Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can't check infinitely many decimal places. You need a proof. I…
Analysis
The Area of a Disk
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know…
Everywhere Continuous, Nowhere Differentiable: The Weierstrass Function and Why It Matters
In 1872, Weierstrass presented a function that's continuous everywhere but differentiable nowhere. It shattered the assumption that smooth curves are…