November 19th, 2014, 06:56 PM  #1 
Newbie Joined: Nov 2014 From: Philippines Posts: 3 Thanks: 0  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. 
November 19th, 2014, 07:34 PM  #2 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  Graph is not everything. Put values and you'll find wrong answers by yourinvented 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 Last edited by Prakhar; November 19th, 2014 at 07:37 PM. 
November 19th, 2014, 08:32 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond 
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. 
November 19th, 2014, 08:40 PM  #4 
Newbie Joined: Nov 2014 From: Philippines Posts: 3 Thanks: 0 
Thanks for the reply. I think I need to go back to my papers and stare to the Circle..XD Lol

November 19th, 2014, 10:30 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1619 
Area of circle = (circumference/2)$^2/\pi$ = radius $\times$ circumference/2.

November 20th, 2014, 01:42 AM  #6 
Newbie Joined: Oct 2014 From: Australia Posts: 27 Thanks: 10  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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