We don't teach pictures that explain a formula. We teach the moves a mathematician makes — guess before you compute, turn the unknown into the known, and prove one fact many ways — until the answer is felt before it is written.
不是「用图解释公式」，而是数学家真正的思考方式 —— 先猜后算、化未知为已知、一题多证，直到心里先有了答案。
Cut a piece, move it — the area never changed.
剪一块，补一块 —— 面积从没变过。
Every concept opens with a hunch — see the answer before proving it. That is a mathematician's first instinct.
One truth, several ways to think. Each proof is a different mental move; together they build a sense of structure.
Every area becomes a rectangle; every volume is compared slice by slice — one tree, not a pile of unrelated formulas.
Each proof trains a different intuition — from cutting and rearranging, to comparing slices, to seeing the algebra cancel. We never substitute a picture for a proof.
Open “many proofs” 一题多证 →81 units across four domains, woven into one growing tree of ideas. The child sees the structure — not a string of isolated lessons.
Around 300 BCE, Euclid found areas by cutting and rearranging shapes. Eudoxus and Archimedes measured a circle by trapping it between polygons — the method of exhaustion, mathematics' first real grasp of the infinite — and Eudoxus proved a cone is one-third of its cylinder. Two thousand years later Cavalieri sharpened the idea that solids with equal cross-sections have equal volume. The same truths were reached independently in other times and places — in China, India, the Babylonian and medieval Islamic worlds — because good ideas recur across humanity. We teach this history honestly, and never pass off an approximation as a proof.
从欧几里得的割补、到欧多克索斯与阿基米德用多边形「逼近」圆、再到卡瓦列里的切片原理 —— 同样的真理，在不同文明中被独立发现。我们如实讲述这段全人类共同的历史，绝不用「看起来差不多」糊弄一个证明。
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