Home > Pascal's triangle
4 History
The first reference to this triangle occurs in Pingala's book on Sanskrit poetics that may be as early as 450 BC as Meru-prastaara, the "staircase of Mount Meru". The commentators of this book were also aware that the shallow diagonals of the triangle sum to the Fibonacci numbers. It was known to Chinese and Islamic scholars in medieval times. It is said that the triangle was called "Yang Hui's triangle" by the Chinese. Several theorems related to the triangle were known, including the binomial theorem. In Italy, it is referred to as "Tartaglia's Triangle", named for the Italian algebraist Tartaglia (born Niccolo Fontana) who live a century before Pascal; Tartaglia is credited with the general formula for solving cubic polynomials.
In modern times, Pascal's triangle takes its name from the Traité du triangle arithmétique (1655) by Blaise PascalBlaise Pascal ( June 19, 1623 August 19, 1662) was a French mathematician, physicist, and religious philosopher. His contributions to the natural sciences include the construction of mechanical calculators, considerations on probability theory, studies of. In that work, Pascal collected several results then known about the triangle, and employed them to solve problems in probability theoryProbability theory Discrete mathematics Mathematical analysis Probability theory is the mathematical study of probability. Mathematicians think of probabilities as numbers in the interval from 0 to 1 assigned to "events" whose occurrence or failure to occ. The "arithmetical" triangle was later called after Pascal by Pierre Raymond de Montmort (1708) and Abraham de MoivreAbraham de Moivre ( May 26, 1667 November 27, 1754), was a French mathematician famous for de Moivre's formula which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was elected a Fellow of the (1730).
5 Construction algorithm
Here is a simple PythonPython is an interpreted, interactive programming language created by Guido van Rossum in 1990, originally as a scripting language for Amoeba OS capable of making system calls. Python is often compared to Tcl, Perl, Scheme, Java and Ruby. Python is develo program which prints out n lines of Pascal's triangle. Each new line is constructed from the previous line using Pascal's identity. An algorithm which instead constructed an arbitrary line without constructing all its predecessors might be preferable in some contexts.
n = 10
a = [1]
print a
for i in range (1,n):
b = [1]
for j in range (1,i):
b.append (a[j-1] + a[j])
b.append (1)
a = b[:]
print a
6 External links
CombinatoricsCombinatorics Discrete mathematics Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria, and is in particular concerned with "counting" the objects in those collections enumerative combinatori
