Math Facts That'll Make You Say "Wait, What?" #1

Math is weird in the best possible way. It's full of surprises that have nothing to do with tests or worksheets.

Here are two facts to share with your kid. Not because they're on any curriculum, but because they're the kind of thing that makes you stop mid-conversation and say hang on, that can't be right.

The Shape That Goes On Forever But Fits in Your Garden

Imagine drawing a triangle. Now add a smaller triangle to the middle of each side. Now add an even smaller triangle to the middle of each of those new sides. Keep going. Keep going. Keep going.

What you're building is called a Koch Snowflake — named after a Swedish mathematician who described it in 1904. It looks a bit like a star, then a spiky circle, then something increasingly intricate the longer you keep adding.

Here's the strange part. The perimeter — the total length of the outline — gets longer every time you add triangles. Do this forever and the perimeter becomes infinite. An outline with no end.

But the area — the space inside the shape — never grows beyond a certain point. You can draw a circle around the Koch Snowflake that it will never break out of. It stays contained, finite, bounded.

A shape with an infinite edge that fits inside a finite space. It shouldn't work. It does.

Koch never proved this to make you feel strange about geometry. He proved it to show that some things in mathematics behave in ways that common sense cannot prepare you for. The snowflake was his evidence.

Pi Has Been Calculated to 105 Trillion Digits and We Still Don't Know If It Ends

Pi — the ratio of a circle's circumference to its diameter — starts 3.14159... and keeps going. No pattern. No repetition. No end that anyone has found.

As of 2024, mathematicians have calculated pi to 105 trillion decimal places. The calculation took 75 days on a specialised computer. The answer filled roughly 1.4 petabytes of storage — about the same as 300,000 feature-length films.

They still don't know if pi ever ends, repeats, or settles into a pattern. Current mathematics says it probably doesn't. But probably is not the same as proved.

The most useful number in all of geometry — in architecture, in engineering, in physics — is a number we can't write down in full and may never be able to. We use approximations. We always have.

Every circle ever drawn, every wheel ever turned, every planet in every orbit: all running on a number that nobody has completely written down yet.

The best math facts aren't the ones that make things clearer. They're the ones that make you realise how much is still strange, unresolved, and genuinely surprising, even in the parts of mathematics that everyone thinks they already understand.

Pi isn't just a number on a school poster. It's an open question.

Math is fun. We just teach it like it isn't.

This is the start of the series. Next: Math Facts #2 — The number so large that Google was named after a spelling mistake