Binomial theorem and coefficient triangle
Teorema del binomio y triángulo de coeficientes
- Date
- c. 1000 · confidence low
- Place
- Baghdad, Iraq
- Credited to
- Al-Karaji; generalised to fractional and negative exponents by Isaac Newton in 1665
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Al-Karaji was the first to state the binomial theorem for integer powers together with the coefficient table, in a now-lost work known through later citations by al-Samawal; centuries later Newton extended it to any exponent.
Al-Karaji's original work was lost; it is known through al-Samawal's 12th-century citation. Indian and Chinese mathematicians knew particular cases earlier.
What it led to
- Systematisation of combinatorial algebra
- Foundation for the generalised binomial theorem used in Newton's calculus