Pythagoras’ Theorem: From Ancient Steps to Modern Screens

You probably first met Pythagoras’ theorem in Year 9 or 10—just a neat formula for right-angled triangles: a² + b² = c². But this simple relationship between side lengths has stories that stretch back thousands of years and quietly runs behind so much of today’s technology, from keeping buildings square to rendering lifelike 3D worlds on your screen.

Where did this come from?

Long before Pythagoras (around 500 BC), Babylonian clay tablets (circa 1800 BC) list number triples like 3-4-5 and 5-12-13—evidence they knew c² = a² + b² in practice. Fast forward to Pythagoras’ own school in Ancient Greece, where legend says his students discovered the square root of 2 couldn’t be written as a fraction. That find of an “irrational” number was so shocking it’s said the whistle-blower, Hippasus, was ostracised—proof that maths can spark drama as much as discovery.

Where you’ll see this in real life

1. Construction: Builders use a 3-4-5 rope to check corners are true right angles, ensuring walls are perfectly square. 2. GPS and navigation: Your phone figures out how far you are from each satellite by treating the earth-to-satellite lines as triangle sides and using Pythagoras under the hood. 3. Computer graphics: Rendering engines calculate light, distance and perspective by finding lengths of vectors (another name for directed line segments) in 3D space using Pythagoras' formula again and again. 4. Robotics and drones: Path planning often relies on calculating the shortest straight-line distance between points, which simply boils down to a² + b² = c² in coordinate form.

A common misconception

Many students think Pythagoras’ theorem works everywhere—but it only holds in flat (Euclidean) geometry. On a curved surface like the Earth’s sphere or in non-Euclidean spaces used in cosmology, the familiar a² + b² = c² needs adjusting (you’d use the Law of Cosines or spherical geometry instead). So, while it’s super powerful, remember its domain is the good old flat plane.