A strange discovery on the floor 👀
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!
📒 My Discovery Table
| flat side | tall side | coral square (tiles) | teal square (tiles) |
gold square (tiles) |
|---|
🔍 Stare at your table. Try adding the coral and teal numbers in each row. Notice anything?
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. Watch the empty floor (gold). Press Slide! — the tables move, but nothing is added and nothing is taken away. So the amount of empty floor cannot change… but its shape can!
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!
Use your new superpower 🦸
Knowing the secret of the square corner means you can measure things without a ruler reaching there! Solve all three missions.
Helper: you need a number that, multiplied by itself, gives the total. (5×5=25, 10×10=100, 13×13=169…)
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.2. Counting Squares 🔢
Draw a triangle with sides 3 and 4 on grid paper and grow squares on each side.3. The Sliding Puzzle 🧩
Cut 4 identical paper right triangles. Put them in a square two different ways.4. The Water Pour 💧
Describe (or rebuild!) the water experiment.Taught somebody at least one way? Then you've earned this:
Certificate of Discovery
This declares that
discovered the Secret of the Square Corner
(known to grown-ups as the Pythagorean Theorem: a² + b² = c²)
and can prove it with tiles, by counting, with a sliding puzzle, and with water —
just like a real mathematician.