FREE! Click here to Join FunTrivia. Thousands of games, quizzes, and lots more!
Fun Trivia
Home: Questions and Answers Forum
Answers to 100,000 Fascinating Questions
Welcome to FunTrivia's Question & Answer forum!

Search All Questions


Please cite any factual claims with citation links or references from authoritative sources. Editors continuously recheck submissions and claims.

Archived Questions

Goto Qn #


What is/was the use of Pascal's Triangle?

Question #151183. Asked by chabenao1.
Last updated May 31 2024.
Originally posted May 31 2024 5:39 AM.

avatar
elburcher star
Answer has 1 vote
elburcher star
25 year member
1589 replies avatar

Answer has 1 vote.
I personally am mathematically declined...!, but see below
Pascal's triangle is named for 17th century French mathematician Blaise Pascal. Pascal wrote a treatise on triangles in his 1654 (published 1655) treatise Traité du triangle arithmétique. However, Pascal did not invent the triangle, so it bears different names in other countries.

In algebra and other branches of mathematics, Pascal's triangle is a triangular array of numbers that lists the coefficients of the expansion of any binomial expression (x + y)n, where n is any positive integer and x and y are real numbers. Its construction is simple: the numbers in each row are the sum of the numbers in the preceding row. So, each row begins and ends with the number 1.

How to Use Pascal's Triangle (Binomial Theorem)
The binomial theorem states that the nth row of Pascal's triangle gives the coefficients of the expanded polynomial (x + y)n.

link https://sciencenotes.org/pascals-triangle/

May 31 2024, 6:15 AM
patrickk star
Answer has 4 votes
Currently Best Answer
patrickk star
18 year member
32 replies

Answer has 4 votes.

Currently voted the best answer.
Pascal's triangle is a wonderful piece of mathematics that can be created and understood by a primary school child and yet hides dozens of fascinating properties and links to real world applications, including probability, combinatorics and algebra. The triangle is constructed starting with '1' in the top row. Each subsequent row is offset by half a place, and has one more number in it. Each number can be found by adding the two above it (if only one number is above, add 0 to it). The triangle is in principle infinite, though I'm not sure anyone has ever managed to write out that many lines. The first 5 rows look like:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

(well technically the first row is the 0th row and the last shown is the 4th, is that still 5 rows?)

The most common application of the triangle is to find the coefficients of the binomial expansion. For the expression "(x+y)^n", the nth row of the triangle lists out the coefficients of the expanded expression - e.g. 1,4,6,4,1 if n = 4

Another application that is perhaps easier to grasp intuitively is that for the nth row, the kth entry in that row (again starting from 0 as the first entry)) is given by the function nCk (n choose k). Put simply this function tells you how many ways there are to pick k objects out a of a group of n. One example is how many teams of 2 can be picked from a group of 4 people - the triangle tells us that the 2nd entry from the 4th row is 6, so 6 different teams can be created.

There are so many other patterns and connections hidden within the triangle, many well beyond my level to comprehend. The practical uses are largely superseded by calculators and computers, but the table still provides a useful reference to do these tasks manually. I think the real use is to demonstrate how interconnected seemingly independent aspects of mathematics and real world applications can be, and just to enjoy a pure piece of wonderful mathematics.

May 31 2024, 6:17 AM
free email trivia FREE! Get a new mixed Fun Trivia quiz each day in your email. It's a fun way to start your day!


arrow Your Email Address:

Sign in or Create Free User ID to participate in the discussion

Related FunTrivia Quizzes

play quiz Beyond "Rent" - Adam Pascal
( Celebrities M-P)
play quiz Francine Pascal's "Sweet Valley" Characters
(Pascal, Francine)
play quiz "Sweet Valley University " by Francine Pascal
(Sweet Valley University)

Return to FunTrivia
"Ask FunTrivia" strives to offer the best answers possible to trivia questions. We ask our submitters to thoroughly research questions and provide sources where possible. Feel free to post corrections or additions. This is server B184.