Wednesday, August 5, 2009

[Insert Title Here] - Trirectangular

A Trirectangular
So the first actual article is going to be on one of my most favorite little pieces of geometry. Now everyone's been taught that a triangle can only be composed of 180 degrees within its three angles, now what if I told you it can have 270? For those who did the math a triangle would need to have three right angles of 90 degrees each in order to accomplish this feat, the same angles found on a square or a rectangle. That would mean that each line would be perpendicular to its connecting line and thus a shape like |_| would ensue, basically an open box (and not a triangle). However the trirectangular (the triangle with 270 degrees is still possible). How you might ask?

The key to the trirectangular is that it isn't confined to the 2 dimensional plane of a sheet of paper, but rather is placed into all three dimensions we see, height, width, and depth. If you place a triangle on a sphere, such as a globe, it is possible to have three straight lines that form three right angles. If you want to experiment yourself take an old globe and draw a line down from the North pole to the equator, then draw another line from the North pole (in respect to a right angle from the first line) and draw it down to the equator. Connect the lines by drawing the final segment along the equator and presto you have three right angles and a trirectangular.

Now there are sure to be the few of you who are skeptical on whether or not this is actually a triangle and I shall prove to you it is through definitions. We'll start off with the definition of triangle from the Merriam-Webster dictionary:
"A polygon having three sides"
The definition for polygon has two definitions that we care about they are:
"A closed plane figure bounded by straight lines" and
"A closed figure on a sphere bounded by arcs of great circles"
So thus as long as it's connected on these arcs it's still legit.

Well that's my first article and I hope you enjoyed it and learned something in the process if you would like to know where I discovered this it was in the book entitled Visual Vexations, authored by David J. Bodycombe. Oh, and you should know that the image was found off of Wikipedia.

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