Coin rotation paradox

Imagine we have 2 coins. The radius of the larger coin is 3 times the radius of the smaller coin.

Raven paradox

The raven paradox was invented by Carl Gustav Hempel in the 1940s. It raises the question of what should be considered evidence for…

Fourier’s ingenious proof that e is irrational

Euler’s number, e, is an important number in mathematics that appears in many…

Factors of a prime squared minus one — a surprising result?

Surprise exam paradox

The surprise exam paradox is a paradox that relates to our knowledge of future events. It is also known as the…

Fundamental theorem of calculus

The 2 main operations of calculus are differentiation (which finds the slope of a curve) and integration…

Zermelo-Fraenkel set theory

In this article, we will look at Zermelo-Fraenkel set theory, why it is necessary, and what it is. And as an…

Gabriel’s horn — a shape with finite volume but infinite surface area

Sleeping Beauty problem

The Sleeping Beauty problem was created in the 1980s. Although it appears to be a fairly simple probability problem, it remains controversial, with no solution being generally accepted.

The problem

Mean value theorem for integrals

The mean value theorem for integrals relates the area under a curve (the definite integral) to the…