Collection: Pascal's Triangle

Pascal's Triangle is named after the seventeenth century mathematician and philosopher, Blaise Pascal. While his name is in the name of the triangle, there were mathematicians before him that knew of and studied the triangle. The earliest known person who studied this triangle was the Persian Mathematician Al-Karaji, who lived from 953-1029.He wrote a now lost book that contained the first description of Pascal's Triangle. The Persian Poet-Mathematician-Astronomer, Omar Khayyam, later repeated Al-Karaji's work in the 11th century. Khayyam used the already known binomial theorem to recreate the triangle. Thus, the triangle is often referred to Khayyam's Triangle in Iran.

Pascal's Triangle was also known to the Chinese in the 11th century. The Chinese Mathematician, Jia Xian devised a triangular representation of the coefficients of the binomial theorem in the 11th century. Later, another Chinese Mathematician Yang Hui further studied Jui Xian's triangle, finding more properties in it. His study and discoveries found in the triangle further popularized the triangle. In China they call the triangle Yanghui's Triangle.

The triangle was first seen in Europe in 1527 when Petrus Apianus featured it on his frontispiece in his book about business calculations. They actually call the triangle Tartagalia's Triangle in Italy, named after the Italian Algebraist Niccolo Fontana Tartagalia. He published six rows of the triangle in 1556. Gerolamo Cardano also studied the triangle in 1570, he published the additive and multiplicative rules for creating the triangle.

Pascal published "Traite du Triangle Arithmetique" (Treatise on Arithmetical Triangle) in 1665. Pascal took the properties already known about the triangle and used them to solve probability problems. Pascal also discovered other properties and created proofs for them. The triangle was named after Pascal by Pierre Raymond de Montmort and Abraham de Moivre, which is now the name used commonly in the western world.