How Does the Hyperbolic Axiom Define a Maximal Triangle?

[Quantum Velocity]

I know that if a triangle have it edge // to each orther then it í the maximum triangle.

Pls explain i don't understand hơ thí even possible

 

[Ricky Lalduhzuala]

i want to ask question but where should i enter
??

 

[Quantum Velocity]

well go on tho the category you want to ask and click the

Post New Thread

<Moderator's note: Link removed, for it otherwise would have led to General Physics only.>

 

[fresh_42]

I know that if a triangle have it edge // to each orther then it í the maximum triangle.

Pls explain i don't understand hơ thí even possible

With parallel sides, it isn't a triangle anymore. Except you're not using Euclidean geometry. So a) where are the triangles defined on, and b) what does "maximal" mean: circumference, area, one angle, a side?

 

[Quantum Velocity]

it's some type of geometry that i don't remember the name

 

[Quantum Velocity]

it's called Lobachevshy-Bolyai geometry

 

[Quantum Velocity]

or sometime called Hyperbolic geometry

 

[fresh_42]

You simply apply the hyperbolic axiom:

For any given line R and point P not on R, in the plane containing both line R and point P
there are at least two distinct lines through P that do not intersect R.

This is a given fact. So with two points on R, and a point P, not on R, we have three different points which define a triangle. And the two lines through P with the line R are parallel and the sides of the triangle. (Not quite sure about the sides.)

What maximal means, still depends on your measure.