This Master's thesis discusses the butterfly theorem of Euclidean geometry and many of its known generalizations. In addition to two proofs of the theorem with basic concepts of Euclidean geometry, the thesis also includes proof of the theorem in the extended Euclidean plane. For the latter, concepts such as cross ratio, harmonic range, inversion and pole-polar relation are introduced in Euclidean geometry and the theorems of Ceva and Menelaus are proven. The thesis addresses the generalizations of the butterfly theorem by Murray S. Klamkin's and Vladimir Volenec's and the double butterfly theorem. To prove the projective butterfly theorem, the thesis focuses on concepts of the real projective plane such as harmonic conjugacy, projectivity, involution, polarity and conics. It also proves Desargues' involution theorem. A generalization of the butterfly theorem in the complex projective plane is proved with the help of Pascal's theorem.
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