# 16 y/o Tamar Barabi Discovered a New Geometric 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

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Tamar Barabi

What seems to be a turned in math homework with a new mathematical theory – discovered by accident – had earned the 16-year-old Tamar Barabi a geometric theory tagged after her name, for proving later a relationship between lines and radii.

According to the “Three Radii Theorem” or “Tamar’s Theorem,” 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.

Here is what the proof looks like when it’s put into practice!

This geometric theory was supported by her dad who is a math teacher, but she pulled off creating three proofs, a series of conclusions and sample exercises on her own to support the theory. The support was sent to math lecturers around the world.

Ron Livne, a professor at the Einstein School of Mathematics at Hebrew University in Jerusalem, said, “Tamar deserves praise for finding a new twist of stating that a circle has only one center and only one radius.”

Ofer Grossman from the Massachusetts Institute of Technology praised the Israeli teen, “It’s cool to see how Tamar’s theorem can give elegant proofs for other important theorems.”

However, Barabi expressed that it’s unlikely that math will be her profession, as she is committed to the theater arts. She studies acting, plays the piano and the guitar, sings, and dances.

Tamar Barabi’s Theory made a lot of mixed reactions from online boards. If the theorem states that: “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” then it must be proven as new. Here are the positive and negative reactions.

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“Actually this is a deeper understanding of the definition of circle” according to Lakshmi Prabha. “All points on the circle are at the same distance from the center.

This theorem is converse. If three Equal Line segments are drawn from a particular point inside the circle to its edge the point is the center of the circle. Well, the astonishing fact is that Tamar has used the property of radii(equal length) and has derived the result. Because for any point other than the center which lies inside the circle, the three lines segments will not be of equal length. So this theorem bears a similar but new concept.”

Another worthy insightful comment came from Emil John Lopez who is currently studying computer engineering. He said that “The implication of the theorem itself is nothing new. As many people have pointed out, it was already proven by Euclid and for anyone who has studied Geometry to some extent, the result is pretty much obvious and intuitive.

This story may very well be the result of humans exaggerating a simple story.

However, I have not seen the proof itself and it may offer a greater number of insights, if it was shown in an unorthodox way.

This is the only way I see this being something bigger than what the media has shown. There is no denying that the girl has love for math and passion so she might be able to pull off something big in the near future and it is quite nice that she proved this. It might be a good idea to keep track of her progress, given that she continues to be a mathematician.”

But according to Daniel R. Page, a Theoretical Computer Scientist, Tamar Barabi’s theorem “isn’t a new result, it is in Euclid’s Elements… Euclid’s Elements, Book III, Proposition 9

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