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Internal angles of a triangle

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638941.  Sat Nov 21, 2009 7:56 am Reply with quote

ColinM wrote:
Lets have a go at explaining some of it then............
Now consider a triangle on the Earth. It has one point at the north pole, and the other two on the equator. Two of its lines are lines of latitude and the other is the equator, so they're all legitimate lines. What are the angles at each corner? Well, every line of latitude meets the equator at a right angle, or 90 degrees. We have two of those, so that's 180 degrees, or π radians. But our last angle can be whatever we like - we can pick anything from almost nothing to nearly a full circle, and still make a triangle. The sum of the angles will thus be more than π (or 180 degrees), contradicting our theorem in plane geometry.

Does that help anyone at all?

Yes, that was helpful, except that I think you meant "longitude" where you typed "latitude"

Just to complete your nice explanation, here's a picture from Wiki.

769744.  Sat Dec 25, 2010 5:04 pm Reply with quote

To clarify a bit:

In plane geometry, a triangle is a figure consisting of three line segments joined at their ends. The angles formed by the three intersections add up to 180 degrees.

A spherical triangle is a figure on the surface of a sphere, consisting of three segments of great circles of that sphere joined at their ends. The angles formed by the three intersections add up to an angle between 180 degrees (representing an infinitesimal triangle) and 540 degrees (representing a great circle that coincides with the other three).

A great circle, by the way, is a circle on the surface of a sphere whose center coincides with the center of the sphere -- called a great circle because it is the largest circle that can be drawn on that sphere.


769833.  Sun Dec 26, 2010 7:59 am Reply with quote

Spamperial wrote:
I also feel rather disappointed that even in my own thought experiment, I can't see Australia without having to go there myself.
Don't lose heart - with a number of extra-planetary objects you could slowly bend light back to earth without needing any event horizons!

But you'd have to accept a very very poor image quality.

You could also opt for "seeing" it in radio frequency - and hope for very unusual ionospheric conditions. Perhaps listen to Radio Brisbane... and join the Summer FUNomenon at Dreamworld...

The QI options are endless...


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