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November 19th, 2014, 06:56 PM   #1
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Lightbulb New Formula of Circle?

Hello guys.. I'm new here at this forum because there is something that is bugging me and I need enlightenment. The area of the circle is = πr^2 right?
But this makes no sense to me.. I have my own formula that seems right to me and it makes sense graphically, and that is (circumference/4)^2. Can anyone evaluate my idea? Thanks by the way..!

Last edited by azztereris; November 19th, 2014 at 07:02 PM.
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November 19th, 2014, 07:34 PM   #2
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Graph is not everything. Put values and you'll find wrong answers by your-invented formula. Why does the actual formula makes no sense to you ? However, did you try to observe the difference in the two graphs ? As it may be minimial. I think that you don't have an idea how irrational $\displaystyle \pi$ is
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Last edited by Prakhar; November 19th, 2014 at 07:37 PM.
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November 19th, 2014, 08:32 PM   #3
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In general, your formula doesn't hold, if one admits πr² as the true area. There's a simple proof
of the formula for the area of a circle here.

Last edited by greg1313; November 20th, 2014 at 01:49 AM.
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November 19th, 2014, 08:40 PM   #4
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Thanks for the reply. I think I need to go back to my papers and stare to the Circle..XD Lol
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November 19th, 2014, 10:30 PM   #5
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Area of circle = (circumference/2)$^2/\pi$ = radius $\times$ circumference/2.
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November 20th, 2014, 01:42 AM   #6
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This image can help you visualise the area of a circle. The circumference of a circle is pi times the diameter, or pi times 2r. If you chop a circle into segments and lay them out like in the image, you end up with an approximate rectangle that is r by pi r, or pi x r^2. The smaller you cut the segments, the more rectangular it looks.

You can also try playing with this applet https://www.geogebratube.org/student/m3632 which lets you adjust sliders to see how the area of a circle works. Give it some time to load.

Last edited by base12masterrace; November 20th, 2014 at 01:44 AM.
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