calculus

About Math Fun Facts

I developed Math Fun Facts in 1994 as a warm-up activity for the calculus courses I taught as a graduate...

Does Order of Addition Matter?

From your earliest days of math you learned that the order in which you add two numbers doesn’t matter: 3+5...

Irrationality by Infinite Descent

The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the...

Dedekind Cuts of Rational Numbers

Given a number line with equally spaced tick marks one unit apart, we know how to measure rational lengths: the...

Rationals Dense but Sparse

Well we all know that between any two real numbers there is a rational. Mathematicians like to say that the...

Devil’s Staircase

Here is a strange continuous function on the unit interval, whose derivative is 0 almost everywhere, but it somehow magically...

Space-filling Curves

Consider a square in the plane. Is it possible to draw a curve in the square that touches every point inside the...

Rational Irrational Power

If you raise an irrational number to a rational power, it is possible to get something rational. For instance, raise Sqrt[2] to...