The Secret of the Square Corner

A math mystery — discover it, prove it, use it, teach it! 🕵️

PART 1

A strange discovery on the floor 👀

PART 2

The Square Machine 🔢

Was the floor a fluke? Or does it work for every triangle with a square corner? Build your own! Drag the two round handles to change the triangle. First guess how many little tiles fit in the mystery gold square… then click the little tiles in the coral and teal squares — each one flies over and lands in the gold square, so you can count and SEE if they fit!

PART 3

The Sliding-Puzzle Proof 🧩

Pythagoras couldn't check every triangle in the world one by one — nobody can. He needed one clever idea that covers all of them at once. Here it is. A square room with 4 identical triangle tables inside. Nothing can be added, nothing taken away — so however the tables slide around, the amount of empty gold floor cannot change… but its shape can!
Your mission: drag the triangles until the empty floor becomes two straight squares. There's more than one way to do it — any arrangement that works counts!

PART 4

The Water Proof 💧

Still suspicious? Good — mathematicians always are! The two small squares are tanks full of water. Flip the whole thing upside-down and let gravity pour every drop into the big square. Make your prediction first: will it overflow, be half-empty… or fill it exactly?
🖐 You can also grab the picture and spin it yourself — the water always flows downhill!

PART 5

The superpower: measure with your brain 🧮

You proved the secret is true. Now for the amazing trick it gives you: you can figure out the length of a slanty side without ever measuring it. Watch — and help!

PART 6

Mission time 🦸

Time to use your recipe on real problems — measuring things no ruler could reach! Solve all three missions.
Your recipe: ① square both short sides ② add them ③ find the number that times itself makes the total. (5×5=25, 10×10=100, 13×13=169…)

PART 7

Now YOU are the teacher 🎓

The best way to really know something is to teach it. You now know four different ways to show the secret to a friend, a parent, or a grandparent. Try teaching each way to a different person!

1. The Tile Story 🏛️

Draw a floor of square tiles. Shade half a tile, then draw the three squares like Pythagoras did.
Say: "Count the little triangles — 2 + 2 in the small squares, 4 in the big one. Equal!"

2. Counting Squares 🔢

Draw a triangle with sides 3 and 4 on grid paper and grow squares on each side.
Say: "9 tiles + 16 tiles = 25 tiles. The squares on the short sides exactly fill the big one!"

3. The Sliding Puzzle 🧩

Cut 4 identical paper right triangles. Put them in a square two different ways.
Say: "Same room, same tables — so the empty floor must be equal: one big square, or the two small ones!"

4. The Water Pour 💧

Describe (or rebuild!) the water experiment.
Say: "Pour the two small squares into the big one — it fills it EXACTLY. Not a drop spilled, not a gap left."

Taught somebody at least one way? Then you've earned this: