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MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

israelhayom.com

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Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#31

Post by jschulenklopper »

hasenj wrote: post #27
jschulenklopper wrote: post #21

Earlier quoted context omitted.

> Equal length would make it correct, I think. And the three lines of equal length should go to different points on the edge of the circle as well. Three lines from a point to the same position on the edge wouldn't work - but perhaps I'm mathematically paranoid now :-)

Well they wouldn't really be three lines if they all go from the same point to the same other point. They would all be the same line. Unless the language of math does allow "references" like programming languages. All you need is to require three different lines of equal length. But I don't see the significance of calling this a theorem. It seems perfectly obvious and elementary and almost just the definition of a ci…

> Well they wouldn't really be three lines if they all go from the same point to the same other point. They would all be the same line.

> Unless the language of math does allow "references" like programming languages.

Ha, that indicates that I'm clearly thinking more as a programmer than as a mathematician :-) Thanks.

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#32

Post by rory096 »

nthcolumn wrote: post #8
jschulenklopper wrote: post #3

From the article: > 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. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

And wouldn't two of equal length do? I think we are missing an explanation of the theorem. edit: oh hang on, I see now: Trump Foundation It's one of those theorems. edit: yes three mean they can't be longer than the radius. Isn't it interesting. You need 3 for a circle. What about other shapes?

>oh hang on, I see now: Trump Foundation

No relation.

http://www.ynetnews.com/articles/0,7340,L-4774818,00.html

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#34

Post by sound_of_basker »

mankash666 wrote: post #26

Seems like the kind of problem solved routinely in city level Olympiads world wide. I believe the kid is certainly bright, but by this article's standard, most Olympiad problem sets, even at the city level, become new theorems. So, keep the enthusiasm going kid, but try your luck at the Olympiads to truly benchmark your standing.

Seriously. I recall proving that there is one and only one circle that can be drawn through 3 distinct points on a Euclidean plane. This "theorem" can be thought of as a corollary of that.

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#37

Post by commenter23 »

It's a fluff piece.

The real story here is that a 10th grader, after using a Theorem that wasn't taught in class, was encouraged to prove it - which she did, successfully. The teacher then sent it to a few academics who were thought that was a rather impressive accomplishment for a 10th grader, so they wrote her some encouraging words. That's it.

The theorem and its proof are in Euclid's Elements, (Book 3 Proposition 9: http://aleph0.clarku.edu/~djoyce/elements/bookIII/propIII9.h...)

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#38

Post by Hydraulix989 »

hasenj wrote: post #27
jschulenklopper wrote: post #21

Earlier quoted context omitted.

> Equal length would make it correct, I think. And the three lines of equal length should go to different points on the edge of the circle as well. Three lines from a point to the same position on the edge wouldn't work - but perhaps I'm mathematically paranoid now :-)

Well they wouldn't really be three lines if they all go from the same point to the same other point. They would all be the same line. Unless the language of math does allow "references" like programming languages. All you need is to require three different lines of equal length. But I don't see the significance of calling this a theorem. It seems perfectly obvious and elementary and almost just the definition of a ci…

The definition of a circle is literally the set of all points whose distance from a point P is r, so yeah, I'm in agreement.

EDIT: in a plane

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#39

Post by dkopi »

hasenj wrote: post #29

Until someone brings a link from MIT's website, I'm calling bullshit on this one. This sounds like what pops up every other day in Egyptian newspapers about genius Egyptian kids who invent this or that. The theorem stated in the article is not a theorem at all. It's a direct consequence of the definition of a circle and is perfectly obvious to anyone who spends two minutes pondering the implications of that definitio…

A circle is defined as all the points in the same distance from a certain center point.

But a point thats distanced from the circle circumference by R isn't necessarily the circles center.

But if you can draw 3 (and hence more) lines from a point to the circles circumference that are all the same lenght, that is the circles center, and the distance is the radius.

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