Three Points Defining a Circle

Learn more: http://www.khanacademy.org/video?v=4_...
Showing that three points uniquely define a circle and that the center of a circle is the circumcenter for any triangle that the circle is circumscribed about

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  Education

[Domino3D]

excuse me sir, can you explain how can we calculate triangle's circumcenter in Cartesian coordinates in THREE dimensions? In 2D its quite simple (like described on wiki) but cant figure out equations for 3D. Can you help?

I am working on 3D delaunay triangulation.

[Teh Randy]

Yeah, I realized minutes after I posted this that two points would be enough to define a circle if and only one of those points are assumed to be the center.

[Ricardo Russo]

No. Try drawing it out yourself for more intuition than my words can explain.

[Teh Randy]

Don't you necessarily just need two points? Considering that the radius is exactly equidistant at any given point of the circle...

[Alexander Roderick]

The earliest records we have of this kind of geometry is from the Greeks a few thousand years later, but the Egyptians did know some math. The angle of the sides of the pyramids is a result of them using square blocks, it's one unit up for every two units over.

[radbcc]

wow, that is cool; wonder if any of this was used in constructing pyramids?