Brahmagupta's formula for cyclic quadrilaterals
Fórmula de Brahmagupta del cuadrilátero cíclico
- Date
- 628 · confidence high
- Place
- Bhinmal, Jalore, Rajasthan, India
- Credited to
- Brahmagupta
- People
- 👤 Brahmagupta598–670
- Field
- Knowledge & symbols
What was discovered
The Brahmasphutasiddhanta gives the area of a quadrilateral inscribed in a circle from its four sides, √((s−a)(s−b)(s−c)(s−d)), and the length of its diagonals. It generalises Heron's formula for the triangle.
Brahmagupta does not explicitly state that the quadrilateral must be cyclic, a necessary condition later commentators clarified.
What it led to
- Indian geometry (Mahavira, Bhaskara II)
- theorems on cyclic quadrilaterals