DimaMazin Posted August 28, 2017 Share Posted August 28, 2017 Circle is shared by infinite quantity of equal triangles. Sides a and b are radiuses of the circle. Side c is chord, At=1/4[(a+b+c)(-a+b+c)(a-b+c)(a+b-c)]1/2 At=1/4[(2r+c)(c)(c)(2r-c)]1/2 At=1/4[(4r2-c2)c2]1/2 At=1/4[4r2c2-c4]1/2 c=2Pi*r / infinity Ac= infinity*At Ac=(1/4)*infinity[4r24Pi2r2 / infinity2-16Pi4r4 / infinity4]1/2 Ac=1/4[16Pi2r4-16Pi4r4 / infinity2]1/2 Ac=Pi*r2 At is triangle area Acis circle area Link to comment Share on other sites More sharing options...
John Cuthber Posted August 28, 2017 Share Posted August 28, 2017 Do you mean like thishttps://en.wikipedia.org/wiki/Area_of_a_circle#Rearrangement_proof Link to comment Share on other sites More sharing options...
DimaMazin Posted August 29, 2017 Author Share Posted August 29, 2017 8 hours ago, John Cuthber said: Do you mean like thishttps://en.wikipedia.org/wiki/Area_of_a_circle#Rearrangement_proof What is similar of those? Link to comment Share on other sites More sharing options...
Strange Posted August 29, 2017 Share Posted August 29, 2017 Your proof is not correct because it includes things like multiplying and dividing by infinity. It could probably be reworked in terms of limits to come up with a valid proof. 1 Link to comment Share on other sites More sharing options...
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