MaplePrimes - answers and comments on Question, How can I create an ellipse and an ellipsoid?

Some answers

Markiyan Hirnyk — Fri, 12 Aug 2011 12:37:16 Z

Download ellipsoid1.mw

ellipsoid

PatrickT — Sat, 13 Aug 2011 13:17:22 Z

A recent discussion related to plotting an ellipsoid appeared here:

http://www.mapleprimes.com/posts/122970-Random-Dots-On-An-Egg

Ellipse

Markiyan Hirnyk — Fri, 12 Aug 2011 13:13:05 Z

Concerning an ellipse in the plane, look at ?geometry[ellipse] .

PS. Let us consider the example from http://www.mapleprimes.com/questions/37116-Intersection-Of-Line-And-Ellipse--How :

> E1 := (1/300)*x^2+(1/1000)*y^2 = 1:
>E2 := y = 2*x+40:
>solve({E1, E2}, {x, y});
{x = 30*RootOf(11*_Z^2+8*_Z+1, label = _L23), y = 60*RootOf(11*_Z^2+8*_Z+1, label = _L23)+40}
> allvalues(%);
{x = -120/11+(30/11)*sqrt(5), y = 200/11+(60/11)*sqrt(5)}, {x = -120/11-(30/11)*sqrt(5), y = 200/11-(60/11)*sqrt(5)}

>plots[implicitplot]([E1, E2], x = -30 .. 20, y = -40 .. 40, grid = [50, 50], scaling = constrained);

#I don't succeed to insert this plot

> solve({E1, y > 0}, y);
[[[{y=1/3 sqrt(-30 x^2+9000)}],And(RootOf(_Z^2-300,index=2)<x,x<RootOf(_Z^2-300,index=1))],[[],otherwise]]

>int((1/3)*sqrt(-30*x^2+9000)-2*x-40, x = -120/11-(30/11)*sqrt(5) .. -120/11+(30/11)*sqrt(5));
#the integrand and the limits can be extracted by Maple commands, but copy and paste seems simpler
-(1200/11)*sqrt(5)+50*sqrt(2)*sqrt(3)*sqrt(5)*arcsin((4/11)*sqrt(3)+(1/11)*sqrt(5)*sqrt(3))
-50*sqrt(2)*sqrt(3)*sqrt(5)*arcsin((4/11)*sqrt(3)-(1/11)*sqrt(5)*sqrt(3))
> evalf(%);#the area of the one piece
57.02091635
>2*(int((1/3)*sqrt(-30*x^2+9000), x = -sqrt(300) .. sqrt(300)));#the area of the ellipse
100*sqrt(3)*sqrt(10)*Pi
evalf(%);
1720.721163
1720.721163-57.02091635#the area of another piece
1663.700247

intersection&area.mw

Volume

Markiyan Hirnyk — Fri, 12 Aug 2011 23:08:08 Z

Download volume.mw