Morioh
Login
Ari Bogisich

Ari Bogisich

3 years ago

Named after the French mathematician, Blaise Pascal, the Pascal’s Triangle is a triangular structure of numbers. The triangle is constructed using a simple additive principle, explained in the following figure.

Pascal Triangle Principle Edited

Each entry, except the boundary of ones, is formed by adding the above adjacent elements. Even though the formation of Pascal’s triangle is simple, it holds a huge number of mathematical properties and applications.

Properties of Pascal’s Triangle

Let us go through some mind-blowing properties of Pascal’s Triangle.

Combinations

Any high-school student with mathematical background must have gone through the course of Permutations and Combinations. The combinations section refers to the number of ways we can choose certain objects from a group of objects.

Pascals Triangle Equation

Using the row and the column number, each value can be replaced as follows:

Pascals Triangle Combinations

This property further extends to the binomial expansions, where each binomial coefficient represents the value of the Pascal’s Triangle.

Hockey Stick Identity

A very unique property of Pascal’s triangle is – “At any point along the diagonal, the sum of values starting from the border, equals to the value in the next row, in the opposite direction of the diagonal.”

Pascal Triangle Hockey Edited

It is quite clear from the figure that, the separate sums form individual hockey sticks.

#c++ #cplusplus #programming-c

Pascal's Triangle in C++

journaldev.com

Pascal's Triangle in C++

Named after the French mathematician, Blaise Pascal, the Pascal’s Triangle is a triangular structure of numbers. The triangle is constructed using a simple additive principle, explained in the following figure. Each entry, except the boundary of ones, is formed by adding the above adjacent elements. Even though the formation of Pascal’s triangle is simple, it holds a huge number of mathematical properties and applications.

6.85 GEEK