4 ms·

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 ge

by hasenj 11y ago

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 definition.

dkopi 11y ago
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.
- Houshalter 11y ago
  I actually used this idea once. I had three known points which were approximately equidistant from an unknown center. I wanted to find the center. So I used a hillclimbing algorithm to search for the center by guessing points and seeing how close they were. The fitness function was the difference between the proposed center and the three points. The idea being to minimize the distance between their. If the lines were exactly the same length, I would have found the center. It didn't work at all though. It gave wildly incorrect answers, and sometimes even converged on infinity... Even when running it many many times to avoid local optima.
  - jschulenklopper 11y ago
    > I had three known points which were approximately equidistant from an unknown center. I wanted to find the center. See this: http://www.mathopenref.com/const3pointcircle.html http://www.mathopenref.com/const3pointcircle.html
    - Houshalter 11y ago
      That looks like it would be quite difficult to program.
      - im3w1l 11y ago
        https://en.wikipedia.org/wiki/Circumscribed_circle#Circumcenter_coordinates https://en.wikipedia.org/wiki/Circumscribed_circle#Circumcen...
- Jugurtha 11y ago
  >A circle is defined as all the points in the same distance from a certain center point. I think they also need to be on the same plane, otherwise it's a hollow sphere. Also, by that definition, there's an infinity of centers. There can be a line that passes through the center and perpendicular to the plane on which the circle lies. Every point of that line is equally distant from the points of the circle. And for an infinity of planes parallel to our plane of interest, the intersection of the line and that plane gives the center of the projection of our first circle onto that new plane.
  - dkopi 11y ago
    Of course were limiting this to a 2d plane.
    - Jugurtha 11y ago
      I believe a plane is two-dimensional by definition. But I get where you're going. Isn't geometry fun!
IkmoIkmo 11y ago
> This sounds like what pops up every other day in Egyptian newspapers about genius Egyptian kids who invent this or that. Haha, finally I come across someone saying this on the internet. But you're right it's exactly like that.

by hasenj 11y ago

dkopi 11y ago

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.

Houshalter 11y ago
I actually used this idea once. I had three known points which were approximately equidistant from an unknown center. I wanted to find the center. So I used a hillclimbing algorithm to search for the center by guessing points and seeing how close they were. The fitness function was the difference between the proposed center and the three points. The idea being to minimize the distance between their. If the lines were exactly the same length, I would have found the center. It didn't work at all though. It gave wildly incorrect answers, and sometimes even converged on infinity... Even when running it many many times to avoid local optima.
- jschulenklopper 11y ago
  > I had three known points which were approximately equidistant from an unknown center. I wanted to find the center. See this: http://www.mathopenref.com/const3pointcircle.html http://www.mathopenref.com/const3pointcircle.html
  - Houshalter 11y ago
    That looks like it would be quite difficult to program.
    - im3w1l 11y ago
      https://en.wikipedia.org/wiki/Circumscribed_circle#Circumcenter_coordinates https://en.wikipedia.org/wiki/Circumscribed_circle#Circumcen...
Jugurtha 11y ago
>A circle is defined as all the points in the same distance from a certain center point. I think they also need to be on the same plane, otherwise it's a hollow sphere. Also, by that definition, there's an infinity of centers. There can be a line that passes through the center and perpendicular to the plane on which the circle lies. Every point of that line is equally distant from the points of the circle. And for an infinity of planes parallel to our plane of interest, the intersection of the line and that plane gives the center of the projection of our first circle onto that new plane.
- dkopi 11y ago
  Of course were limiting this to a 2d plane.
  - Jugurtha 11y ago
    I believe a plane is two-dimensional by definition. But I get where you're going. Isn't geometry fun!

IkmoIkmo 11y ago

> This sounds like what pops up every other day in Egyptian newspapers about genius Egyptian kids who invent this or that. Haha, finally I come across someone saying this on the internet. But you're right it's exactly like that.