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Why can I draw a triangle with two 90 degree angles and one 0 degree angle?
Posted:
Oct 14, 2009 1:08 PM
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So this is a little thought experiment I came up with after hearing that 0.99999999.... exactly equals 1. I have searched around the internets with no luck at finding this proof or theorem.
Basically I was thinking about triangles, and limits, and realized this:
If I have a Right triangle (one 90 degree angle) with short side y and leg x with hypotenuse z and other angles Q and W, If I take the limit as x approaches infinity, Q approaches 90, effectively giving this triangle two 90 degree angles and one zero degree angle.
Here's an image I drew: http://imgur.com/OU7Pc.png
So I was basically wondering what kind of mathematical laws/proofs this violates, if any, aside from the logical impossibility of having a triangle with such properties as two parallel legs, two 90 degree angles, as well as the hypotenuse seemingly being colinear with the infinite leg (x).
What I want to know is if its useful to try and describe a figure like this, or if it forms some sort of logical impossibility. When I try to imagine this figure, there is a disparity between the start and end of the triangle, which is most certainly attributed to the properties of infinity and its "unquantifiable aspect."
I feel there should be a way to evaluate this triangle from either end, IE you can think about it from the left with 2 parallel lines, or Start from the right, with a 0 degree angle and with the hypotenuse colinear to leg x.
Heres a picture of my mental disparity http://imgur.com/tFGSK.png
I know its usually fruitless to try and imagine infinity, but please indulge me on how to reconcile the seemingly two different situations at either end of the figure. I realize the solution may be that its only visualiz-able or makes any sense in certain conditions (such as in a Riemann Sphere) but this impossible figure has plagued my rationality ever since I conceived of it.
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