Heron formula and iterative square roots
Fórmula de Herón y métodos iterativos de raíces
- Date
- c. 60 CE · confidence medium
- Place
- Alexandria, Egypt
- Credited to
- Hero of Alexandria
- People
- 👤 Herón de Alejandría10–75
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
The area of a triangle as a function of its three sides, and an iterative method for approximating square roots (the average of x and n/x). Examples of mathematics applied to numerical calculation and engineering.
The area formula is attributed to Archimedes by Arabic sources; the root method was already used by the Babylonians.
What it led to
- numerical analysis
- Newton's method
Built on
- Archimedes (possible author of the formula)
- Babylonian square roots
Made possible
- Brahmagupta's formula for cyclic quadrilaterals628
- surveying
- Heron's automata and machines