Can Triangulation Describe Distance in Spherical or Euclidean Geometry?

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In summary, the conversation discusses the formulation of a general formula for describing distance on a quadrant using triangulation in either spherical or Euclidean geometry. It is mentioned that the formula may depend on the method of triangulation used on the surface. The conversation also touches on the definition of distances in ordinary, spherical, and hyperbolic geometry. Finally, a trianglature formula is proposed as a solution to the problem.
  • #1
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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  • #2
a general formula?
IMO it is dependant on the way in which you make the triangulation of the surface...
 
  • #3
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.
 
  • #4
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?
 
  • #5
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...
 
  • #6
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...
 
  • #7
GT,

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

FAQ: Can Triangulation Describe Distance in Spherical or Euclidean Geometry?

What is geometry?

Geometry is a branch of mathematics that deals with the study of shapes, sizes, and positions of objects in space.

What are the basic principles of geometry?

The basic principles of geometry include points, lines, planes, and angles. Points are represented by a dot and have no dimensions. Lines are straight paths with infinite length and no width. Planes are flat surfaces that extend infinitely in all directions. Angles are formed when two lines intersect and measure the amount of turn between them.

What are the different types of geometric shapes?

There are many different types of geometric shapes including circles, triangles, rectangles, squares, polygons, and more. Each shape has its own unique properties and can be classified by the number of sides and angles it has.

How is geometry used in real life?

Geometry has many practical applications in daily life, such as in architecture, engineering, art, and design. It is used to create and analyze structures, design buildings and bridges, and create computer graphics. It also plays a role in navigation, surveying, and mapmaking.

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To improve your understanding of geometry, it is important to practice solving problems and working with geometric concepts. You can also use visual aids such as diagrams and models to help you visualize and understand geometric principles. Additionally, seeking help from a teacher or tutor can also improve your understanding of geometry.

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