IdentityForge

See why the identities are true. Cut a square, watch the pieces, and the algebra becomes a picture.

(a + b)² = a² + 2ab + b²

Box It Build (a+b)², (a+b)(c+d) and numbers as area — and snip-test an identity. Concepts 16 focused rounds across the identities — squares, differences, cubes, Pascal & the seven remarkable identities.

Cast, stories & more

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Quiz Arena Identity Run

Meet the cast — the characters who teach this

Each one stands for an idea you’ll practice. Tap a character to read their illustrated story and hear their audio drama.

Tila The whole square
Miro & Moro The matching twins
Kerf The snip test
Boxer The box method
Overlap The corner counted twice
Dreamer The protege - a daydreaming fox who keeps only the two corner squares and forgets the two middle strips (the Freshman's Dream); the friend the learner teaches to count all four lots

Ensemble stories — the cast together

Miro & Moro

Explore all the stories →

What next? Pick a door

More like this ProofQuest Is this always true, or just sometimes?
A bit harder MentalForge Can you work it out in your head?
Something different EffectsForge How do movies fake giant and tiny?

Chosen from what this app is about. What you open is remembered on this device only.

Every piece and every check is computed by a deterministic engine — the picture is a proof, not a decoration. On-device · no accounts · nothing that names you leaves the device.

IdentityForge

How are you feeling?

Cast, stories & more

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😄 Brain break

Meet the cast — the characters who teach this

What next? Pick a door

Reading Access