MIT mathematician confirms: Israeli 10th-grader postulated new geometric theorem


Although a MIT mathematician confirmed Tamar Barbi’s discovery of a working theorem she used solving geometry homework problems wasn’t previously known, she still prefers a future in theater rather than mathematics.

By Yael Branovsky


Tamar Barbi from Hod Hasharon is only in the 10th grade, but she has already chalked up an impressive achievement: developing a new geometric theorem.

Israeli 10th grader, Tamar Barbi: The theorem is very logical and basic.

Barbi, who is studying mathematics on the highest matriculation track offered in Israel, discovered while doing her geometry homework that the theorem she was using to solve one of the problems on her homework didn’t actually exist.

“I checked with my teacher, Sean Gabriel-Morris, I asked relatives abroad who are involved with mathematics, and I consulted my parents, and [then] I realized that the theorem really didn’t appear anywhere, even though it’s very logical and basic.”

According to the new “Three Radii Theorem,” if three or more equal lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii.

Gabriel-Morris, a former chef who retrained as a math teacher, worked with Tamar to research the subject and helped her develop the new mathematical theorem, proving that it could serve as an easy, convenient solution for many geometry problems. The teacher-student team sent the theorem along with proof to a mathematician from the Massachusetts Institute of Technology, who became excited and wrote back that “it’s good to see how Tamar’s theorem provides elegant proof for other important mathematical theorems.”

The proof was also sent to math lecturers at the University of Haifa, and Barbi and Gabriel-Morris were invited to give a lecture on it to some of the top math instructors in Israel.

Barbi remains unexcited. She is involved with theater arts, studies acting, plays the piano and the guitar, sings, and dances.

“I don’t think math will become my profession. I hope to work in theater arts,” Barbi says.

Eli Hurvitz, executive director of the Trump Foundation, which promotes math and science studies in Israel, said: “Once again, it’s been proven that a great teacher, who challenges and supports [students], along with an ambitious and curious student, are a winning combination.”

Hurvitz added that in the future, Israeli students would use math to “develop medicines and technologies and make scientific breakthroughs.”


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  1. Alexander Mayer says:

    Why does the theory require a 3rd line? If two lines coming from the same point to the edge are of equal length mustn’t they be radii as well? What disproves r=AO=BO?

    • no, if it’s only 2 straight lines, they could be LONGER than the radius, and the point they meet will not be the center. Only when at least three are the same length, it can not be longer than radius, and they can only meet in the center.

      • Yael says:

        If it’s only two lines, they could also be shorter than the radius.

        • Yael- Totally agree. I drew shorter lines, touched the edge, but were not radii of that circle– they would be radii of smaller circle. In my humble opinion- not a valid new theory.

          • Yael says:

            No, the theorem is valid. My comment was in response to the one above me that said that if it were only two lines (rather than the three required by the theorem), then they could be longer than the radius. I was adding the point that two lines of equal length could also be shorter than the radius.

            But if you have three or more lines of equal length, then they must all be radii.

          • Yael’s comment is correct that the theorem is valid. It is the next step proving radii from Euclid’s Book III, Proposition 9, that proves a circle’s center.

    • Anon says:

      Easiest way to disprove it is not to think of lines coming out of a point, but a circle. Take a circle, and consider any point in that circle other than the center. Imagine a second circle centered on that point (large enough to intersect with the first circle, but not so large that the first circle is entirely contained within it).

      You will see that the two circles intersect at two points – that defines the two lines that have an equal distance from your point whose ends lie on the first circle, and clearly that point isn’t in the center.

      It’s also possible to make circles with only one intersection (think of a snowman, a circle with a circle on top, on just barely touching). And of course, circles with zero intersections (draw two circles far away).

      So for the 0, 1, and 2 line cases, we can’t say that the point is the center. Now try to draw a circle that intersects three times with another circle. You can’t. The only way to do more than two points intersecting is to draw the same exact circle again, which means that every point is intersecting.

      Therefore, if three or more equal length lines come out from the same point and all lie on the same circle, that circle they lie on must be the circle that has the point at its center.

      Also, for the author/editor’s edification, this is not new in the sense that it was previously unknown. It dates back to at least Euclid, where it can be found in Euclid’s Elements, Book III, Proposition 9.
      “If a point is taken within a circle, and more than two equal straight lines fall from the point on the circle, then the point taken is the center of the circle.”

      Hope this helps everybody!

  2. Jorge says:

    Yes, it is. It is an obvious consequence of that, I can’t understand why this is something new.

  3. sabin says:

    its so simple idea but noone thought of it before its quite amazing

  4. Sk says:

    There is already a similar theorem – Circle through Three Points.
    “Three Radii” is just a variant of “Circle through Three Points” theorem

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