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You are not logged in. #1 20131010 19:42:32
Expected area of a triangle in an ellipse.Hi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #2 20131011 15:12:41
Re: Expected area of a triangle in an ellipse.Reposting the J code here: Code:samp=:1000000 k1=:%:(11%3) k2=:%:(11%4) 'x1 y1'=: (k1&*@:cos;k2&*@:sin) 2p1*?samp$0 'x2 y2'=: (k1&*@:cos;k2&*@:sin) 2p1*?samp$0 'x3 y3'=: (k1&*@:cos;k2&*@:sin) 2p1*?samp$0 d1=:(((x1x2)^2)+(y1y2)^2)^%2 d2=:(((x1x3)^2)+(y1y3)^2)^%2 d3=:(((x3x2)^2)+(y3y2)^2)^%2 s=:(d1+d2+d3)%2 area=: %:(s*(sd1)*(sd2)*(sd3)) (+/%#) area "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #3 20131011 16:21:54
Re: Expected area of a triangle in an ellipse.What is J? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #4 20131011 17:11:00
Re: Expected area of a triangle in an ellipse.Hi, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." 