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Does Every Game have a Winner?
Why can a computer always win in tic-tac-toe? Is it true for games in general?
What does this infinite trigonometric identity have to do with probability?
Recently I came across this surprising trigonometric identity…
A Devious Bet 2: Law of Large Numbers
You meet up with a slightly familiar mustached squid “man” He may or may not have bankrupted you infinitely times over in the past, but you’re over it. In fact he has a new deal for you! Every day he will modify your bank balance in one of two ways. With probability 0.6, your balance … Read more
Arrow’s Theorem (or: How I Learned to Stop Worrying and Love Dictatorships)
Elections never really feel fair (or, if talking about the electoral college, are never fair) Here is an example, say there is an internal election in some political party, to determine the order of members of the party. To do so, each voter votes for their favorite party member, and the party members are ranked … Read more
Update #2
Hi Currently I am rather busy and don’t have much time for making more posts. Unfortunately I am not sure there will be one this month 🙁 Suggestions for what to cover next will be appreciated!
5 Holiday Math Puzzles
Happy Holidays! Here are a couple Christmas and Hanukkah puzzles just for you: The 2n-Menorah: In an alternate universe, instead of the flask in the temple lasting for just 8 days, it lasted for 2n days for a positive integer n. Thus, Hanukkah in that universe is celebrated for 2n days, and the menorah has … Read more
The Paradox of Periodicity (of Functions)
You know periodic functions right? Functions that after a certain place start repeating, for example sin(x): More formally, a function f is called periodic is for some constant p>0, f(x+p)=f(x). In other words, shifting by p does not affect f(x). The constant p will be called the period of the function (sometimes we say f … Read more
Why does this fraction give the Fibonacci sequence? It’s no coincidence
You may have seen one of the following viral math facts: The first fraction seemingly gives the Fibonacci numbers. That is, the sequence of numbers that starts with 1, then 1, then each successive term is the sum of the two prior terms. So the first few Fibonacci numbers are 1,1,2,3,5,8,13,21,… Which appear on the … Read more
Quick Update
Hi I started grad school recently so I am not sure when I will have time to work on this blog as I am very busy :/ I will try, however, to at least get a new post out this month, suggestions for topics to cover would be appreciated