Can Triangulation Describe Distance in Spherical or Euclidean Geometry?

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The discussion centers on the application of triangulation to describe distances in both spherical and Euclidean geometry. Participants debate the formulation of distance using triangulation, emphasizing that the method of triangulation significantly influences the results. A specific formula is mentioned, where the diameter of a circle divided by the square root of 2 provides the hypotenuse length of a right triangle, which can then be adjusted with a conversion factor. The conversation also highlights the complexities of defining spherical geometry, particularly the challenges in visualizing spherical circles and right triangles. Ultimately, the triangulation formula is presented as a solution to the distance problem in Euclidean geometry.
Jug
What is the formula in either spherical or Euclidean geometry for describing distance on the quadrant by triangulation?? Can it be done?
 
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a general formula?
IMO it is dependant on the way in which you make the triangulation of the surface...
 
Originally posted by Guybrush Threepwood
a general formula?
IMO it is dependant on the way in which you make the triangulation of the surface...

Let's say a simple Euclidean circle where any distance on the diameter defines base of the right angle triangle.
 
please could you rewrite the question so it makes more sense (to me): what quadrant, which triangulation, spherical geometry does not a have right angled triangle inscribed inside cicles ( a spherical circle is a weird thing to draw btw). In fact what do you mean by tringulation and what do you think it has to do with length?

Distances on ordinary, spherical and hyperbolic geometry are well defined, is that not what you want?
 
Originally posted by matt grime
please could you rewrite the question so it makes more sense (to me): what quadrant, which triangulation, spherical geometry does not a have right angled triangle inscribed inside cicles ( a spherical circle is a weird thing to draw btw). In fact what do you mean by tringulation and what do you think it has to do with length?

Distances on ordinary, spherical and hyperbolic geometry are well defined, is that not what you want?

Matt, answered my own question (Euclidean):

A trianglature formula states that diameter of circle divided by root 2 gives length to the hypotenuse of a right angle triangle, the hypotenuse defining distance on the quadrant when multiplied by a conversiom factor of pi/4 (root 2). Thanks for the input...
 
Originally posted by Jug
A trianglature formula states that diameter of circle divided by root 2 gives length to the hypotenuse of a right angle triangle, the hypotenuse defining distance on the quadrant when multiplied by a conversiom factor of pi/4 (root 2). Thanks for the input... [/B]

WHAT?
this is what is usually understood by triangulation...
 
GT,

I have no argument with the system of triangulation. Merely saying that the trianglature formula solves the given problem.
 

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