Pythagorean theorem
In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. History: about 500 BC (known to Babylonians much earlier).
How to work it out
- 1
The statement:
- 2
In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ a^2 + b^2 = c^2 \]
All Pythagorean triples with hypotenuse up to 50 (computed)
| Triple (a, b, c) | Check | Kind |
|---|---|---|
| 3, 4, 5 | 9 + 16 = 25 | primitive |
| 6, 8, 10 | 36 + 64 = 100 | multiple |
| 5, 12, 13 | 25 + 144 = 169 | primitive |
| 9, 12, 15 | 81 + 144 = 225 | multiple |
| 8, 15, 17 | 64 + 225 = 289 | primitive |
| 12, 16, 20 | 144 + 256 = 400 | multiple |
| 15, 20, 25 | 225 + 400 = 625 | multiple |
| 7, 24, 25 | 49 + 576 = 625 | primitive |
| 10, 24, 26 | 100 + 576 = 676 | multiple |
| 20, 21, 29 | 400 + 441 = 841 | primitive |
| 18, 24, 30 | 324 + 576 = 900 | multiple |
| 16, 30, 34 | 256 + 900 = 1156 | multiple |
| 21, 28, 35 | 441 + 784 = 1225 | multiple |
| 12, 35, 37 | 144 + 1225 = 1369 | primitive |
| 15, 36, 39 | 225 + 1296 = 1521 | multiple |
| 24, 32, 40 | 576 + 1024 = 1600 | multiple |
| 9, 40, 41 | 81 + 1600 = 1681 | primitive |
| 27, 36, 45 | 729 + 1296 = 2025 | multiple |
| 30, 40, 50 | 900 + 1600 = 2500 | multiple |
| 14, 48, 50 | 196 + 2304 = 2500 | multiple |
Questions
What is the pythagorean theorem?
In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides.
Who is the Pythagorean theorem associated with?
Pythagoras, Euclid.