An intuitive explanation for why sample means should be normally distributed. There have been many excellent articles and videos about the Central Limit Theorem (CLT). But besides formal proofs, I was not able to find a good intuitive explanation for why it is true. So here goes… Theorem Statement The…

A spider and a fly are on opposite walls of a 30 × 12 × 12 meter room. The spider is 1 meter above the floor, the fly is 1 meter below the ceiling. They are both 6 meters from adjacent walls, as shown in the diagram below. If the…

From Gauss and the birth of statistics to modern data science and machine learning — Ordinary least squares (OLS) regression is one of the first items on the menu in an introductory Statistics or Data Science course. But why do we need to square the errors? It’s a common question even high school students ask. After all, comparing the size of the errors (absolute value)…

An intuitive explanation of why summing random variables gives rise to a normal distribution. — Did you ever wonder why bell curves are everywhere? Heights, weights, neurons firing, the apparent brightness of stars… why should they all just happen to follow a similar bell curve distribution? “It reigns with serenity and complete self-effacement amidst the wildest confusion. The larger the mob, the greater the apparent…

The two squares shown both have area 10 cm² and their bases are parallel. Is it possible to find the area of the hexagon shaded in pink? — How would you go about it? I went with the algebraic method explained in Method 1 below. But there is actually a much nicer solution, which would even allow a bright primary school student to solve this problem. It is explained below as Method 2. Method 1 — Algebraic

*Simple to state. Not so simple to solve. — This article is about Problem 2 from the 2022 Indian National Mathematical Olympiad. The problem statement is beautifully concise:

Why must this sequence eventually become constant? — The European Girls Mathematics Olympiad (EGMO) is the highest profile girls-only international mathematics competition. It follows the same structure as the International Mathematics Olympiad (IMO), with two 4.5 hour papers over 2 days, each with 3 problems requiring mathematical proofs. …

An intuitive explanation of Kuratowski’s Theorem and Wagner’s Theorem, with lots of diagrams! — A planar graph is one that can be drawn in a plane without any edges crossing. For example, the complete graph K₄ is planar, as shown by the “planar embedding” below. One application of planar graphs would be designing a rail network without any intersections. Another…