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Occasional Random thoughts from us.
What Is Infinity? And Why Are There Different Sizes of Infinity?
There are exactly as many even numbers as whole numbers, but more real numbers than either. Here is how Georg Cantor learned to measure infinity by pairing things up.
How Math Flashcards Can Help Teach Students
Math Flashcards Can Help Teach Students remember Math facts and tricks.
What Is a Complex Number Actually Good For?
The power grid, your phone's radio, airplane wings and quantum physics all run on complex numbers. Here is what they actually do in each case, with worked examples.
Why You Can't Take the Square Root of a Negative Number — Or Can You?
No real number squares to −1. But in 1572, an Italian engineer found that using √−121 anyway was the only way to reach a perfectly real answer. Here is how "impossible" roots became essential.
The Strange World of Imaginary Numbers
Raise an imaginary number to an imaginary power and you can get a real number: i to the i is about 0.2079. Here is a tour of how i behaves, and why Gauss wished it had a different name.
Unlocking the Secrets of Set Operations: A Beginner's Guide to Union, Intersection, and Complement
Set theory is a fundamental concept in mathematics that provides a foundation for many other areas, including logic, computer science, and statistics. At…
Why Some Numbers Cannot Be Written as Fractions
The diagonal of a 1×1 square can't be written as any fraction. Here is the ancient proof, how to tell rational from irrational decimals, and why almost every number is irrational.
The Weirdest Numbers in Mathematics
A number that exists but can never be computed. A decimal made by writing every whole number in order. A number so big it can't be written in the observable universe. Here are the strangest numbers mathematicians have defined.
10 Numbers With Surprisingly Interesting Properties
The only number squeezed between a square and a cube. A prime proven unique by a TV sitcom puzzle. The smallest number divisible by 1 through 10. Here are 10 ordinary-looking numbers with extraordinary properties.
Triangular Numbers, Square Numbers, and Other Figurate Numbers
Arrange pebbles into triangles, squares and pentagons, and number patterns become pictures. Here is how figurate numbers work, and the theorem Gauss celebrated with "EUREKA" in his diary.
Why 6174 Is Called the Kaprekar Constant
Pick almost any four-digit number, sort its digits high-to-low and low-to-high, and subtract. Repeat, and within seven steps you always land on 6174. Here is why.
John Forbes Nash Jr.: Mathematician and Modern Genius
John Forbes Nash, Jr. will go down in history as a Math God of his time. His contributions to game theory, differential geometry, and the study of the…