The Joy of Rediscovery

Even if you are not the first to find something, the thrill of finding it independently is still every bit as real.

So, this morning, as I often do, I’m playing with triangles.  I constructed a triangle’s incircle, using its three angle bisectors. I also constructed the perpendicular bisector of each side, in order to construct the circumcircle.

What I didn’t expect was to find each angle bisector intersecting a perpendicular bisector on the circumcircle. The three such points of intersection (N, O, P) are the  vertices of the yellow triangle below, while the original triangle, ABC, is in bold black.

Image

“Hey, that’s pretty cool,” I thought, using Geometer’s Sketchpad to move A B, and C around, to test what I was seeing. This was certainly no proof, but now I was wondering if it was an original discovery. Google, however, revealed to me that this discovery had already been made:

http://demonstrations.wolfram.com/TheIntersectionOfAnAngleBisectorAndAPerpendicularBisector/

Well, I could be upset that someone else beat me to this discovery, I suppose, but I think I’d rather take comfort in knowing someone else has already written the proof, for I really don’t feel up to that.

At least not today.

And there is joy in rediscovery. As much as in discovery? Well, no, of course not, but life can be such that no joy should be overlooked. When you know something, and no one taught it to you, but you found it out yourself, does that not make you happy? It certainly works for me.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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