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.

Pascal's Triangle - dCode

Tag(s) : Arithmetics, Series

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*!

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.

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.

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 $$ V = \binom{A}{B} = \frac{A!}{B!(A-B)!} $$

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**.

dCode retains ownership of the online 'Pascal's Triangle' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Pascal's Triangle download for offline use on PC, tablet, iPhone or Android !

Please, check our community Discord for help requests!

pascal,triangle,binomial,combination,sum

Source : https://www.dcode.fr/pascal-triangle

© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲