Practical Uses for Pascal's TriangleDate: 2/27/96 at 20:14:58 From: Andrew Cotton Subject: Help with Pascal's Triangle Hi, I teach 7th grade math. Some of my students are trying to find "practical uses" for Pascal's triangle. All I have been able to find has been related to probability. I remember hearing in the past of other uses, but I cannot remember them nor can I find any other info. Can you help? We will appreciate any help you can give us. Date: 3/1/96 at 14:44:2 From: Doctor Ethan Subject: Re: Help with Pascal's Triangle Hey, Great Question, Here are a few areas they can explore. 1. The triangular numbers * * ** * ** *** * ** *** **** * ** *** **** ***** * ** *** **** ***** ****** 1 3 6 10 15 21 First see if they can discover through examination what the pattern to the triangular numbers is (building triangles with pennies then, counting the pennies is a good way). Then see if they can draw a line through Pascal's triangle that will intersect the triangular numbers in sequence. For a reference on this and much more check out _More Joy of Mathematics_, p. 51. 2. This is in my opinion the clearest example of its usefulness: I assume that if you talked about probabilities then you talked about binomial expansions. A clear way to see this is by: (x+y)^n The coefficients for the terms will be the n+1 row of Pascal's triangle. (x+y)^3 = x^3 + 3x^2 y + 3xy^2 + y^3 1 3 3 1 the 4th row. In general I recommend the book I mentioned above. It is awesome. -Doctor Ethan, The Math Forum |
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