When do the angles of a triangle add up to more than 180 degrees?

[scooterscot]

5th October 2013 12:34 eek

Thread: When do the angles of a...
uppet

Was Bernhard Riemann one too?

[MarillionFan]

Do you kiss Eek with that mouth?

[mudskipper]

Isn't a triangle a two-dimensional shape? Therefore a triangular figure drawn on a sphere isn't, mathematically, a triangle...

[bless 'em all]

Isn't a triangle a two-dimensional shape? Therefore a triangular figure drawn on a sphere isn't, mathematically, a triangle...

It's a non planar triangle, but still a triangle.

[mudskipper]

It's a non planar triangle, but still a triangle.

[doodab]

Isn't a triangle a two-dimensional shape? Therefore a triangular figure drawn on a sphere isn't, mathematically, a triangle...

The surface of a sphere has two dimensions. The geometry is non euclidean.

[NotAllThere]

What kind of surface yields triangles whose angles add up to less than 180°?
What kind of surface yields triangles whose angles add up to more than 270°?

What is the ratio of the circumference of a circle to its diameter when drawn on a sphere?

[scooterscot]

What kind of surface yields triangles whose angles add up to less than 180°?

A surface that only exists in two dimensions

What kind of surface yields triangles whose angles add up to more than 270°?

A surface that that exists in three dimensions, like that on the surface of a sphere.

What is the ratio of the circumference of a circle to its diameter when drawn on a sphere?

a perfect sphere, and by that I mean an object with the most symmetries; pi

[NotAllThere]

What kind of surface yields triangles whose angles add up to less than 180°?

A surface that only exists in two dimensions

No. Any negative curved surface, such as a hyperbolic surface. The surface is always with 3D.

What kind of surface yields triangles whose angles add up to more than 270°?

A surface that that exists in three dimensions, like that on the surface of a sphere.

No. Here you need some surface that's wrapped around itself. (Should have said 360° though).

What is the ratio of the circumference of a circle to its diameter when drawn on a sphere?

a perfect sphere, and by that I mean an object with the most symmetries; pi

Bit of a trick question. It varies according to where you draw the circle. If you do it in the right place, you can have pi = exactly 3.

[Old Greg]

It's nice to see you all polishing your chat up lines on a Saturday evening.