- Why are certain PDE called elliptic, hyperbolic, or parabolic?
Why are the Partial Differential Equations so named? i e, elliptical, hyperbolic, and parabolic I do know the condition at which a general second order partial differential equation becomes these,
- Relationship Between Hyperbolas and Hyperbolic Spaces
2) When searching for images of "Hyperbolic Spaces", the following types of images always come up: What is the relationship between the above diagrams and hyperbolic spaces? Are these pictures trying to illustrate some concept in particular (e g the projection of some shape from Euclidean Space to Hyperbolic Space, e g dodecahedral tessellation)?
- What are the interesting applications of hyperbolic geometry?
By contrast, in hyperbolic space, a circle of a fixed radius packs in more surface area than its flat or positively-curved counterpart; you can see this explicitly, for example, by putting a hyperbolic metric on the unit disk or the upper half-plane, where you will compute that a hyperbolic circle has area that grows exponentially with the radius
- Distance in hyperbolic geometry - Mathematics Stack Exchange
Is there any formula like this for distance between points in hyperbolic geometry? I know that for example in the Poincaré disc model we have a certain formula, another in the Klein model, and so on, but I was wondering if we can have some distance formula that exists independent of the model
- hyperbolic geometry - how to generate tessellation cells using the . . .
a way to generate the coordinates in the hyperbolic plane, for each vertex of several cells (polygons) in such a tiling; and the formula to convert those coordinates to the Cartesian plane, using the Poincare Disk model
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