Math Curiosities

No video gets me more email from students! How few colors can you use to color in any map so that no two, neighboring regions are the same color?

Imagine a 3×3 square in which every row, column, and diagonal have the same sum. That’s a magic square!

The Collatz Conjecture: start with any number and get to 1 using just two rules. It seems to always work…

Can any perfect square be written as the sum of two primes?

Prime numbers are unpredictable! How can we possibly find them all? An Ancient Greek mathematician found one way!

It seems like there’s always a prime number between two perfect squares… but is this always the case!?

Can you make each side of this triangle add up to 9 using the digits 1-6?

Pi is mysterious and strange! Why not let students discover it on their own?

What if we make a huge spiral of numbers and then highlight only the primes? Well, a bunch of weird patterns show up!

Why does the sum of the first 5 odds also equal 5 squared?

In 1932, a leading authority on rattlesnakes, Laurence Klauber, discovered a startling pattern within a triangle of primes.

What do you call two prime numbers who are very close together?

How can you cross each bridge in this city exactly once?

What if this triangle pattern just kept repeating… forever!?

You could keep zooming in on this snowflake forever!

Using this one weird trick, it seems that you can turn any number into a palindrome!

Can any even number be written as the sum of two primes? Goldbach thought so, but we haven’t proven it… yet!

Every positive integer can be written as the sum of (at most) four perfect squares!

So, can you write every odd (greater than 3) as the sum of three primes?

Pascal’s pattern-packed triangle is a potent puzzle for pupils to ponder.