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 more

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!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Thanks to your feedback and relevant comments, dCode has developed the best 'Pascal's Triangle' tool, so feel free to write! 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)

### How to create a pascal triangle?

The principle of Pascal triangle is based on a pyramidal/triangular construction, write 1 on the first line, and 1 1 on the second line. For the next lines, take two adjacent numbers, add their values and place this new number directly above. (The missing start and end are equal to 1).

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 call 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 online "Pascal's Triangle" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Pascal's Triangle" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Pascal's Triangle" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Pascal's Triangle" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

## Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!