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feynmanisbest
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Does the inside of a sphere have negative curvature?
Inside Sphere: Does It Have Negative Curvature?
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Discussion Overview
The discussion centers on the question of whether the inside surface of a hollow sphere exhibits negative curvature. Participants explore the nature of curvature in relation to the geometry of spheres and provide examples of shapes with different curvature properties.
Discussion Character
- Debate/contested
Main Points Raised
- Some participants question if the inside of a sphere has negative curvature, specifically referring to a hollow sphere.
- One participant argues that the inside surface of a hollow sphere does not have negative curvature, asserting that a sphere, regardless of being viewed from the inside or outside, has positive curvature.
- Another participant suggests that the sphere is infinitely thin, implying that it lacks a distinct inside or outside, and claims that the curvature remains consistent from any perspective.
- A participant provides an example of a saddle shape to illustrate negative curvature, noting that it curves differently in different directions, contrasting it with the uniform curvature of a sphere.
Areas of Agreement / Disagreement
Participants express differing views on the curvature of the inside of a sphere, with no consensus reached on whether it can be considered to have negative curvature.
Contextual Notes
Some assumptions about the definitions of curvature and the nature of the sphere may not be explicitly stated, leading to potential misunderstandings in the discussion.
- #2
feynmanisbest
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I mean does the inside surface of a hollow sphere have negative curvature?
- #3
lavinia
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feynmanisbest said:
the sphere is infinitely thin so it really has no inside or outside. The curvature is the same no matter how you look at it.
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DaveC426913
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The answer is no.
A sphere (inside or outside) has positive curvature. Any direction in which you choose to measure, it will curve in the same direction. If the surface is extended far enough it will be closed.
An example of a shape that has a negative curvature is a saddle. If you go front-to-back it curves one way; but side-to-side it curves in a different direction. A saddle shape, if extended indefinitely, is open.
A sphere (inside or outside) has positive curvature. Any direction in which you choose to measure, it will curve in the same direction. If the surface is extended far enough it will be closed.
An example of a shape that has a negative curvature is a saddle. If you go front-to-back it curves one way; but side-to-side it curves in a different direction. A saddle shape, if extended indefinitely, is open.
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