Two Butterflies Theorem III
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A Mathematical Droodle


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This is a further generalization of the Two Butterflies theorem. One was suggested by Nathan Bowler who observed that the two butterflies need not live on the same circle as long as the circles intersect. It appears that the latter restriction is unnecessary. If the circles do not intersect the role of AB - the meeting place of the butterfly contours - is taken up by the radical axis of the circles.

Butterfly Theorem and Variants

  1. Butterfly theorem
  2. 2N-Wing Butterfly Theorem
  3. Better Butterfly Theorem
  4. The Lepidoptera of the Circles
  5. The Lepidoptera of the Quadrilateral
  6. The Lepidoptera of the Quadrilateral II
  7. Butterflies in Ellipse
  8. Butterflies in Hyperbola
  9. Butterflies in Quadrilaterals and Elsewhere
  10. Pinning Butterfly on Radical Axes
  11. Shearing Butterflies in Quadrilaterals
  12. The Plain Butterfly Theorem
  13. Two Butterflies Theorem
  14. Two Butterflies Theorem II
  15. Two Butterflies Theorem III
  16. Algebraic proof of the theorem of butterflies in quadrilaterals
  17. William Wallace's Proof of the Butterfly Theorem
  18. Butterfly theorem, a Projective Proof

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