A small rectangle on a large ball - distortion?

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SUMMARY

The discussion centers on the distortion of a rectangular object (10 cm x 20 cm) when placed on the surface of a large sphere with a radius of 1 meter. It highlights the inherent challenges of fitting a 2D shape onto a spherical surface, leading to distortion. The topic is linked to spherical trigonometry, which is relevant in navigation and astronomy. The user seeks numerical information regarding this distortion, indicating a gap in accessible resources on the subject.

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  • Spherical trigonometry fundamentals
  • Understanding of geometric distortion
  • Basic knowledge of navigation principles
  • Familiarity with mathematical modeling techniques
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  • Research spherical trigonometry applications in navigation
  • Explore mathematical models for 2D to 3D shape distortion
  • Learn about geodesic calculations on spherical surfaces
  • Investigate numerical methods for geometric transformations
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Mathematicians, navigators, astronomers, and anyone interested in the geometric implications of placing 2D shapes on 3D surfaces.

gerbil
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Hi

Let's assume we have a, say, 10 cm * 20 cm, not very thick, rectangular object. We also have a huge ball, with a known radius of about 1 m. Now be put that rectangle onto the ball surface. What happens to the rectangle?

I know that a 2D-object doesn't fit very well onto a spherical surface, of course. Just wondering, does anyone know a way to get some numerical information about the distortion? I have googled A LOT but haven't really found anything.

I guess that a few great mathematicians have already solved this problem..?
 
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The topic is called spherical trigonometry -it's widely used in navaigation ( we live on a ball) and astronomy. The wiki article on spherical trig is a good intro.
 

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