I remember reading somewhere about a diagram that had two overlapping circles such that the area of the intersection of the two circles was equal to that of the the non-intersecting part of each circle. Any idea what this is called, where I can find out about it?
2007-12-22 10:34:08 · 3 answers · asked by tateurrea 2 in Science & Mathematics ➔ Mathematics
You need to find a formula for the area of intersection of the two circles as a function of the distance between their centres.
For simplicity, assume the raduis of the circles is 1. Let the distance between the centres of the circles be d. We must find the area of the circular segment defined by the chord that runs between the points of intersection of the circles.
The angle of the sector of the circle which contains this segment is theta, and its area is theta/2 since we have set radius to one. theta = 2 arccos(d/2). The area of the segment is the area of the sector minus the area of the triangle formed by drawing radii to the points of intersection of the circles. The area of this triangle is cos(theta/2)sin(theta/2). Recall that 2sin(x)cos(x) = sin(2x) and we get sin(theta)/2. So the area of the segment is (theta - sin(theta)/2. The total area of intersection is twice that = theta - sin(theta). Plug d back in and you get an expression for the intersecting area of arccos(d/2) - sqrt(1 - d^2/4).
2007-12-22 11:12:50 · answer #1 · answered by David G 6 · 1⤊ 0⤋
What you're describing sounds a bit like a Venn diagram of two sets. A Venn diagram shows two overlapping regions that represent sets of things or data points. If an item in the diagram is in the overlapping area, it belongs to both sets. If not, it belongs to only one of the sets. The Venn diagram does not require that the area of the intersection be equal to the non-intersecting area of each circle; however, it would be possible to construct it in such a way.
2007-12-22 10:39:38 · answer #2 · answered by DavidK93 7 · 1⤊ 0⤋
Cluster Diagram
2016-04-10 21:17:33 · answer #3 · answered by Erica 4 · 0⤊ 0⤋