Pascal's triangle
Coefficients in triangular array
Pascal's triangle is a triangular arrangement of numbers where each row starts and ends with 1, and every other number is the sum of the two numbers directly above it.
The triangle reveals patterns useful in combinatorics, probability, and algebra—particularly for expanding binomial expressions.
Though named for the French mathematician Blaise Pascal, the pattern was known centuries earlier in China, Persia, and India.
Pisan mathematician, numeral importer
- hockey stickCurved implement for ice sports
- diagonalsLines joining opposite corners
- rowsSide-by-side sequences
- entriesItems logged or submitted
sums · identity · fractal · modular · odd · even · divisibility · coloring
Expression with two terms
- coefficientsNumerical multipliers in expressions
- combinationsUnions of separate parts
- expansionIncrease in scope
- factorialDescending multiplication of integers
probability · permutations · counting · polynomial · theorem · recursive · sequence · algebra
Returned light or thought
- mirrorReflective viewing surface
- bilateralInvolving two parties
- axisRotation reference line
- balanceSteadiness or amount owed
palindrome · diagonal · isosceles · proportion · alignment · invariant · harmony · self-similar
Fibonacci
Pisan mathematician, numeral importer
- hockey stickCurved implement for ice sports
- diagonalsLines joining opposite corners
- rowsSide-by-side sequences
entries · sums · identity · fractal · modular · odd · even · divisibility · coloring · visual
binomial
Expression with two terms
- coefficientsNumerical multipliers in expressions
- combinationsUnions of separate parts
- expansionIncrease in scope
factorial · probability · permutations · counting · polynomial · theorem · recursive · sequence · algebra · arrangement
reflection
Returned light or thought
balance · palindrome · diagonal · isosceles · proportion · alignment · invariant · harmony · self-similar
Khayyam
Tentmaker who versified
- Trianglesequilateral, isosceles, scalene, hypotenuse, vertex
- EponymsDarwinian, Alzheimer's disease, Freudian slip, cardigan, Parkinson's disease
- number sequencesFibonacci sequence, arithmetic sequence, prime numbers, natural numbers, integers
- polynomialspolynomial, polynomials, binomial, monomial, binomials
- combinatoricspermutation, combinations, combination, counting, arrangements
- Pascalcycloid, probability theory, hydraulic press, syringe, religious conversion
triangle, triangles, triangular, triangulation, triangulate, Pascal, triangulated, triangulator