Theoretical analysis demonstrates nineteen proofs of the angle bisector theorem across geometry, highlighting the evolution from Euclid to artificial intelligence.
We give 19 proofs of the famous Angle Bisector Theorem from Euclid's Elements. The first proof is the Euclid's original proof, the remaining proofs use the methods of Euclidean Geo\-metry, Trigonometry, Analytic Geometry, Complex Numbers, and Gr\"obner Bases. The Gr\"obner Bases proof is in the area of Automatic Proving and Artificial Intelligence, so that the proofs in a way symbolise the development of mathematics from 300 BC (the Euclid's time) to modern days. We discuss what the proofs illustrate and why they are important for Math Education. All the proofs, except the first one, are original.
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Kulosman et al. (2024) studied this question.
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