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Israeli 10th-Grader Discovers Elegant Geometry Theorem

Posted by timothy on from the or-at-least-a-nice-proof dept.

An anonymous reader writes with a report that: Tamar Barbi, a 10th grade student living in Hod Hasharon, Israel, discovered that the theorem she was using to solve one of the problems on her geometry homework didn't actually exist. With the help of her teacher and mathematicians, she wrote up a proof for the theorem, which helps provide new and more elegant proofs for many other mathematical theorems. Posters at Hacker News have some skeptical words about the theorem's novelty, but also about the phrasing of the news report, which seems to omit some crucial words.

11 of 173 comments (clear)

  1. If this was an American high school... by supremebob · · Score: 5, Insightful

    They probably would have marked the answer on her homework as wrong because she didn't use the Common Core government approved method of solving the problem.

    1. Re:If this was an American high school... by Sarten-X · · Score: 5, Insightful

      Last I checked, the actual standard doesn't actually include any testing standards or teaching methods. It's really pretty loose for a standard (though my engineering bias rears its ugly head here).

      Rather, the actual standard says what concepts must be taught at what grade levels... and that's about it. There are some examples and the set of minimal facts to be understood, but it doesn't prescribe any curriculum, and it doesn't say how to evaluate students' progress toward that basic comprehension.

      It's also not a "federal standard". States are adopting it on their own, and if your state has chosen to legislate partucular testing methods to ensure compliance, that's your legislators' fault, not Common Core.

      From what I've seen (from association with a highly-regarded educator's college), Common Core is a great step forward. Previously, every state had their own standard, so a Louisiana high-school student, for (a fictitious, as I've forgotten all states' relative rankings) example, might be far behind a similar Oregon student in mathematics, but still meet their state's standards. For high-achieving students who relocated and were then told that their education wasn't good enough for their new location, it was devastating. For students transferring the other way, they'd often end up skipping grades, leaving holes in their understanding that wouldn't appear until later, when the curriculum assumes a particular concept was covered.

      Common Core has actually done the impossible: It is being adopted as a One True Standard to gauge a student's understanding, based on a set of concepts, rather than a district's particular placement test. Well-written tests against Common Core can also indicate whether a student has understood the concepts adequately for their grade level, based on real-world needs, rather than the opinions of a teacher who hasn't seen business needs in the past decade.

      --
      You do not have a moral or legal right to do absolutely anything you want.
    2. Re:If this was an American high school... by CimmerianX · · Score: 5, Insightful

      I'll tell you this... my 5th grader asked for help on his homework consisting of dividing 2 and 3 digit numbers.

      So we worked through all the problems together.

      He got a 0 on the homework even though all the answers were correct.

      When I went in to see the teacher about it, she said that we used long division and not the new math method of solving the problem. Thus he got a 0 even though all the answers were correct and my kid now knew how to do the work after I showed him the method I was taught.

      Stupid as far as I am concerned.

    3. Re:If this was an American high school... by Anonymous Coward · · Score: 2, Insightful

      What is stupid is you. You thought the homework was about getting the right answer. The homework ( as is ALL homework, until maybe Grad School ) is about validating that the student is understanding the concepts presented.
      What you did, using long division, got him the answer, but it did not teach him how to do proper grouping or estimation skills. Your same attitude should have told him to use a calculator... because he would get the answer right.
      These are building blocks for the future. Of course these methods are silly now... they won't be silly when you child can use the same estimation skills to divide a 10 digit number by a 6 digit number without even sweating or more importantly, be able to easily understand how (2x^2 + 4x)/16x = (x+2)/8

  2. Moral by Deadstick · · Score: 4, Insightful

    Don't try to learn about math from news media.

    1. Re:Moral by __aaclcg7560 · · Score: 4, Insightful

      Don't try to learn about news from news media.

      FTFY

  3. "Didn't actually exist" = "No dedicated name" by Anonymous Coward · · Score: 0, Insightful

    The theorem is trivial to anyone with even a minimal background in proving shit. Much like the fact that a+b+1 > a+b for integers a and b, this theorem didn't need its own name.

    1. Re:"Didn't actually exist" = "No dedicated name" by heretical_thoughts · · Score: 5, Insightful

      And how do you know they are not Muslim?

      The summery said Israeli not Palestinian. The Jews wouldn't allow Muslims into their country.

      According to the CIA world factbook, 17.5% of Israelis are Muslim.

  4. Even if it's wrong, it's right by Sarten-X · · Score: 3, Insightful

    Even if the proof isn't novel, or if there's some glaring error, Israeli secondary-school students now have a champion for a while, who found something interesting. That student in particular has a vested interest in a particular area of her field, and hopefully that will grow into a later expertise, and ultimately significant contributions to human knowledge.

    Faults and all, this is how mankind progresses... Stumbling forward one mistake at a time.

    --
    You do not have a moral or legal right to do absolutely anything you want.
  5. Non-invention by Sigma+7 · · Score: 3, Insightful

    Tamar Barbi, a 10th grade student living in Hod Hasharon, Israel, discovered that the theorem she was using to solve one of the problems on her geometry homework didn't actually exist.

    Okay, the article says:

    According to the new "Three Radii Theorem," if three or more 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.

    That's a definition, not a theorem. Even if you're generous enough to fix the wording, it's been proven centuries ago. 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.

    Not to mention that the article doesn't actually give the proof, and is simply a "yay, new invention by youngster" fluff.

    Posters at Hacker News have some skeptical words about the theorem's novelty

    And if you need to include that in the blurb, it's perhaps a good reason the article itself is garbage, especially when the topmost comment shows exactly why it's wrong.

  6. Theorem wrong as stated by Roger+W+Moore · · Score: 5, Insightful
    Actually if the theorem is exactly as the article states then it should have been marked wrong because it is wrong:

    According to the new "Three Radii Theorem," if three or more 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.

    I think what they meant to say was three lines of equal length in which case this just defines three points on a circle which is of course enough to uniquely define it. It also only works in two dimensions otherwise the point does not have to be the centre. This is the sort of geometric proof problem we used to get at secondary school. Have standards really fallen so incredibly far that this is noteworthy now let alone publishable? If so me and my old schoolmates can probably rustle up quite a few more "theorems" for publication in the journal of bleeding obvious mathematics.