Search for a tool
Pascal's Triangle

Tool to compute value for Pascal's triangle. Pascal's Triangle is an arithmetic list of number imagined by Blaise Pascal where each item is either 1 or the sum of the two elements above it.

Results

Pascal's Triangle -

Tag(s) : Arithmetics, Series

Share dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Pascal's Triangle tool. Thank you.

# Pascal's Triangle

## Pascal Triangle Calculator

 Index 0 (the first row is noted 0) 1 (the first row is noted 1)

## Position of a number in Pascal Triangle

 Index 0 (the first row is noted 0)

Tool to compute value for Pascal's triangle. Pascal's Triangle is an arithmetic list of number imagined by Blaise Pascal where each item is either 1 or the sum of the two elements above it.

### How to create a pascal triangle?

The principle of Pascal triangle is based on a triangular contruction, write 1 on the first line, and 1 1 on the second line.

For the next lines, add the values of the two numbers directly above.

Example: Start of the Pascal Triangle :
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1

Values can be calculated using binomial coefficient, also used in calculation of combinations.

Pascal triangle values can be compared to the Fibonacci sequence where each number is the sum of the two preceding numbers.

Usually, mathematicians note the first line 0, same for the first column.

### How to calculate a precise value in the Pascal's triangle?

A value $$V$$ of the Pascal triangle at the position (line A, column B, 0-indexed) can be calculated with the binomial coefficients (and thus with factorials) and the formula $$V = \binom{A}{B} = \frac{A!}{B!(A-B)!}$$

### How to create a Pascal Triangle with Excel?

Write 1 in the cell B1, and =A2+B1 in the cell B2 and copy the contents in as many cells as you wish but do not touch column 1 and line 1. Each line is a new row of the Pascal triangle.

## Source code

dCode retains ownership of the source code of the script Pascal's Triangle online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Pascal's Triangle script for offline use on PC, iPhone or Android, ask for price quote on contact page !