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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.

32 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, Funny

      Never mind that that's not actually how Common Core guidelines work, but hey... it's the current target of hate, and we've got two minutes to spare...

      --
      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 Anonymous Coward · · Score: 3, Interesting

      You'd believe that, but you'd be wrong, see, Common Core Math was designed as a collection of best practices for teaching mathematics. However, the fucking idiots didn't realize that, and made it into a federal standard that must be taught and tested to, so now we must test children on their ability to alorithmically apply a teaching tool towards computations. It's the most amazingly fucking stupid thing we've done against education in the last 30 years.

    3. 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.
    4. Re:If this was an American high school... by jbolden · · Score: 2

      It does when you claim it is common core and not State X's misapplication of common core.

    5. Re:If this was an American high school... by Sarten-X · · Score: 3, Interesting

      Conspiracy theories aside, you're sorely mistaken on a few key details. Common Core is a set of concepts, and a timeline for when they should be understood. It is not a curriculum, and it does not change the organizational structure of any school. The teachers are accountable to the school district, as they always have been. The school district is accountable to the state, as it always have been.

      Yes, schools that aren't producing employable graduates will face pressure to improve. On the other hand, schools whose students understand the concepts listed in the two standards will have no reason or requirement to change what they're doing.

      Common Core also has absolutely nothing to do with your decision to send your child to an out-of-district school, should you desire to do so, and it has nothing to do with the additional expenses you may incur. Instead, the extra expenses are because you are opting out of the services provided by your local government, such as buses and shared textbooks, and must then cover those costs on your own. Yes, you do still have to pay taxes to support your local school district, because that's what your duly-elected representatives have written into law, and you do still benefit from having schools. Though you say you "derive zero direct benefit" from your local school district, you do still receive an indirect benefit in the community improvement. The benefit may not be as great as a well-performing school might provide, but that does not give you any right to stop contributing to it. If you want that right, feel free to petition your local representative government.

      --
      You do not have a moral or legal right to do absolutely anything you want.
    6. Re:If this was an American high school... by Smidge204 · · Score: 2

      Let's suppose the standard will shape the qualification process for instructors, leading to instructors who spend far too much time in their own careers learning a standard instead of learning real math and how to teach it

      Based on what the post you replied to said, I don't see how this could possibly be the case.

      The "standard" only dictates what must be taught at a certain grade level, and not how it should be taught. From the teacher's perspective it's exactly the same as before since the school or state typically sets the curriculum requirements anyway.
      =Smidge=

    7. Re:If this was an American high school... by houghi · · Score: 3, Informative

      States are adopting it on their own

      Is this the same adoption as the states that can decide on the drinking age, but if it is below 21, they loose a lot of money on roads?

      This does not mean that I am for or against states or the governement deciding what the law is. It is just that is seems like childish behaviour and pointing fingers I would expect from a 5 year old.

      --
      Don't fight for your country, if your country does not fight for you.
    8. 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.

    9. Re:If this was an American high school... by stealth_finger · · Score: 2

      1. The "new math" method is designed to teach more than just how to get the answer. It teaches estimation skills and done right can teach how the numbers interact rather than just having your kid memorize an algorithm, both of which will make learning more advanced math easier (a number of "math is easy" people have remarked that the way "new math" teaches arithmetic is how they've always broken down numbers).

      2. Learning the method that will be used as the base of further learning is important. If his teachers are using "new math", not learning how to use it will put him further behind with each new concept he's learning. Part of the assignment was learning how to use this method for division, which he did not complete. This is not substantially different from when I was a kid and being given a 0 for not showing my work (i.e. demonstrating that I understood more than just what the result was).

      3. "Long Division" is not the "one true math standard". Various forms of it came into practice sometime between the middle ages and the renaissance, and the form which we were taught during the 20th century didn't even come into existence until the 19th century. "New math" is no weirder than when researchers figured out that teaching kids music also improves math skills.

      I guess the math that we all learned was shit then and isn't relevant anymore?

      http://s3.amazonaws.com/mathna...

      --
      Wanna buy a shirt?
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    10. 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. 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.
    1. Re:Even if it's wrong, it's right by superwiz · · Score: 5, Informative

      As the MIT discussion (linked in the slashdot summary) shows, it's actually in the Elements. But the theorem was not in the textbook used by the school and the student did stumble on it on her own. Good for her.

      --
      Any guest worker system is indistinguishable from indentured servitude.
    2. Re:Even if it's wrong, it's right by superwiz · · Score: 2

      The Ycombinator is apparently the link with all the info rather than the "news" source. I mistakenly said it was "MIT". Her proof is original. The theorem is not.

      --
      Any guest worker system is indistinguishable from indentured servitude.
    3. Re:Even if it's wrong, it's right by GrumpySteen · · Score: 2

      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.

      Not so much. If you'd read the article, you'd have seen this:

      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.

  4. Common Core is just a set of standards by rs1n · · Score: 5, Informative

    Do you realize that the common core is nothing but a set of standards as far as what students should be able to achieve at various levels? It does not dictate how teachers are supposed to teach the standards. That is left completely up to the teachers. The problem is that private companies are taking advantage of the fact that there currently is a lack of teaching materials that address the common core. Then to compound the problem are teachers who are often not specialists in their own area. I have taught an entire class of future math teachers, and most of them chose that profession because 1) they will always be in demand and 2) because they like to work with kids -- neither of which necessarily result in strong math teachers. (In fact, most of them would probably never become great math teachers, to be perfectly honest.) Anyway, your beef with the common core lies with the companies trying to cash in on the teaching materials void.

  5. Re:"Didn't actually exist" = "No dedicated name" by Aighearach · · Score: 2

    Euclid's Elements, Proposition 9.

    Her proof is either elegant, or clumsy but a great effort, depending who you ask.

    You thought you were going to sound smarty, didn't you? I don't doubt your background is as you imply, more than minimal, but you simply forgot the relevant details and then presumed they don't exist. You even made up an argument for why! So no matter how smart you were, you'd still be an idiot.

    http://aleph0.clarku.edu/~djoy...

  6. 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.

  7. 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.

    1. Re:Theorem wrong as stated by fph+il+quozientatore · · Score: 2

      Segment. The word you are looking for is segment.

      --
      My first program:

      Hell Segmentation fault

  8. Re:the news article misses key word by K.+S.+Kyosuke · · Score: 2

    Euclid apparently didn't consider it necessary either. Variables vs. values, perhaps?

    --
    Ezekiel 23:20
  9. Way to disuade potential talent. by EzInKy · · Score: 2

    When I was 11 I had a newspaper route. I bought a light for my bike that used a generator to produce light when I pedaled and that got my young mind thinking. Why not make a generator that produced the electricity and use its energy to turn the wheel? Of course I had no understanding of the conservation of energy at the time. I brought the idea up to my stepfather, his answer was "somebody smarter than you has already thought of that, you need to learn a trade." So I learned a trade and gave up exploring possibilities.

    --
    Time is what keeps everything from happening all at once.
  10. Proof by fph+il+quozientatore · · Score: 2

    I don't know what she came up with, but a possible proof is a one-liner: draw another circle with center in the given point and radius equal to the length of the three given line segments. This circle intersects the existing one in three points (the endpoints of the segments), hence they must coincide (because of https://proofwiki.org/wiki/Two...).

    --
    My first program:

    Hell Segmentation fault

  11. Incorrect report, now gets copied to Slashdot :-( by urdak · · Score: 5, Informative

    It's sad how stupid reporters report wrong "news", the error gets repeated all over the Internet, and finally lands in Slashdot whose editor didn't know the original news report was wrong.

    The 16-year-old girl did not invent a previously-unknown theorem. What she did is to re-invent a theorem which Euclid already listed and proved over two thousand years ago (http://aleph0.clarku.edu/~djoyce/elements/bookIII/propIII9.html). But Euclid listed hundreds of theorems, most have simple and basic proofs, and most of them are never specifically taught. In this case, the girl was not taught this theorem, but she thought that she could have used such a theorem in her homework, so she went about proving it (with help from her teacher, who was also not familiar with Euclid's mention of this theorem).

    The girl's proof is different Euclid's, but still very simple and elementary, and is in no way a profound addition to Mathematics. But this girl is still admirable, in that she had the creativity and resourcefulness to imagine a "new" (to her) theorem, and to go around proving here - rather than sticking to the "cheat sheet" of theorems she was taught in class. This girl definitely deserves an A in her math class, but not worldwide mention on news classes.

    Of course, it's not her fault, but rather that of the reporters who blew this story out of proportions, and reported this stuff as a new theorem, a breakthrough, or other irrelevant adjectives - without checking the validity of this "story" with any Mathematician worth his salt. This "story" should never have made headlines, and definitely not slashdot. But the girl still deserves praise, and of course an A :-)

  12. Re:Fun Common Core problem! by TapeCutter · · Score: 2

    There is insufficient information since they haven't explicitly marked the right angles.

    --
    And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
  13. 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.

  14. Re:"Didn't actually exist" = "No dedicated name" by TapeCutter · · Score: 2

    The Jews wouldn't allow Muslims into their country.

    Wrong and woefully ignorant
    Disclaimer: I do not support Zionists or any other terrorist group.

    --
    And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
  15. Be careful... by denzacar · · Score: 2

    ...where you Putin that reference.

    --
    Mit der Dummheit kämpfen Götter selbst vergebens
  16. Re:Barbi is a scientist by stealth_finger · · Score: 3, Interesting

    Look she is a scientist too! She is female and non white, this is so great, much greater than the theorem. We have so few theorems we can name after women, its really great we now can prove the patriarchists that cunts are smarter than dicks!

    Yeah but she doesn't want to do maths she wants to be an actress, just like the rest of them....../sigh

    --
    Wanna buy a shirt?
    https://www.redbubble.com/people/stealthfinger/shop?asc=u
  17. Re:"Didn't actually exist" = "No dedicated name" by heretical_thoughts · · Score: 2

    The US doesn't recognize Palestine.

    The CIA World Factbook does recognize The West Bank as a distinct entity, just not under the name Palestine.

    Groups that believe that the West Bank and Gaza are a part of Israel, such as the Jewish Virtual Library, place the percentage of Muslims in Israel at 20.7% of the total Israeli population.