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Area of circle explaination

by: Jessica Kuglitsch

Area of circle explaination MTH 225 Cr.4

Jessica Kuglitsch
UW - L
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About this Document

Awesome notes and further explanation of the area of a circle and an explanation of the formula
Logic and Discrete Mathematics
Dr. Allen
Class Notes
Math, Calculus




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This 2 page Class Notes was uploaded by Jessica Kuglitsch on Sunday October 16, 2016. The Class Notes belongs to MTH 225 Cr.4 at University of Wisconsin - La Crosse taught by Dr. Allen in Fall 2016. Since its upload, it has received 9 views. For similar materials see Logic and Discrete Mathematics in Math at University of Wisconsin - La Crosse.


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Date Created: 10/16/16
Area of a Circle- Write-up 1 kuglitsc.jessica January 2016 We start with a picture of a circle and draw the diameter, slicing the circle in half. Ultimately resulting in two semicircles, which then can be cut in half again which give you triangular shapes. As the triangles are sliced in half continuously, it results in smaller and smaller triangles. This also means that when we cut the circle in half we cut straight 180 degrees, when we sliced the two parts in half again that resulted in 90 degree angles, then 45 degrees and so on. This process continues and angles along with the size of the triangles continue to get smaller as the number of triangles increases. Essentially, you can continue to split the parts of the circle in half an in▯nite amount of times, giving you a total of n isosceles triangles. The more sections that the circle is split into the more accurate the answer will be for the area of the circle. So to summarize, we start with a circle, then two parts, then 4, 8, 16, and so on. If we line these parts up to form a parallelogram, they would make a rectangle. However, in order for this to happen, the pieces would need to be cut in half many times. Now that we have a parallelogram that is basically a rectangle, we must calculate the area of the parts of the circle we put together to form this parallelogram. So we know that the circumference of the circle can be calculated by using the formula C = 2(pi)(r). The height of the parallelogram is the radius of the circle we originally started, in other words h = r. In addition, since we know that C = 2(pi)(r) and considering the fact that we continually split parts of the circle in half to form the parallelogram, we can conclude that half of the distance covers the top of the parallelogram and the other half covers the bottom of the ▯gure. In other words, b = 2(pi)(ror simply b = (pi)(r). 2 Considering all that has been said in previous paragraphs, we can now use the area formula A = (b)(h) and plug in the information we have acquired. I used this equation due to the fact the beginning ▯gure was a circle. I took the circle, divided it in half, and then divided those parts in half and so on. The parts became so small that when put together they formed a rectangle as the parallelogram. Ultimately, I concluded that the area of a circle is equivalent to the area of a rectangle, so A = (b)(h) A = (b)(h) A = ((pi)(r))(r) A = (pi)(r ) 1 So everything from above goes further to explain how Archimedes calculated the information related to the area of a circle. 2


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