Binomial triangle and early induction
Triángulo binomial y primeras pruebas por inducción
- Date
- c. 1000 · confidence medium
- Place
- Baghdad, Iraq
- Credited to
- Al-Karaji; Ibn al-Haytham (sum of fourth powers)
- People
- 👤 Alhacén965–1038👤 Al-Karaji953–1029
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Al-Karaji describes the triangle of binomial coefficients up to degree 12 and argues by inductive steps; Ibn al-Haytham calculates the sum of fourth powers to find the volume of a paraboloid.
The binomial triangle appears independently in China (Jia Xian, c. 1050; Yang Hui, 1261), in Persia (Omar Khayyam) and in India (Pingala, much earlier, in prosody).
What it led to
- Pascal's triangle
- formal mathematical induction
- integral calculus of powers
Built on
- Al-Khwarizmi algebrac. 820
- Archimedes