I developed Math Fun Facts in 1994 as a warm-up activity for the calculus courses I taught as a graduate...
Continue reading...calculus
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...
Continue reading...Irrationality by Infinite Descent
The traditional proof that the square root of 2 is irrational (attributed to Pythagoras) depends on understanding facts about the...
Continue reading...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...
Continue reading...Rationals Dense but Sparse
Well we all know that between any two real numbers there is a rational. Mathematicians like to say that the...
Continue reading...Devil’s Staircase
Here is a strange continuous function on the unit interval, whose derivative is 0 almost everywhere, but it somehow magically...
Continue reading...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...
Continue reading...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...
Continue reading...Multidimensional Newton’s Method
You’ve probably heard of Newton’s Method from your calculus course. It can be used to locate zeros of real-valued functions. But did...
Continue reading...Continuous but Nowhere Differentiable
You’ve seen all sorts of functions in calculus. Most of them are very nice and smooth— they’re “differentiable”, i.e., have...
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