## The Pancake Theorem

We all know pancakes and how delicious they can be if prepared properly, and it is only natural wanting to share it with your closest friend. However, cutting a pancake exactly in half, one for you and one for your … Continue reading

## The isoperimetric inequality

Our story begins at around 800 BCE in ancient Greece with Dido of Tyre. As many stories from that time, this too started with a murder, when Dido’s brother Pygmalion killed her husband. Fleeing her brother, Dido eventually reached north … Continue reading

## The 15-Puzzle and the symmetric group

Almost 150 years ago the game 15-puzzle was invented and quickly gain lots of popularity. The rules are quite simple – you start with a board with 15 numbered pieces as in the image below, where the pieces are ordered … Continue reading

## Breaking up Pythagorean Triples

One of the thing I really love in mathematics is how different subjects, which at least when starting to learn mathematics seem far apart, can come together in interesting ways. While the first reaction of many people might be that … Continue reading

## Mediants in Mathematics

In the previous post we learned about the mediant, which is the “wrong” way to add rationals : . While this operation is not well defined, and depends on the presentation of the rational numbers and not just their values, … Continue reading

## On one weird rational average

One of the things that I love about Mathematics, is how one can come across a mathematical problem or a phenomenon which you can look at from several points of views, each one different, yet they all combine together to … Continue reading

## Linearity testing: Checking proofs for the lazy person

Taking a final exam in a course is not really a celebration cause for most students, but it is just not as fun to be on the other side as exam checkers. It can easily take several days to grade … Continue reading

## The Peg Solitaire and its unbeatable games

In the previous post we considered a simple domino game where we needed to cover a board with dominos. We wanted to find a way such that if a board couldn’t be covered, then we could prove it easily, and … Continue reading