Properties of Pascal Triangle

Warning! Some information on this page is older than 3 years now. I keep it for reference, but it probably doesn't reflect my current knowledge and beliefs.

19:10
Thu
12
Nov 2009

Properties of Pascal Triangle

Pascal Triangle is a mathematical object that looks like triangle with numbers arranged the way like bricks in the wall. Each next row has one more number, ones on both sides and every inner number is the sum of two numbers above it. It can span infinitely.

Despite simple algorithm this triangle has some interesting properties. First, if you draw only odd numbers, you get a fractal - Sierpinski Triangle.

Second, graph of numbers in each row resembles Gaussian distribution function. The lower row you take from the triangle (containing more numbers), the more precise graph you get.

I've made these images with Octave - a free Matlab alternative. I like it and I think concepts behind this Matlab programming language can be quite useful for doing computations, but doing graphics is painfully slow. Whole seconds to draw several dozens of texts or rectangles? WTF?!

Comments (19) | Tags: fractals math tools | Author: Adam Sawicki | Share

Comments

dikshak
2015-06-06 13:47:48
it is nicely explained but there is about 8 properties of pascal triangle which are not given here
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xyz
2015-06-21 07:25:44
This is SOOOOooooooooo not helpful. Actually, it is shit. Total crap.
plte
2015-08-16 17:55:44
oh, you've found something very interesting. Actually, it's natural for the triangle to follow the gaussian distribution. think like this. each floor means one coin throw. the leftmost is when only one is front. the next one means two fronts. and the rightmost is when one is back. The number inside each box means the number of cases. So - it naturally follows Gaussian.
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2016-03-25 07:44:14
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STAT NO AD [Stat] [Admin] [STAT NO AD] [pub] [Mirror] Copyright © 2004-2017 Adam Sawicki
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