# Math Curiosities

### Math Curiosity: The Coloring Problem

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?

### Math Curiosity: Magic Squares

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

### Fractals: Sierpinski’s Triangle

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

### Fractals: Koch Snowflake

You could keep zooming in on this snowflake forever!

### Math Curiosity: Palindromic Number Conjecture

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

### Math Curiosity: A Pattern Packed Triangle

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

### Math Curiosity: Finding Primes

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

### Crossing Every Bridge Exactly Once (aka Eulerian Paths)

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

### Math Curiosity: Odds & Squares

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

### Math Curiosity: Collatz Conjecture

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

### Math Curiosity: Klauber’s Triangle

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

### Math Curiosity: Four Squares

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

### Math Curiosity: Primes and Squares

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

### Math Curiosity: Ulam Spiral

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

### Math Curiosity: Goldbach’s Conjecture

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

### Math Curiosity: Twin Primes

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

### Math Curiosity: Magic Triangles

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

### Math Curiosity: Waring’s Conjecture

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

### Math Curiosity: Legendre’s Conjecture

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