MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem • Hacker News Board

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

#61

Post by lpmay » Sun, Mar 13, 2016, 2:14 PM UTC

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?

I think it's important that they are talking about lines not line-segments. By definition, lines extend to infinity in both directions. But I agree, the wording is still confusing. I would have worded it more like "if three lines pass through the same point and the edge of a circle, then the point is the center of the circle and the lines lie along the radii of the circle."

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

#62

Post by qwerty823 » Mon, Mar 14, 2016, 3:14 AM UTC

db48x wrote: post #40

It's already fairly well established that any three points define a circle. Similarly, most circles have a center, and will therefore have radii which join those points to the center.

Actually, they can't be co-linear as well.

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

#63

Post by dogmatix » Mon, Mar 14, 2016, 4:22 AM UTC

hydroo wrote: post #7

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?

The theorem as stated in the article is definitely wrong. Equal length would make it correct, I think.

As well as hitting the edge of the circle at right angles.

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

#64

Post by vonfraginoff » Mon, Mar 14, 2016, 6:03 AM UTC

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?

Different Trump.

http://www.crainsnewyork.com/article/20150806/BLOGS02/150809...

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

#65

Post by fche » Mon, Mar 14, 2016, 5:04 PM UTC

randlet wrote: post #49

adt2bt wrote: post #25

Earlier quoted context omitted.

How common is that?

Pretty common (in North America anyways) I think. In speaking with teacher friends my impression is that math education has become quite formulaic with a large focus on learning algorithms to solve problems that occur in standardised tests.

(that's not the same as scolding being common)

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

#66

Post by j238 » Tue, Mar 15, 2016, 3:11 AM UTC

Seems like something most people who do geometry know intuitively without having to say out loud. I'm guessing she said something, the teacher questioned it. Then when the teacher realized she was right, she went overboard and made the case that a statement of the obvious constituted a "new theorem."

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

#67

Post by canucount » Tue, Mar 15, 2016, 2:56 PM UTC

aharonovich wrote: post #59

Luc wrote: post #35

I never know what these 'grade' designations mean. Anyway, it appears to refer to 15 to 16-year-olds. https://en.wikipedia.org/wiki/Tenth_grade

In Israel, first grade is for 6 year olds, getting out of kindergarten and into elementry school, so if you want grade to age conversion just add 6, ie 10th grade = 16 yo

So first grade is 1 + 6 = 7 by your algorithm?

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

#68

Post by natalys » Wed, Mar 16, 2016, 2:00 PM UTC

Badly translated into english. I read the Hebrew. Should say something like. "If 3 or more equal lines extend from a single point to the edge of an arc, then the arc is part of a circle, the point being the center and the lines the radii"