;colony/science / Mathematics, Made Visual
∑ Mathematics, Made Visual
Mathematics, Made Visual
Probability you can drop, geometry you can drag.
Read it your way
Every answer here is written twice. Flip the switch and the page rewrites itself.
Try it now · Plate 30
What is the Pythagorean theorem really about?
Drag the legs and watch the two small squares exactly fund the big one.
PLATE 30 · AREAS, NOT ALGEBRA
Leg a 4 units
Leg b 3 units
a² + b²
16+9
c²
25
Hypotenuse
5whole!
Forget the formula for a second — look at the actual squares drawn on each side.
Whatever you do to the legs, the two small squares' areas exactly fill the big
tilted one. Try 3 and 4: the slanted side comes out a perfect 5. That triangle is how
ancient builders made corners square with a knotted rope.
Every question
Mathematics, Made Visual, answered twice.
Plate 30Open → What is the Pythagorean theorem really about? Draw the most famous equation in school and the real story lives in the squares, actual ones with area, more than the triangle they sit on. Plate 31Open → Why does pure chance build the same curve every time? Drop a hundred balls of pure chance and watch them organise themselves into the most famous curve in science. Plate 35Open → Why can't you fold paper eight times? Folding paper feels easy until, suddenly, it is impossible. The wall you hit at fold seven is the same maths behind epidemics and compound interest. Plate 38Open → The Monty Hall problem Three doors, one car, one simple question, and an answer so unintuitive that thousands of mathematicians once wrote in to call it wrong. Plate 84Open → Why are prime numbers special? Some numbers refuse to be split into a neat rectangle. They are the atoms every other number is built from. Plate 85Open → How can a shape be endless? A snowflake edge you can draw in a notebook, yet walk along it and you would never reach the end. Plate 86Open → How should evidence change your mind? A test that is right 99 times out of 100 can still be wrong about you most of the time. The arithmetic is brutal and exact. Plate 129Open → What is pi, really? Pi answers a real geometric question, and you can pin its value down just by throwing darts at random. Plate 130Open → The birthday paradox In a room of just 23 people, it is more likely than not that two of them share a birthday. It feels wrong, and it is dead right. Plate 131Open → What is a derivative? A derivative sounds like scary calculus. It is really one simple idea: how steep a curve is at a single point — and you can see it by zooming in. Plate 132Open → What is the butterfly effect? In some systems a change too tiny to measure keeps growing until it flips the whole outcome. That is the butterfly effect, and it is hard physics rather than poetry. Plate 133Open → The law of large numbers A handful of coin flips looks lopsided and unfair. Flip thousands and the unfairness vanishes — and that promise is what casinos and insurers are built on. Plate 155Open → Why does 0.999… equal exactly 1? 0.999… and 1 are the very same point on the number line, written two different ways. Once you see why, there is no gap left to shrink. Plate 159Open → What is the golden ratio, and why does it keep showing up? The golden ratio, about 1.618, is the one proportion that repeats itself: cut a square off a golden rectangle and a smaller golden rectangle is left. Plants use its matching angle, 137.5°, to pack seeds with no wasted space.
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