A very small area of the hyperbolic plane looks more Euclidean as the curvature approachs 0. Any more evidence? Or reference would help? Thanks
2026-03-31 20:21:14.1774988474
Hyperbolic plane shrinking
78 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in EUCLIDEAN-GEOMETRY
- Visualization of Projective Space
- Triangle inequality for metric space where the metric is angles between vectors
- Circle inside kite inside larger circle
- If in a triangle ABC, ∠B = 2∠C and the bisector of ∠B meets CA in D, then the ratio BD : DC would be equal to?
- Euclidean Fifth Postulate
- JMO geometry Problem.
- Measure of the angle
- Difference between parallel and Equal lines
- Complex numbers - prove |BD| + |CD| = |AD|
- Find the ratio of segments using Ceva's theorem
Related Questions in HYPERBOLIC-GEOMETRY
- Sharing endpoint at infinity
- CAT(0) references request
- Do the loops "Snakes" by M.C. Escher correspond to a regular tilling of the hyperbolic plane?
- How to find the Fuschian group associated with a region of the complex plane
- Hyperbolic circles in the hyperbolic model
- Area of an hyperbolic triangle made by two geodesic and an horocycle
- Concavity of distance to the boundary in Riemannian manifolds
- Differential Equation of Circles orthogonal to a fixed Circle
- Is there a volume formula for hyperbolic tetrahedron
- Can you generalize the Triangle group to other polygons?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
This is one of those things where as you learn more about non-euclidean geometry the "evidence" just accumulates. The distance formula is $$ds^2=\cosh^2 y dx^2+dy^2$$ and we see that $\cosh y\to 1$ as $y\to 0$ another formula is the pythagorean formula $\cosh c=\cosh a\cosh b$ limits to $c^2=a^2+b^2$ for small $a$ and $b$. Good refs are Carslaw, and Hartshorne's excellent "Euclid and beyond".