As far as I understand, points on a circle have the same distance to one point. Further, points on an ellipse have the same distance to the sum of two points (foci) within it. Is there an analogous structure for the sum of three or more points? Or any other higher order structure?
2006-08-04 20:06:20 · 4 answers · asked by Ejsenstejn 2 in Science & Mathematics ➔ Mathematics
What about in three dimensions?
2006-08-05 10:15:52 · update #1
Yes. It is possible to perceive such a structure. But as i could see, there is no application for such a curve and hence no specific name is given. Ellipse find application when considering two bodies having gravitational force between them. It is a good question! I will try to work out such a curve and post some answers!!
2006-08-04 20:19:15 · answer #1 · answered by natanan_56 2 · 0⤊ 0⤋
No the sum of three points can't be constant.
Imagine you draw an ellips like this. Put two pins into the paper and a loose string loop over them. Stretch it with a pencil and go round both pins while the string remains tight. As the length of the string remains constant, and the gap between the pins is also a constant, you should get an ellipse.
Now you will see why I say that you wont get a figure if you try to do it your way.
2006-08-04 21:05:56 · answer #2 · answered by blind_chameleon 5 · 0⤊ 0⤋
Given 3 points in the plane forming a triangle,
consider a taut string surrounding the points.
Trace the maximal curve of the string.
In general, this will be a closed curve with
three elliptical arcs.
Similarly for n points forming a convex polygon in the plane.
In higher dimensions we get analogous convex regions.
2006-08-09 13:20:11 · answer #3 · answered by David Y 5 · 0⤊ 0⤋
first one -4x² + 4y² + 6x - 2y + 3 =0 is hyperbola by using fact of fact for ellipses and circles the two the cofficient of x² and y² ought to be +ve. 2d one 6x² + 17x - 9y - 7 = 0 is parabola by using fact of fact no y² term
2016-12-14 19:41:10 · answer #4 · answered by milstead 4 · 0⤊ 0⤋