Israeli 10th-Grader Discovers Elegant Geometry Theorem

If this was an American high school... by supremebob · 2016-03-13 14:09 · 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.

Re:If this was an American high school... by Sarten-X · 2016-03-13 14:12 · 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...

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Re:If this was an American high school... by guruevi · 2016-03-13 14:21 · Score: 1

In an American high school you don't have to prove anything, you just have to tick the right boxes.

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Re:If this was an American high school... by Anonymous Coward · 2016-03-13 14:36 · 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.
Re:If this was an American high school... by Sarten-X · 2016-03-13 15:01 · 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.

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Re:If this was an American high school... by jbolden · 2016-03-13 15:03 · Score: 2

It does when you claim it is common core and not State X's misapplication of common core.
Re:If this was an American high school... by WarJolt · 2016-03-13 15:59 · Score: 1

It matters how it's applied.
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. This may lead to a circumstance where the instructor can't understand a method that the student used to solve a math problem. I fear an overall decline in teaching quality. I hope this isn't happening, but when it comes to children's education you can't blame people for speculating. Based on my pre-common core public school math experience it's always hit or miss with instructors. Common core shapes the metrics that they use to evaluate instructors as well as students. Not every instructor is great and I can imagine that the poor ones may depend on common core as a crutch.
Then again everything might work out fine. Maybe it will actually improve teaching quality. Nothing has been proven either way. It's a grand experiment that may take decades to yield any meaningful results.
Re:If this was an American high school... by arglebargle_xiv · 2016-03-13 16:01 · Score: 1

In an American high school you don't have to prove anything
In Russian high school, proof anythings you.
OK, it's gonna need a bit more work, but it's a start, it's a start. Probably need to work in a Putin reference somewhere.
Re:If this was an American high school... by Sarten-X · 2016-03-13 19:14 · 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.

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Re:If this was an American high school... by Smidge204 · 2016-03-13 22:30 · 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=
Re:If this was an American high school... by dywolf · 2016-03-14 00:44 · Score: 1

no.
no test requirements
no actual curriculum either.
CC is merely a set of standard goals that students should be able to achieve.
actually getting to achieve that is something entirely different, and up to the individual states/schools and the publishers they should to purchase.

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Re:If this was an American high school... by houghi · 2016-03-14 01:21 · 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.

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Re:If this was an American high school... by CimmerianX · 2016-03-14 01:58 · 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.
Re:If this was an American high school... by LifesABeach · 2016-03-14 02:14 · Score: 1

For all the wrong reasons, you're right. Stop self medicating.
Re:If this was an American high school... by stealth_finger · 2016-03-14 03:28 · 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...

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Re:If this was an American high school... by stealth_finger · 2016-03-14 03:34 · Score: 1

Doesn't matter what policy your country has, the truth is it's quite common in various countries for high school level math to be taught as a recipe that must be followed and many teachers will mark answers correctly derived in alternative and more creative ways to be incorrect. Ultimately it's up to the teacher not the policy with these details, and it's hard to get lots of good quality math teachers at a high school level.
That's what I love about math. The answer doesn't matter and it's all about the journey......No, wait.

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Re:If this was an American high school... by virtualXTC · 2016-03-14 03:54 · Score: 1

Actually, having found a similar therom when I was in HS geometry, I can tell you that in the US they would of spent the time to try an publish it only to have academic journal editors figure out it wasn't novel at all and make allegations of plagiarism...
Re:If this was an American high school... by Anonymous Coward · 2016-03-14 04:28 · Score: 1

Agreed - it's not the (new math) (method), it's the (new) (math method).
Although giving the kid a zero is a bit much, particularly when the parent's knowledge of the (new math) (method) is nonexistent, and the parent can successfully teach the child the (old math) (method), and the child can repeat such learning to the teacher to prove that dad didn't just do the homework for him.
Re:If this was an American high school... by Anonymous Coward · 2016-03-14 04:53 · 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
Re:If this was an American high school... by dywolf · 2016-03-14 07:19 · Score: 1

another AC that doesn't know the difference between a Learning Objective (or goal, or standard) and the word "curriculum".
the point 2nd and 3rd math problem btw, is to learn how to break a problem into its parts, and illustrate the same process you use in your head (or most people do, being a stupid AC, that may be too much credit) when you simplify or chunk up a more difficult problem to solve it.
borrowing and carrying 1's works great on paper, and a quick simple process for solving math. on paper.
for many students its learning by rote, without understanding. its a magic black box little different from a calculator.
how does it work? they don't know. they just 'know' (they trust or believe really) that it works.
but its not so good in your head, and not so good at developing an intrinsic almost instinctual understanding of math.
which is what the goal of that particular lesson is. and which that process is good for.
this lesson isn't merely about teaching you had to add and subtract, but about building an intuitive foundation of numbers that other lessons down the road can build upon. merely learning the rote algorithm of carrying and borrowing 1's doesn't accomplish that. if you go farther in the study of math you need that foundation, and if you don't have it cause you never moved past that rote algorithm, you wont go far.
check out http://www.patheos.com/blogs/f...
it explains even better than I.

On the surface, it seems ridiculous. The top makes sense; the bottom is silly; screw you, Common Core!
Except that the top doesn’t make sense, the bottom does, and the connection to Common Core is completely misunderstood. (Says this math teacher.)
Here’s what’s going on: The top is how most of us learned subtraction. I’m sure your teachers taught you what was going on mathematically, but do you really remember what they said? Probably not. For us, it’s just an algorithm. You can do it without thinking. You hope there’s no “borrowing” of numbers involved, but if you had to do it by hand, you could probably pull it off.
The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”
That’s where the bottom solution comes into play. I admit it’s totally confusing but here’s what it’s saying:
If you want to subtract 12 from 32, there’s a better way to think about it. Forget the algorithm. Instead, count up from 12 to an “easier” number like 15. (You’ve gone up 3.) Then, go up to 20. (You’ve gone up another 5.) Then jump to 30. (Another 10). Then, finally, to 32. (Another 2.)
I know. That’s still ridiculous. Well, consider this: Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill. How much change should the barista give you back? (Assume for a second the register is broken.)
You sure as hell aren’t going to get out a sheet of paper and do this:
Instead, you’d just figure it out this way: It’d take 70 cents to get to $5 and another $15 to get to $20 so you should get back $15.70.
That’s it. That’s the sort of math most of us do on a regular basis and it’s exactly the sort of thinking the “new” way in the picture is attempting to explain. Granted that was an *awful* example to use, but that’s the idea. If students can get a handle on thinking this way instead of just plugging

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Re:If this was an American high school... by david_thornley · 2016-03-14 09:14 · Score: 1

And your point would be? There have always been crappy teachers.

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Re:If this was an American high school... by david_thornley · 2016-03-14 09:17 · Score: 1

Do all states apply Common Core that way? Or are they using something else that is rigid? There seems to be a movement towards rigid uniformity, but that isn't Common Core.

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Re:If this was an American high school... by ChrisMaple · 2016-03-14 10:03 · Score: 1

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...
You seem to think that's a good thing.

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Re:If this was an American high school... by Anubis+IV · 2016-03-14 10:35 · Score: 1

What about long division suggests someone doesn't understand math? It's an algorithm that allows its practitioners to solve simple, two-digit division problems and then iterate recursively on the remainder. The basis for it is founded on solid math, and you won't be able to practice long division effectively without understanding base systems, radixes, subtraction, and a whole host of other concepts that are appropriate to that age level. Admittedly, they may not yet know each of those concepts by those names, but that fact does not in any way diminish their understanding of the underlying principles.
I mean, if you were suggesting we should be teaching Geometry students how to use Calculus to derive the formulas for calculating the areas and volumes of various shapes, rather than having them memorize those formulas, I'd think you were out of touch with reality, but at least you'd have a self-consistent principle on which you were making your stand. Instead, you're trying to relegate long division and its use to the land of tricks and shortcuts that are the crutches of people who don't understand math.
If anything, suggesting long division is just a trick or shortcut seems to suggest to me that you yourself don't understand math very well.
Re:If this was an American high school... by ChrisMaple · 2016-03-14 10:45 · Score: 1

Despite Gates’ and others’ assurances that the Common Core reform was “state-led,” the former director of the Race to the Top competitive grant program, and outgoing U.S. Education Secretary Arne Duncan’s chief of staff, recently admitted the federal government had “forced” full support for adoption of the Common Core standards from each state by requiring its governor, chief state school officer, and head of the state board of education to sign off on the grant application.
Common Core is also a deceptive trap, a lure to escape Bush's destructive "No Child Left Behind". From the frying pan to the fire.

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Re:If this was an American high school... by Maritz · 2016-03-15 02:48 · Score: 1

You sound like you might be right. Shame you had to be a total prick about it.

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Re:If this was an American high school... by BadgerRush · 2016-03-15 02:56 · Score: 1

Let me try and give and example to show why you are wrong: Imagine your kid where learning multiplication methods and had a homework with the simple multiplication 345*10, and he answered all the assignment by doing repetitive sums (345+345+345+345+345+345+345+345+345+345=3450). In this case wouldn't you agree with the teacher to fail the student's assignment? After all, the objective of the assignment is not to give the result to the teacher, the teacher already knows the answer, instead the objective is to practice a method, a tool, that will be useful later on. If we allow that student to pass like that, how do you think he would fare later when he had bigger multiplications like 2345*2345?
That is the problem with the kind of math teaching that we had when we where kids. They would teach inefficient methods to everyone, then the few students with "predisposition to math" (I imagine a large part of Slashdot readers where in that group) would devise their own more efficient mental methods to complement the taught method. Then later, the students without "predisposition to math" would fall behind more and more at each step, with each new teaching piling up on top of the inefficient foundations. So I support this new initiative of trying to teach to every kid all the tools that I (like many Slashdoters) had to devise by myself when I was kid; so hopefully this new generation don't become as math illiterate as the vast majority of mine.
Re:If this was an American high school... by BadgerRush · 2016-03-15 03:08 · Score: 1

Well, the math that we all were taught failed the vast majority of our generation. With only a few students understanding basic math when graduating school (most Slashdot readers probably being in this group), and the others, the vast majority being otherwise completely math illiterate. And guess what, those few who managed to learn math actually devised different mental methods and tools to do the job whenever the taught method failed them, and that is how they managed to succeed even thou the official method was crap. So the new initiative is just to try and teach every to kid the tools and methods that the few of our generation actually used.
Re:If this was an American high school... by stealth_finger · 2016-03-15 04:33 · Score: 1

How so? Take addition. You put the numbers ontop of each other and add them up by row, if it's more than 10 carry the one. You can do this counting your fingers if needed. The new way you have to split the numbers into easily addable bits but inorder to do this you need to do math to split the number before you even start! Madness!

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Re:If this was an American high school... by mattack2 · 2016-03-15 11:11 · Score: 1

With only a few students understanding basic math when graduating school (most Slashdot readers probably being in this group), and the others
The geeks shall inherit the earth.
Re:If this was an American high school... by beastofburdon · 2016-03-16 01:51 · Score: 1

No, common core is best saved for the full ten minutes hate.
Re:If this was an American high school... by beastofburdon · 2016-03-16 02:08 · Score: 1

Have you talked to many recent high school graduates lately? Their grasp of math makes some of the worst of my graduating class look like geniuses of math. I'm talking about the same school, predominantly the same teachers, and the same general population of students. It is disturbing.
Re:If this was an American high school... by beastofburdon · 2016-03-16 02:16 · Score: 1

If it is not a curriculum, then why do the worksheets have the damn name on them?
Re:If this was an American high school... by stoatwblr · 2016-03-16 03:33 · Score: 1

The whole thrust of common core (as mentioned) is best common practices.
Kids should be taught XYZ by ABC age, but what all these legislators (and a bunch of "teachers" who should be sacked) don't grasp is that the "best" method is _what works best for that child_
Different methods work differently for different children. Mandating any particular method is a guarantee that some will "fail", but it keeps jobsworths happy and as jobsworths invariably end up at the controls (they know how to work the system but not WHY the system is setup that way), the outcome is inevitable.
Re:If this was an American high school... by stoatwblr · 2016-03-16 03:45 · Score: 1

"the math that we all were taught failed the vast majority of our generation"
The more pointed truth is that most teachers are crap.
Disclosure: My parents are teachers. I've circulated among the teaching community for decades. There are a few brilliant ones, some good ones, some effective ones, many substandard ones and a few awful ones - with about 2/3 being the latter two categories. Most of the teachers my parents worked with had trouble balancing their checkbooks (I know this because they'd often get me to do it) and couldn't comprehend simple interest calculations, let along compounding interest - which doesn't hold out much hope for more complicated activities. In addition most lacked any form of curiosity or basic problem-solving abilities.
Most elementary teachers come to the job from humanities-type backgrounds. Maths grads tend towards "harder" science jobs, which is likely to have a bearing on the personalities encountered. (Poor teacher pay across the board means most competent people will go where they can be paid more. Teacher salaries have declined in real terms by at least 50% worldwide since the 1960s, even more in countries such as the USA and UK.)
If a teacher comes to the subject with the attitude of "maths is hard" then they'll impart that onto the kids. One of the most important "fixes" needed in education is not to fix what kids are taught, but to fix (or remove) broken teachers and administrators.. The current structures mean that they're the ones most likely to stick around.

Moral by Deadstick · 2016-03-13 14:11 · Score: 4, Insightful

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

Re:Moral by __aaclcg7560 · 2016-03-13 14:18 · Score: 4, Insightful

Don't try to learn about news from news media.
FTFY
Re:Moral by Anonymous Coward · 2016-03-13 15:49 · Score: 1

Don't try to learn from news media.
FTFY

Even if it's wrong, it's right by Sarten-X · 2016-03-13 14:16 · 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.

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Re:Even if it's wrong, it's right by superwiz · 2016-03-13 14:23 · 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.

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Re:Even if it's wrong, it's right by superwiz · 2016-03-13 14:30 · 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.

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Re:Even if it's wrong, it's right by Anonymous Coward · 2016-03-13 14:45 · Score: 1

Israeli secondary-school students now have a champion for a while,
No. If anything, their mathematical secondary-school level mathematical champions are the IMO participants and so on who worked hard enough to hone their math skills to the point where they can prove this while blacked out. The theorem she proved is the type of thing I used give college freshmen on their first or second in-class 5-minute pop quiz back when I used to teach a proof writing class. A class that is taught at a level every IMOer or AMC10/AMC12 regular (or the Israeli equivalent) is far beyond. She's a false idol fabricated by the media, and acting like she did something praiseworthy is an insult to those who actually work towards eventually doing so.
Re:Even if it's wrong, it's right by aliquis · 2016-03-13 14:48 · Score: 1

In the actual article it says she want to do theater ..
Also if you know the radius can't you just put down a compass (weird name in English) along the edge and draw a part of a circle inside the circle and then put it down somewhere else and repeat that and see where they meet?
Isn't the third line only needed to not put the center along the edge of the circle rather than the middle?
Or if you have a straight angle with 45 degrees marked onto it hold that towards the circle and mark out the 45 degrees and then hold it onto some other place on the circle and mark it out again?
If you don't know the radius or have the square thingy but have the compass you can draw two circles from the edge of the circle and then draw a line which passes those two to get a straight line passing through the middle of the circle, repeat once more and you're done?
To mark a line the length of a radii without the compass is just cumbersome. To measure out the point with compasses or whatever surely has been done before?
As for the evidence .. I'll leave that up to someone else =P
Re:Even if it's wrong, it's right by Krishnoid · 2016-03-13 15:38 · Score: 1

Besides, give her a break -- after all, math *is* hard.
Re:Even if it's wrong, it's right by GrumpySteen · 2016-03-13 23:58 · 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.
Re:Even if it's wrong, it's right by Mordaximus · 2016-03-14 04:05 · Score: 1

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.
Well actually, from TFA:

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.

the news article misses key word by superwiz · 2016-03-13 14:20 · Score: 1

The linked news article misses the key features of the line segments: "of equal length". The "theorem" as mentioned in the news article is patently false.

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Re:the news article misses key word by superwiz · 2016-03-13 14:33 · Score: 1

Circle is all the points equidistant from a given point. The theorem mentions "more than 2" rather than "all". This allows to prove a number of other basic facts.

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Re:the news article misses key word by ClickOnThis · 2016-03-13 14:37 · Score: 1

The linked news article misses the key features of the line segments: "of equal length". The "theorem" as mentioned in the news article is patently false.
Not only that, the three line-segments must intersect the edge of the circle at three distinct points. That may seem like nitpicking, but precise language is important in mathematics.

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Re:the news article misses key word by superwiz · 2016-03-13 15:34 · Score: 1

Well, if you want to see why it's interesting, consider that it's not true for 2 points. And think about why it's not true for 2 points. Notice that it is not the hypothesis that these line segments are radii, but the conclusion of the theorem. Then suspend your belief that it seems intuitively true and try to actually prove it from the postulated properties of lines and points in a euclidean plane.

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Re:the news article misses key word by ClickOnThis · 2016-03-13 15:49 · Score: 1

If you have two line segments that start and stop in the same place then you only have one line segment, therefore you do not have the three line segments needed.
If you have two numbers a and b, then 1/(a-b) is always defined. Oh, wait ... it is not defined if a=b. You might claim "well then, you only have one number" but that doesn't change the fact that you must exclude the case a=b.

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Re:the news article misses key word by K.+S.+Kyosuke · 2016-03-13 16:26 · Score: 2

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

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Ezekiel 23:20
Re:the news article misses key word by AgNO3 · 2016-03-14 02:38 · Score: 1

HEEEEYYYYY, This is slashdot, you can't patent "false" here. Not only are we anti-patent, Our whole site is previous art on "false."

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Re:the news article misses key word by david_thornley · 2016-03-14 09:23 · Score: 1

Euclid isn't the last word in geometry. Given the definitions, axioms, and postulates as written, it is impossible to prove Proposition I of Book I.

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"When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
Re:the news article misses key word by superwiz · 2016-03-14 11:59 · Score: 1

The center of said circumscribed circle is the intersection of the bisectors of the three sides of the triangle.
"bisectors" are rays which divide angles in two equal angles. Maybe the place of points equidistant from the endpoints of a line segment? That's a perpendicular bisector of the sides.

Three non aligned points define one circle (the circumcircle of the triangle).
This is not axiomatic. It's a theorem. And you can prove that it's logically equivalent to the theorem proved by the student, but that doesn't prove either one of the two theorems. You need a separate proof of one of the two theorems before they both can be considered as having been proved. In fact, proving the theorem that the student proved is easier than proving that 3 points define a circle. So it presents a more elegant proof of the fact that 3 points define a circle.

That's basic geometry.
The basics are usually the hardest to prove in geometry. It is too easy to mix up what's known and what's hypothesized. That's why it makes it such a good training ground in suspending your intuition when seeing what can be logically deduced.

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Re:the news article misses key word by K.+S.+Kyosuke · 2016-03-16 00:16 · Score: 1

There's been attempts at completely formalizing current mathematical knowledge so that computers understand it. So far, this has failed. Mathematics, as executed by humans, still relies on how human brains work with stuff. Including resolving ambiguities. Including such ambiguities as "two line segments". Clearly, to me and to many other people, these are two distinct entities. Quite unlike two named variables bound to the same value, or even two named variables with two different bindings that lead to the same value.

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Ezekiel 23:20
Re:the news article misses key word by superwiz · 2016-03-17 14:04 · Score: 1

the ensemble of all the points that are the same distance from each end point of the segment.
Not the "ensemble". The "place" of all the points which are the same distance from each end point of the line segment. And you have to say perpendicular bisector, because even if "line segment bisector" were a standard term, it would not mean perpendicular. There is infinitely many non-perpendicular lines intersecting a given line segment in the middle.

Her "theorem" also needs to use the fact that three distinct points define at most one triangle.
The fact that three distinct points define a unique triangle follows from the definition of a triangle and the fifth postulate. It does not use her theorem or any circles. So this is pretty clean.

And this is also basic math to prove: a circle is defined by three variables (the coordinates of the center, a and b, and the radius)
This is waaaay unnecessary. You are bringing in a DesCartian geometry into a proof which only requires Euclidean geometry (and precedes it by roughly 2000 years). And if you do think of the center of a circle as its coordinates, then why only 2? Circle can be embedded in a hyperplane with as many dimensions as you want.

You can derive from that that the center of said circle is the intersection of the line segments bisectors (the center has to be the same distance from all the points, hence on the line segments bisectors). If the points are non aligned, the circle exists and thus the three bisectors cross at the same points. And finish again : if a point is the end point of three segments of equal length, it is therefore on the bisectors of the three sides of the triangle made by the three other end points. Therefore it is the the center of the circle passing through the other three points and the length of the segments is the radii.
You are more or less proving that a circle is defined by 3 points by first proving the student's theorem and then using it.

True, but what she proved had probably been proven countless times by countless students as part of math exercises. Maybe her young age makes it noteworthy, but it's definitely not worth an article and it's not a new theorem.
The academic claim (rather than the news-article's claim) is that she provided an original proof for the theorem rather than proved an original theorem.

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Re:Trump Foundation by amiga3D · 2016-03-13 14:42 · Score: 1

Paranoid much? It might indeed be bullshit but I'm not seeing Trump everywhere I look....or Hillary either for that matter. Enough with the political hysteria already.

Common Core is just a set of standards by rs1n · 2016-03-13 14:44 · 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.

Re:Common Core is just a set of standards by war4peace · 2016-03-13 18:04 · Score: 1

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?
I do. Question is whether all (or even most) teachers do, as well.

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Re:Common Core is just a set of standards by TapeCutter · 2016-03-13 22:03 · Score: 1, Funny

Who let the Trump voter in?

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Re:Common Core is just a set of standards by tsqr · 2016-03-14 02:06 · Score: 1

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.
Yes, I do. I also realize that when many implementations of a standard are clearly defective, there may actually be something wrong with the standard.
Re:Common Core is just a set of standards by Raenex · 2016-03-14 03:25 · Score: 1

I actually watched the linked videos. Do you have a refutation beyond wrong-vote accusations?
Re:Common Core is just a set of standards by david_thornley · 2016-03-14 09:19 · Score: 1

How many implementations are there out there? I've only read of one big corp trying to impose its version of the standard. When we have several, and they're all bad, then we'll talk.

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"When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
Re:Common Core is just a set of standards by tsqr · 2016-03-14 11:02 · Score: 1

How many implementations are there out there? I've only read of one big corp trying to impose its version of the standard. When we have several, and they're all bad, then we'll talk.
A quick search turned up this,this, this, this, and this. But wait, those are more or less commercial offerings. It seems that individual states, districts, and schools are rolling their own implementations as well.
Re:Common Core is just a set of standards by david_thornley · 2016-03-15 02:58 · Score: 1

Thank you; I hadn't heard of them. Are all, or most, of these implementations bad? If so, is there something else (like NCLB) going on?

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"When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
Re:Common Core is just a set of standards by tsqr · 2016-03-15 05:05 · Score: 1

Thank you; I hadn't heard of them. Are all, or most, of these implementations bad? If so, is there something else (like NCLB) going on?
I honestly can't say whether they're all bad. I can say I've seen examples of implementations that I personally consider pretty tragic; particularly in math, where methods presented for solving simple algebraic equations fail when coefficients aren't integers, where addition and subtraction are called 'put together' and 'take apart' and where terms like 'zero pairs' (aka, 'additive inverses' - two numbers whose sum is zero) seem to be preferred over traditional concepts like associative, distributive, and commutative properties.
Yeah, I'm an old guy. I caught the leading edge of 'New Math' in elementary school, and I was frequently marked down for finding answers through knowing multiplication tables instead of using tortured estimation/iteration techniques. I guess that makes me a bit biased.

Re:"Didn't actually exist" = "No dedicated name" by Aighearach · 2016-03-13 14:46 · 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...

Feelgood story about how "smart" israeli kids are by Anonymous Coward · 2016-03-13 14:46 · Score: 1

Feelgood story about how smart israeli kids are, same as egyptian stories bubbling up from time to time...

This is what she "invented".
http://www.mathopenref.com/const3pointcircle.html

Non-invention by Sigma+7 · 2016-03-13 14:53 · 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.

WTF?!? This is the very definition of circle! by Anonymous Coward · 2016-03-13 15:06 · Score: 1

How is this novel, or a theorem or anything for that matter? What is the definition of a circle - a line, all points on which lay an equal distance from a single point, being the circle's center. All lines connecting the center are of same length, and are radius(es) of that same circle. This is a definition, not a theorem. 3 lines with a common ending, define 3 points in space. Every circle can be defined either by a center coordinates and radius, or by coordinates of 3 points, laying on the ark line. This is a simple coordinate system transformation, very obvious if you start using vectors.

Re:WTF?!? This is the very definition of circle! by I4ko · 2016-03-13 18:21 · Score: 1

Agreed
Re:WTF?!? This is the very definition of circle! by bluefoxlucid · 2016-03-14 03:37 · Score: 1

For all points on a line to be equidistant from the center of a circle, an infinite number of line segments of equal length must extend from the circle's center to the circle's edge. If the circle *is* a circle, then any three line segments of equal length extending from one point to three distinct points on the circle's edge are extended from the circle's center.

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Geometric construction makes this obvious, IMO by mark-t · 2016-03-13 15:23 · Score: 1

It's precisely why three points unambiguously define a unique circle that passes through each of them. Obviously the center of the circle must be equidistant form all of them.

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I "discovered" all sorts of theorems by RightwingNutjob · 2016-03-13 15:27 · Score: 1

when I was in the 9th grade. Part of learning math. Good for Tamar that she's likes math enough to play with it, but must've been a slow news day in Israel.

Theorem wrong as stated by Roger+W+Moore · 2016-03-13 15:35 · 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.

Re:Theorem wrong as stated by fph+il+quozientatore · 2016-03-13 19:08 · Score: 2

Segment. The word you are looking for is segment.

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Re:Theorem wrong as stated by reboot246 · 2016-03-14 07:13 · Score: 1

You're right. The lines have to be equal. Otherwise, next time I need to find the center of a circle all I'd have to do is pick any point within the circle.

Draw a circle. Pick a point anywhere within the circle. Now draw three lines from that point to the edge of the circle. According to how it's stated in the article, you've chosen the exact center of the circle. Fat chance of that! In reality, though, your chances of finding the center that way are too low to even talk about.

Way to disuade potential talent. by EzInKy · 2016-03-13 16:28 · 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.

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Time is what keeps everything from happening all at once.

Misleading. Described only c. 2316 years ago by Anonymous Coward · 2016-03-13 16:58 · Score: 1

This algorithm was described by Euclid (the Greek) in his book "Euclids Elements" about 2300 years ago. She used it to do homework, was asked to make a proof by her teacher, which she did (with help). And why everyone is getting excited is somehow odd, especially the one from MIT who should know better (and should know the algorithm already or at least know of it. It makes for good internet theater though.

Re:Congratulations Tamar by Dog-Cow · 2016-03-13 18:07 · Score: 1

Tamar doesn't live in Turkey. What are you going on about?

Re:Fun Common Core problem! by ls671 · 2016-03-13 18:09 · Score: 1

It looks like about 2 square inches...

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Proof by fph+il+quozientatore · 2016-03-13 19:15 · 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...).

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My first program:

Hell Segmentation fault

Re:Fun Common Core problem! by Sarten-X · 2016-03-13 19:27 · Score: 1

70 square units.

The interesting part of that diagram is that the length of the nonparallel sides is inconsistent with the other measurements given. In practice, that means that students who don't understand how to properly calculate the area of the figure (using reasonable methods for that grade level) will have a noticeably different answer than those who do understand it.

Sure, it's an inaccurate diagram, and could be considered lazy teaching, but it's utterly unrelated to Common Core.

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You do not have a moral or legal right to do absolutely anything you want.

Incorrect report, now gets copied to Slashdot :-( by urdak · 2016-03-13 20:45 · 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 :-)

Re:Fun Common Core problem! by TapeCutter · 2016-03-13 21:44 · Score: 2

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

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

Re:"Didn't actually exist" = "No dedicated name" by heretical_thoughts · 2016-03-13 21:49 · 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.

Re:"Didn't actually exist" = "No dedicated name" by TapeCutter · 2016-03-13 21:54 · 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.

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

Re:"Didn't actually exist" = "No dedicated name" by Anonymous Coward · 2016-03-14 00:45 · Score: 1

No you see, she's a Jew so we're obligated to fawn over every little trivial discovery. Kind of like when a baby takes its first steps.

Meanwhile, a few miles away at a Palestinian school, teachers instruct their students on the best way to kill Jews.

Re:I did the same thing in 1982... apk by tehcyder · 2016-03-14 01:06 · Score: 1

Blimey, APK is a Scouser.

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To have a right to do a thing is not at all the same as to be right in doing it

Be careful... by denzacar · 2016-03-14 01:11 · Score: 2

...where you Putin that reference.

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Mit der Dummheit kämpfen Götter selbst vergebens

IMHO, the theorem is gilbish by e70838 · 2016-03-14 01:42 · Score: 1

"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". Could someone reformulate this in english to give it some meaning ?

Re:Again, you're being duplicitous by bidule · 2016-03-14 02:56 · Score: 1

By implementation, do you means you are unable to follow a general plan, or do you mean you're unwilling to teach evolution and other religous controversies?

More facts, less fantasies.

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ID: the nose did not occur naturally, how would we wear glasses otherwise? (apologies to Voltaire)

Re:Fun Common Core problem! by stealth_finger · 2016-03-14 03:40 · Score: 1

See, now I would do 12x12 + 5x4 but that's probably wrong.

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Re:"Didn't actually exist" = "No dedicated name" by stealth_finger · 2016-03-14 03:41 · Score: 1

Wtf, why do you bring up this persons Jewish background that way? And how do you know they are not Muslim. So shut the fuck up you fucking piece of worthless anti-Semite shit. What the fuck does religious background have to do with anything here, apart from showing the fugly face of dirt bag filth-filled bellybutton scum like you. Go fuck yourself you fucking gutter rat.

Wow, someone touched a nerve.

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Re:Barbi is a scientist by stealth_finger · 2016-03-14 03:52 · 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

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Re:"Didn't actually exist" = "No dedicated name" by heretical_thoughts · 2016-03-14 03:53 · 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.

Theorem please? by GuB-42 · 2016-03-14 04:02 · Score: 1

Can anyone give the actual theorem as formulated by Tamar?
Because what she found sounds obvious, the proof is well within reach of a relatively gifted 10th-grader helped by a teacher and isn't new. In itself, nothing impressive.
The interesting part would be if she found some particularly clever way of solving the problem of if her proof shows some particularly deep understanding of maths.

Re:Aggregation by stealth_finger · 2016-03-14 04:05 · Score: 1

What about the appy app appers? Where'd that guy go?

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Re:I did the same thing in 1982... apk by 110010001000 · 2016-03-14 04:16 · Score: 1

You mean you did it the long and complex way and "didn't even listen" to anyone else? I find that hard to believe apk!

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Israeli 10th-Grader Discovers Elegant Geometry Theorem

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