KIKARAKU - Geometry Puzzles

Add up a polygon's exterior angles? Roll a coin around another—how many turns? The answers defy intuition. 12 counterintuitive puzzles, from surprise to insight.

Your intuition is about to be proven wrong, beautifully.

Geometry is full of properties that most people get wrong on instinct. KIKARAKU is an educational app that lets you experience 12 famous counterintuitive themes through four interactive phases: be surprised, verify it with your own hands, and understand why it works.

■ Four phases, from surprise to understanding

[Intuition Quiz] Answer with your gut first. These are the questions most people get wrong.

[Hands-on Experience] Move the shapes with a slider and watch the moment your intuition flips.

[Explanation] Why is it true? Clear visual explanations that turn the basic theorems into the tools that resolve the surprise.

[Comprehension Check] Confirm your understanding with another counterintuitive or applied problem.

■ 12 counterintuitive themes

• Angle Puzzle — a polygon's exterior angles always sum to 360 degrees
• Triangle Secrets — Napoleon's theorem (joining the centers always gives an equilateral triangle)
• Pythagoras — the vanishing square (a missing-square illusion)
• Tangram — the same area, yet a very different perimeter
• Area Master — the isoperimetric problem (for a fixed perimeter, the circle wins)
• Symmetry & Transform — the coin rotation paradox (two turns, not one)
• Circle Theorems — the rope around the Earth (about 16 cm, no matter the radius)
• Nets — spider and fly, the shortest path across a surface
• Similarity & Ratio — the square-cube law (twice as tall, eight times heavier)
• Golden Ratio & Beauty — the golden angle 137.5 degrees and densest packing
• Coordinate Geometry — taxicab geometry (where a circle becomes a square)
• Volume & Surface Area — Gabriel's horn (finite volume, infinite surface area)

■ Features

• Interactive, hands-on understanding
• Dark / light mode
• Japanese / English

Part of the "RAKU" educational series — the 11th installment.