Can Triangulation Describe Distance in Spherical or Euclidean Geometry?

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Discussion Overview

The discussion centers on the applicability of triangulation for describing distances in both spherical and Euclidean geometry. Participants explore the conditions and definitions surrounding triangulation and its relationship to distance measurement on different geometric surfaces.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the clarity of the original question, suggesting that the specifics of the quadrant and triangulation method are crucial for understanding the problem.
  • Another participant proposes that in Euclidean geometry, the diameter of a circle divided by the square root of 2 gives the length of the hypotenuse of a right triangle, which can then be used to define distance on the quadrant with a conversion factor.
  • There is a challenge regarding the concept of triangulation in spherical geometry, with a participant noting that right-angled triangles cannot be inscribed in spherical circles.
  • Some participants express confusion over the terminology used, particularly the term "trianglature," and its implications for distance measurement.
  • One participant asserts that distances in ordinary, spherical, and hyperbolic geometries are well-defined, questioning whether this is the intended focus of the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions and applicability of triangulation in different geometries. There are competing views on what constitutes a valid triangulation method and its implications for measuring distance.

Contextual Notes

There are limitations in the clarity of terms used, such as "triangulation" and "trianglature," which may affect the understanding of the discussion. Additionally, the assumptions regarding the types of triangles and their properties in spherical versus Euclidean geometry remain unresolved.

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 dependent on the way in which you make the triangulation of the surface...
 
Originally posted by Guybrush Threepwood
a general formula?
IMO it is dependent 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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