that it would take to pay someone who continued to flip heads. Its also improbable to get something like 20 heads in a row. The odds of this happening are better than winning most state lotteries. People routinely play such lotteries for five dollars or less. So the price to play the St. Petersburg game should probably not exceed a few dollars.

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The St Petersburg paradox is about a coin flip game that has an infinite winning potential. The player has to flip a coin and if they get heads they win but if they lose their winning odds are doubled (2,4,8,16).

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The St Petersburg paradox is a paradox involving the game of flipping a coin where the expected payoff of the theoretical game approaches infinity but nevertheless seems to be worth only a very small amount to the participants and it is a theoretical game to represent a classical example were, by taking into account only the expected value as the only decision criterion, the decision maker will be misguided into an irrational decision.

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The St. Petersburg Paradox is a coin flip game where one flips until the coin lands tails. The main concept to grasp is expected value, which is pretty simple given elementary knowledge in probability. The expected value of an event tells you how much you can expect to gain or lose by participating in that event. The expected value of is calculated by taking the amount
gained or lost for each possible outcome of the event, multiplying it by the probability of that outcome happening, and then adding them all.

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The St. Petersburg paradox is a situation where the expected value is infinite while the actual value is finite. Meaning that no matter what the outcome is, the player will always gain a some finite amount of utility.

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The paradox is that people easily converge in the game if the bet is close to winning, respectively, too. And they almost always refuse to participate if the stake is high. If the number of game sessions is unlimited, winnings are almost guaranteed. The very first hit in a long sequence of falling coins with the "money" side compensates for previous unsuccessful sessions of the game, and the total win is greater than the sum of all previously made bets.

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The St. Petersburg paradox is a situation where a decision criterion which takes only the expected value into account predicts a course of action that presumably no actual person would be willing to take.