A small rectangle on a large ball - distortion?

In summary, a question is posed about a rectangle being placed on the surface of a large ball and the resulting distortion. The topic is found to be related to spherical trigonometry and its applications in navigation and astronomy. The conversation ends with a recommendation to read the Wikipedia article on spherical trigonometry for more information.
  • #1
gerbil
2
0
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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  • #2
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.
 

1. What causes the distortion of a small rectangle on a large ball?

The distortion of a small rectangle on a large ball is caused by the curvature of the surface of the ball. As the rectangle is placed on the curved surface, the straight lines of the rectangle will appear curved due to the change in angle and distance from the viewer's perspective.

2. Does the size of the rectangle affect the distortion on a large ball?

Yes, the size of the rectangle can affect the distortion on a large ball. A larger rectangle will cover more surface area of the ball, resulting in a greater distortion compared to a smaller rectangle.

3. Can the distortion of a small rectangle on a large ball be corrected?

No, the distortion of a small rectangle on a large ball cannot be corrected. It is a natural phenomenon caused by the shape of the ball and cannot be altered.

4. Does the material of the ball affect the distortion of a small rectangle?

Yes, the material of the ball can affect the distortion of a small rectangle. A softer and more pliable material may result in a greater distortion compared to a harder and more rigid material.

5. Is the distortion of a small rectangle on a large ball the same from all viewing angles?

No, the distortion of a small rectangle on a large ball can vary depending on the viewing angle. As the angle changes, the perspective of the viewer also changes, resulting in a different perception of the distortion.

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