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I am trying to find the equations to calculate:

  1. The intersection surface area generated by the intersection of 3 circles (3 circles
    like a Venn Diagram).
  2. The 3 circle's radius could be be different one from others but always 0 < radius <= 1
  3. The circles centres positions are fix and they are separated by 1 unit each from other (the circle's centres are located in the vertexs of an equilateral triangle of side=1)

To be clearer... the intersection "of the 3 circles" area will result in a figure like an "irregular Reuleux triangle". That means a Reauleaux triangle where the internal triangle could be any (and not only an equilateral triangle) and the three radius could be different one from the others

Thanks a lot in advance

Georges L

  • 0
    very interesting, but first of all is such an equation exists?2012-09-13
  • 0
    I can see that trigonometry will work quite well. If $A_1, B_1$ and $C_1$ is your Reuleux triangle, and $ABC$ is your equilateral triangle all you really need are the angles $\angle B_1 A C_1$ and its other two counterparts. Those can be derived by trigonometry.2012-09-13

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