Areas and volumes
He proved that a sphere has two thirds the volume of its tightly fitting cylinder.
05 / ANTIQUITY TO THE RENAISSANCE
Archimedes of Syracuse
How do you measure a curved edge with straight lines? Trap the curve between two shapes you can measure.
Explore the mathematics ↓
The person behind the ideas
- Worked in Syracuse, on the island of Sicily.
- Used inscribed and circumscribed polygons to put bounds on π.
- Also studied levers, floating bodies, and the areas and volumes of curved shapes.
01 / MEASURING π
Trap a circle between two polygons
π is how many diameters fit around a circle: a little more than 3, for every circle there is.
Measuring a curve directly is hard. Archimedes trapped it between straight-sided shapes he could measure.
How far does a wheel go in one turn?
The wheel is exactly 1 diameter tall. Roll it along the ruler and see how many diameters it covers.
Distance rolled
÷Wheel’s diameter
=π
THE IDEAYou do not need an exact answer to know how close you are. A lower bound and an upper bound trap the truth between them.
More of the mathematics
Balance and buoyancy
His work connected mathematics with lever balance and the upward force a fluid exerts on an immersed object.