A short video — about ninety seconds — sets a trap: a challenge, a trick, or a "proof" that can't possibly be true.
Then the proof becomes a toy: sliders, buttons and games that let you test the idea yourself, as hard as you like.
Stuck or suspicious? Highlight any sentence on a lesson and ask Sensei — our AI helper answers just for you, privately.
Wing 1 · taming infinity
Why is a circle's area π × r²?
Archimedes traps a circle with a 96-sided polygon, and pizza slices rearrange into a rectangle. Bathtubs, ship-grabbing claws, and the method of exhaustion included.
Open → 🍫 Vault № 2The snack that never ends: ½ + ¼ + ⅛ + … = 1
Eat half, then half of what's left, forever — and finish exactly one bar. Zeno's 2,500-year-old "you can never reach the door" trap, and the limit that escapes it.
Open → 🃏 Vault № 3Add ten numbers in one second
The odd numbers 1 + 3 + 5 + … secretly build perfect squares — count them, square the count, done. Pebble-math from the Pythagoreans, a party trick for you.
Open → 🎭 Vault № 4The proof that lies: π = 4 ?!
The internet's favorite fake proof — every step true, conclusion false. Fold the square, fall for it, then zoom in and catch the lie. A defense class for your brain.
Open →Wing 2 · slicing & stacking
The circle's third key is an onion
Peel the circle into rings, unroll them, stack them — a triangle appears and πr² falls out. A 900-year-old proof that is secretly your first integral.
Open → 🏀 Vault № 6Measuring a curve — exactly
Archimedes fills a parabola with endless triangles, each generation ¼ of the last, and sums the series exactly — in 250 BC, with receipts.
Open → 🪦 Vault № 7The shape on the tombstone
Why Archimedes chose a ball-in-a-can for his grave: slice by slice, the sphere's share of its cylinder comes out perfectly clean. Coin stacks, a lost book, and tennis balls.
Open → ❄️ Vault № 8A shape with an endless edge
The Koch snowflake fits in your hand but its border never ends — edge → ∞ while area stays finite. Two infinities, one shape, plus the coastline paradox.
Open →Wing 3 · the calculus eye
How fast — right now?
The falling ball's 1, 3, 5, 7 finally explained: steadily growing speed, seen from outside. A prediction game, and your first derivative.
Open → 🔍 Vault № 10Why is your street flat on a round planet?
Zoom into any smooth curve and a straight line appears — that's why Earth feels flat. The snowflake refuses, and that refusal is the dividing line of calculus.
Open → 🐌 Vault № 11The pile that breaks the rule
½ + ⅓ + ¼ + … shrinks forever, yet Oresme's 1350 grouping trick shows where it's headed. Plus a block tower that leans past the table edge.
Open → 🎺 Vault № 12Fill it — but never paint it
Gabriel's horn holds three liters of paint but its wall can never be painted. Both proven. Torricelli's headache, resolved by asking: which quantity?
Open →Three lessons — Circle Area, the Infinite Chocolate and the Adding Trick — are fully translated into Kannada (English video with Kannada subtitles).
ಕನ್ನಡದಲ್ಲಿ ಓದಿ →These lessons introduce real mathematical ideas — limits, proof, the difference between convincing and true — through stories and play, aimed at ages 10–12 but honest enough for anyone. Everything is free, there are no accounts and no tracking, and the AI helper answers live — we never store what kids type (questions go to the AI service only to be answered; details on the grown-ups page). History is told playfully but fact-checked (we credit Eudoxus, da Vinci and Satō Moshun where credit is due). New to the site? The Basic training scrolls build the foundations, belts and all.