What is the maximum triangle?

In summary: If it's the length of the sides, it might be possible to go from P to any point on R and define a triangle. In summary, the conversation discusses the concept of a maximum triangle with parallel sides in Lobachevshy-Bolyai geometry or hyperbolic geometry. This is based on the axiom that for any given line and point not on the line, there are at least two distinct lines through the point that do not intersect the line. The definition of "maximal" in this context depends on the measure used, such as the length of the sides.
  • #1
Quantum Velocity
73
6
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
 
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i want to ask question but where should i enter
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  • #3
well go on tho the category you want to ask and click the

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  • #4
Quantum Velocity said:
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?
 
  • #5
it's some type of geometry that i don't remember the name
 
  • #6
it's called Lobachevshy-Bolyai geometry
 
  • #7
or sometime called Hyperbolic geometry
 
  • #8
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.
 

What is the maximum triangle?

The maximum triangle is a triangle with the largest possible area, given a certain set of parameters such as side lengths or angles.

How do you find the maximum triangle?

To find the maximum triangle, you can use various methods such as the Heron's formula, trigonometric equations, or optimization techniques.

What are the properties of a maximum triangle?

A maximum triangle has all three angles measuring less than 180 degrees, and its sides are all unequal lengths. It also has the largest possible area within a given set of parameters.

What real-life applications use the concept of maximum triangle?

The concept of maximum triangle is used in various fields such as engineering, architecture, and physics. For example, it can be applied in designing structures with maximum stability and strength.

Can there be more than one maximum triangle for a given set of parameters?

Yes, there can be more than one maximum triangle for a given set of parameters. This is because the maximum area is not always unique and can be achieved by different combinations of side lengths and angles.

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