The Euclidean algorithm
Repeatedly taking remainders finds the largest whole number that divides two numbers exactly.
04 / ANTIQUITY TO THE RENAISSANCE
Euclid of Alexandria
A picture can suggest that something is true. A proof explains why it has to be true.
Explore the mathematics ↓
The person behind the ideas
- Worked around 300 BCE; little is known with certainty about his life.
- The Elements brought earlier mathematical knowledge into a systematic presentation.
- Its 13 books cover plane geometry, number theory, and solid geometry.
01 / CONSTRUCTION & PROOF
Make a triangle with three equal sides
Start with two points, A and B. Can you find a third point exactly as far from each of them as they are from each other?
No ruler allowed: just a compass and a straightedge, the tools of Greek geometry. A compass draws every point at one fixed distance.
Draw a circle around A
The compass is open exactly as wide as AB. Drag the pencil all the way around.
AB
=AC
=BC
THE IDEAEvery side has the same length as AB. We know why they are equal, even without measuring them.
More of the mathematics
Infinitely many primes
The Elements includes a proof that no finite list can contain every prime number.