MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
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Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#2Hm, a clever little theorem. I'm surprised it isn't recorded somewhere. Perhaps it's just under a different name because of it's relative... simplicity? Not to belittle her accomplishment. This is something you'd expect Euclid to write about or something.
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#3From 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?
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#4Hm, a clever little theorem. I'm surprised it isn't recorded somewhere. Perhaps it's just under a different name because of it's relative... simplicity? Not to belittle her accomplishment. This is something you'd expect Euclid to write about or something.
> This is something you'd expect Euclid to write about
Which is what makes the lack its history so fascinating.
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#5From 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?
The article is missing something -- a mathematically accurate description. Not you.
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#6From 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?
I have no idea what this means, but can't imagine how it could be significant as a theorem, assuming the correct statement is reasonably similar.
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#7From 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?
The theorem as stated in the article is definitely wrong. Equal length would make it correct, I think.
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#8From 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?
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#9Hm, a clever little theorem. I'm surprised it isn't recorded somewhere. Perhaps it's just under a different name because of it's relative... simplicity? Not to belittle her accomplishment. This is something you'd expect Euclid to write about or something.
Well remember Euclid's geometry is fundamentally flawed. The parallel postulate, that fact that parallel lines never meet, can be be used to really mess with a grade 7-12 math teacher's head if you invest the time to teach a couple of tricks to your kid.
The simplest example is to show that an obtuse angle and a right angle are the same through a construction. The placement of points is crucial to make that work.
Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem
#10From 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?
The theorem as stated in the article is definitely wrong. Equal length would make it correct, I think.
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