🌍 Archimedes map

Demo

🎯 A demonstration Helion’s concise and powerful graphic capabilities
🧠 Inspired by Archimedes map by Steve Trettel
👉 Why Is a Sphere’s Surface Area 4πr²? Visual Proof, No Calculus

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From Why Is a Sphere’s Surface Area 4πr²? Visual Proof, No Calculus:

Why is the surface area of a sphere exactly $4\pi r^2$? Archimedes found the answer over 2,000 years ago, with no calculus.

In this 2-minute visual proof, you’ll see: 🍊 Why the skin of a sphere covers exactly 4 circles of the same radius
📐 How Archimedes compared a sphere to a cylinder (a can) wrapped around it
🔍 Why a patch of the sphere and its “shadow” on the can’s wall have the same area: where one stretches, the other shrinks
🧮 Why the can’s wall is $2\pi r \times 2r = 4\pi r^2$

Key idea: sphere’s skin = can’s wall, so they have the same area.

0:00 The orange and the paper circles 0:20 Archimedes and the can 0:40 Patch and shadow: stretched sideways, squeezed toward the pole 1:20 The can’s wall = 4πr² 1:50 Why this equals 4 circles