Binomial theorem expands (x + y)n into sum of terms with coefficients. Formula: (x + y)n = nC0 xny0 + nC1 xn-1y1 + ... + nCn-1 x1yn-1 + nCn x0yn. First mentioned by Greek mathematician Euclids in 4th century BC
Binomial theorem expands expressions of form (x + y)n for positive integers n. Expansion pattern follows pattern xn-kyk. Any expression with exponent n has n + 1 terms
Pascal was a 17th Century scientist, philosopher and mathematician. He wrote Pascal's Theorem at age sixteen about hexagons in circles. Built functional calculating machine for father's tax calculations
Expands powers of sums using terms' powers. Generalizes binomial theorem to multinomials. Sum of terms' exponents must sum to n. For m=2, reduces to binomial theorem
The Sierpiński triangle is a fractal with equilateral triangles subdivided recursively. It has zero area and a Hausdorff dimension of 3. The area of the triangle approaches zero with infinite iterations
Expands powers of binomial x + y into polynomial terms. Each term has coefficients that form Pascal's triangle. Coefficients are positive integers depending on x and y