Saturday, November 19, 2011

The Geometric Pattern Theorem

When I was experimenting with certain patterns, I found something interesting within the pattern. Here is the work:

As you may notice, as you do the samething to every basic shape, the value increases 1, from the values 2.5, 3.5, and 4.5. Now, add all those values up, and you will get 10.5. Now, divide that by 3, since that is how many numbers there are, and you will get 3.5, which is the value of the triangle.

Now, let me show you why, with the diagram below:

As you can see, if you were to turn ever curved angle into a straight line, you would get triangles that make up the circle, meaning that the circle is made of triangles, approximately. Now, since the values of the triangles are 3.5, you would multiply 3.5 by 8, which then you get 28, and then divide that by 3, you get 9.3333333333333333333333333333333, which then you would subtract by 8, since you multiplied it by 3.5, and then using the process of getting the golden ratio, you would get 1.618, or the approximation.

What you also can do is add up all the values, or 10, 21, and 36, you will get 67, which then you divide by 3 to get 22.33333333333333333333333, and then subtract this number by 21, and then use this number to go through the process of getting the golden ratio, and you also get 1.618, or the approximation.

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