intuition
Visual proofs of
beautiful ideas.
A small site of one-idea posts. Every entry answers one mathematical why with a single diagram you can drag.
Posts
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The angle every sunflower agrees on
Drop seeds onto a disc, each a small turn from the last. At one angle - and only one - the seeds pack into a perfect sunflower. At every other angle, the magic dies. The angle is 137.508°.
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Why a cube is literally a cube
A cubed number is n stacked floors of n² cells each. Pull the floors apart and the third dimension stops being a trick of the projection - it's the stack itself.
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What '42' actually means
A number is just a count of things. The digits are an artefact of which base you happened to grow up counting in. Slide the base, watch the bricks regroup.
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Why φ keeps showing up
The golden ratio is the unique aspect ratio that survives a square cut. Watch the spiral come together at exactly one number.
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Why multiplication is a stretch
Multiplication isn't really repeated addition. It's stretching the number line. Drag the slider and watch.
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Why π is what it is
Roll a circle along a number line. It always lands on π, no matter the size. The ratio is the point.
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Why 1 + 3 + 5 + ... = n²
The sum of the first n odd numbers is always a perfect square. Watch the L-shaped layers add up.
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Why a² + b² = c²
A visual proof of Pythagoras' theorem you can scrub through.
In the queue
- · Why φ is the most irrational number (continued fractions)
- · Why π emerges from random throws (Monte Carlo)
- · Why a single rule can make complexity (Rule 30)
- · Why a recursive tree never finishes
- · Why sharing a pizza is just division
- · Why √2 fits A4 inside A3
- · Why sin and cos chase each other