Fun fact! In the real world, if you take a triangle and add up the angles, they can equal more than \(180^{\circ}\)!

In school we always learn that the angles of a triangle always add up to \(180^{\circ}\), but that is not always the case, especially when you look at our planet! Don’t believe me? Let’s prove it!

Proof:

First let’s define what a triangle is. A triangle is 3 ‘straight’ lines that intersect at 3 points. By straight we mean a line that doesn’t curve to the right or to the left. We also notice that since we are using Earth as our reference point, we are doing all calculations on a sphere.

Ok, so let’s start! Pretend you are standing somewhere on the equator on Earth. Also, pretend you have outrageously long legs that allow you to travel really really far really quickly. Now walk north until you hit the North Pole. That’s 1 straight line, 2 more to go. So make a \(90^{\circ}\) turn right and walk south all the way back down to the equator. That’s 2 lines, 1 more to go. Now in order to walk to our starting point we need to make a right turn. In fact we need to make a \(90^{\circ}\) turn. (Cause we are heading directly south and now need to go directly west) Once we get to our starting point we notice that this final angle also equals \(90^{\circ}\). (Since we are looking west, but must turn north in order to ‘retrace’ the triangle) And that’s 3 straight lines. Adding up the angles we get: \(90^{\circ} + 90^{\circ} + 90^{\circ} = 270^{\circ}\)

Oh yeah! Take that geometry. I just kicked your butt!!! This type of geometry is called Spherical Geometry and a lot of mathematicians study it in order to better understand the universe.

And thats all from me until after the holidays. Armenian Christmas isn’t until January 6 so Ill be gone for the next 2-3 weeks and will return with some more math funness afterward. *lates*