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Maths and nature - golden rectangle and Pascal's triangle
By Emily Tildesley (P3504) on Thursday, December 28, 2000 - 12:58 pm:

Hello, Im Emily, a 13 year old girl. We are currently studying the relationship between maths and nature. We've done the Fibonacci series in relation to natural things (e.g an apple has a five point star cross section and a daisy has 13, 21 or 34 petals.They are in the Fibonacci series :- 1,1,2,3,5,8,13,15,21,34.............)

Now I've been asked to find out how the golden rectangle or pascals triangle relate to nature.

Please help me , my parents don't know the answer and I'm stuck. Emily.

By Richard Samworth (Rjs57) on Tuesday, January 2, 2001 - 12:07 pm:

Emily,

There's an excellent website which describes how the golden ratio / rectangle relates to nature here.

I haven't found anything quite so well suited to what you need for Pascal's triangle, but you may find that this is of some use.

I hope this helps.

Richard

By Brad Rodgers (P1930) on Tuesday, January 2, 2001 - 07:34 pm:

This is probably looking for something that isn't there, but if you assign all of the odd numbers in the pascal triangle black and all of the even numbers white, you end up with a shape that is very similar to Sierpinski's Gasket (I'll try to find a picture of this). In fact, if you were to do this forever, you would end up with the Gasket exactly. The significance of this is that Sierpinski's Gasket is a Fractal. And fractals, self repeating objects, can be used to describe a number of pictures in nature. As I said, it's very weak link if that, but it is an interesting little fact, and if you don't find anything else this could be helpful.

[For that picture, see the second link above. - The Editor]