Math Curiosities
Mathematical oddities. Puzzling patterns. Unexpected outcomes. Fascinating phenomena.
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!
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?
Fractals: Sierpinski’s Triangle
What if this triangle pattern just kept repeating… forever!?
Math Curiosity: Palindromic Number Conjecture
Using this one weird trick, it seems that you can turn any number into a palindrome!
Fractals: Koch Snowflake
You could keep zooming in on this snowflake forever!
Math Curiosity: A Pattern Packed Triangle
Pascal's pattern-packed triangle is a potent puzzle for pupils to ponder.
Crossing Every Bridge Exactly Once (aka Eulerian Paths)
How can you cross each bridge in this city exactly once?
Math Curiosity: Finding Primes
Prime numbers are unpredictable! How can we possibly find them all? An Ancient Greek mathematician found one way!
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: Magic Triangles
Can you make each side of this triangle add up to 9 using the digits 1-6?
Math Curiosity: Twin Primes
What do you call two prime numbers who are very close together?
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: 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!?