- #1
Paige_Turner
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- TL;DR Summary
- Can a plane curve have negative curvature?
It's probably the hyperbola, but I don't see how it's curvature is negative. It looks like 2 parabolas.
thanx, paige turner
thanx, paige turner
Negative curvature in low dimensions
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- Thread starter Paige_Turner
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- Curvature Dimensions Negative
In summary, the conversation discusses the concept of negative curvature in a curve and how it can be possible for a curve to curve downward. The speaker is autistic and interested in understanding the universe and the conversation ends with concerns about being banned.
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If f(x) has positive curvature, then -f(x) has negative curvature. It is possible for a curve to curve downward
- #4
Paige_Turner
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Well, I'm autistic--not human at all. Ask my friends. The subject line indicates that "it" is a plane curve with negative curvature.BvU said:Hello and!
> You may be able to see what "it" looks like, but we are mere humans and not telepathic.
> Please present a complete case.
A case for what? I don't have an agenda.I don't have the answer. I just want to understand WITW is going on around me, and what's "around me" is the universe.
> if all you want is an answer
Um... what else could I want? I asked a question.
I just got here and I'm already in trouble with the mods. If past is indeed prologue, I will be banned and not have the slightest idea why--even when I'm polite and only talk about hypergeometry.
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1. What is negative curvature in low dimensions?
Negative curvature in low dimensions refers to a geometric property of a space or surface where the curvature at a point is negative. This means that the space or surface is curved in a way that the angles of a triangle formed by three points will add up to less than 180 degrees.
2. What are some examples of spaces with negative curvature in low dimensions?
Some examples of spaces with negative curvature in low dimensions include hyperbolic surfaces, such as the surface of a saddle or a Pringle chip. Other examples include negatively curved manifolds, such as the Poincaré dodecahedral space.
3. How is negative curvature in low dimensions measured?
Negative curvature in low dimensions is measured using various mathematical tools, such as the Gaussian curvature, sectional curvature, and Ricci curvature. These measures help quantify the amount of curvature at a specific point or in a specific direction on a surface or space.
4. What are the implications of negative curvature in low dimensions?
Negative curvature in low dimensions has significant implications in fields such as differential geometry, topology, and physics. It allows for the existence of non-Euclidean geometries, which have been essential in understanding the universe and developing modern theories of gravity.
5. How is negative curvature in low dimensions relevant to everyday life?
Negative curvature in low dimensions may seem like an abstract concept, but it has practical applications in fields such as architecture and computer graphics. Hyperbolic surfaces, for example, are used in the design of buildings, furniture, and art. Negative curvature also plays a role in the development of algorithms for 3D modeling and animation.
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