Introduction: How to Find Pi

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pi is an infinite number that goes on forever, without stopping, so how is it possible to calculate?

in this inscrutable, i will teach a simple way to find pi.

Step 1:

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the first thing you need to know is that the more sides a polygon has, the more circle like it gets. soon a shape with enough sides has a perimeter that approximates a circumference of a circle the same size. but for now, we will start off by using a square

Step 2:

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now that we have a square, lets set the diagonal length to 1 and make a point in the center called a

Step 3:

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now that we have a, we will make a triangle from a to a corner and to the middle of the face

Step 4:

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lets now lable angle x into the triangle, along with the sides of the triangle as j k and l.

Step 5:

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now in order to find the perimeter of this shape, we must find the length of one of its sides. one side length is actually equal to twice the length of triangle side j. but for calculator use, conveniently, every time you enter Sin(x) on a calculator you get j/(1/2) which equals 2J, the side length of the square.

Step 6:

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now that we know that we can calculate the perimeter by multiplying the number of sides by sin(x). in order to find x, take the number of sides and divide by 360. this will tell you twice the number of degrees because the triangle that we used to calculate x only took up half a side so we will divide by 2. that means that x = number of sides divided by 2.

Step 7:

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if we set the number of sides to n and the diameter of the shape is 1, then this means that the total formula for the circumference of the shape is n * sin(180/n). that means this square's circumference is about 2.83

Step 8:

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but what does this have to do with pi? well, what if we do a bigger number than 4? lets say 100. 100 * sin(180/100) = we get about 3.1410. do any of those numbers look familiar? do this with 1,000,000 and you get 3.1415926. practically pi! this would mean that the real answer to pi would be ∞ * sin(180/∞). i hope you enjoyed learning how to find pi!


russ_hensel (author)2015-03-02

Perhaps you could follow up with a routine to find sin(x)?

CadeL1 (author)russ_hensel2015-03-02

sin(x) is found by first finding x. x is the angle at point a on the triangle, and you can fit two triangles exactly(one normally, and the other inverted). all of the triangles will meet at point a, thus there is 360 degrees total of angles around point a, and since there is two triangles that take up an equal amount of degrees from the 360 degrees on every side, you take the 360 divided by the number of sides, and divide that number by two, but its simplified by having 180 divided by the number of sides. that means that x = 180/number of sides. sin is a complex math number that equals the opposite side of the triangle divided by the hypotenuse and was derived by methods i don't know. but that said, sin(x), or sin(180/number of sides) equals j/i. i hope this clears things up for you

russ_hensel (author)CadeL12015-03-04

You make it pretty clear how to find x, but not sin(x). If you drop degrees and move the the angle measure used by most mathematicians, radians, there is the neat fact that sin(x) = x, almost, for small angles. But if you work through the math you will find that in the end you find that pi = pi, which is not too helpful ( but better than pi = 2 * pi ). Try it.

JavaProgrammer (author)2015-03-03


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