Favourite Geometry Theorem. (1 Viewer)

[HappyFeet]

What is your favourite Theorem in Geometry (Synethetic, Projective, Analytical, etc.)

My favourite (at the moment anyway) is:

Desargues Theorem.

 

[watatank]

wtf is that?

 

[jemsta]

http://en.wikipedia.org/wiki/Desargues_Theorem

 

[LoneShadow]

The simplest and the best: Pythagoras Theorem

 

[vulgarfraction]

Sif you'd ever use Desargues. Even if there was a situation where you could you'd never be able to pick it out.

Current favourite is power of a point/radical axis, just because it's so useful.

 

[Captain Gh3y]

Napoleon's Theorem

 

[sen00]

Personally, I think Desargue's is quite cool and i have only ever used it once, so its pretty rare. here is the problem.

ABC is a non-isosceles triangle with incenter I. The smaller circle through I tangent to CA and CB meets the smaller circle through I tangent to BC and BA at A' (and I). B' and C' are defined similarly. Show that the circumcenters of AIA', BIB' and CIC' are collinear.

 

[HappyFeet]

Oh well, Projective Geometry is not so popular among Australians (I mean it's not like Euclidean Plane or Solid Geometry).

 

[HappyFeet]

Napoleon's Theorem

Ah yes, very nice. Can easily be proved using Complex Numbers (try it).