Tamar Barabi spends most her time after school taking ballet lessons. While doing her geometry homework she discovered that the theorem she was using to solve one of the problems on her homework didn’t actually exist. Like most discoveries, the eureka moment happened by accident. Yes, the teacher said the theory she used to solve the homework problem didn’t actually exist. Further, she was told if she could prove it, it could be her theory. So that’s what happened. ‘Three Radii Theorem’ or ‘Tamar’s Theory’ came to existence, though there are some disputes comparing it to Euler’s work (for a point in a circle that is not the center at most two points lie on the circumference at any distance from that point). With help from her dad, who is also a math teacher, they sent the theorem to experts around the world. According to Tamar’s Theory **if three or more equal lines leave a single point and reach the boundary of a circle, the point is the center of the circle and the lines are its radii**. As said by Professor Ron Livne, Einstein School of Mathematics at Hebrew University, Tamar deserves praise for finding a new twist of stating that a circle has only one center and only one radius. The teacher-student team sent the theorem along with proof to a mathematician from the Massachusetts Institute of Technology. Tamar’s theorem can give elegant proofs for other important theorems as recognized by Ofer Grossman from MIT.

http://gineersnow.com/details/new-geometric-theory-accidentally-discovered-by-a-16-year-old

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