New Zealand Mathematical Olympiad Student Association
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Introduction to Circle Geometry - Part I
Circles are pretty cool. They're really round and rolly. But they also have some cool geometric properties too! You will come across these in high school with enough time, but have you ever wondered why these facts were true? All this and more, explained in this video.
Why is √2 irrational? - Part I
First you learn to count. Then you learn to add and subtract. Then you learn negative numbers, decimals, and fractions. But then you learn that there are these weird numbers that can't be written as fractions. Behold, the irrational numbers. The square root of 2 is a common example of an irrational number... but why is it irrational? This video explains why, with a proof by contradiction.
Why is √2 irrational? - Part II
The previous video proved that the square root of 2 is an irrational number. This is a pretty standard proof, with talk about whole numbers, squares, factors, and so on... but did you know that you can prove this with geometry?
Proofs: What and why?
Proofs form the foundational basis of mathematics, and being able to write proofs are essential tools for logical thinking in mathematics and the sciences (and probably beyond!). This video is the first of a series about proofs, what they are, why we do them, how to do them, and useful techniques that are often used in proofs.
Before we even get onto writing proofs, we have to know how to solve a problem. In this video, we explain one approach to a famous problem - the theorem on friends and strangers - or in our case, friends and enemies.