This article considers only curves in Euclidean space. Most of the notions presented here have analogues for curves in Riemannian and pseudo-Riemannian manifolds. For a discussion of curves in an arbitrary topological space, see the main article on curves.Differential geometry of curves is the branch of geometry that deals
with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.
Starting in antiquity, many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves ar...
I'm looking for any 3D surface such that given any two lines on the surface, they intersect and only intersect in right angles.
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Use define: in Google and you will get dictionary definitions and etymologies. For instance: define: dictionary.
Where is Google getting the definitions, etymologies, and pronunciations? I doubt they are compiling it themselves—they probably license it from somewhere.
Please, I need some help with this exercise
Consider the space
$X=\bigcup_{n\in \mathbb{N}} \{\frac{1}{n}\}\times[0,1]\cup ([0,1]\times\{0\})\cup(\{0\}\times [0,1]),$
With the topology of subspace of $\mathbb{R}^2$. Show that $X$ is connected but not locally connected
An ellipse reflects an incident ray through one focus to the other as reflected ray and its special case of parabola likewise reflects rays parallel to symmetry axis after bouncing to go through its focus.
But what geometric property excludes the hyperbola to have such reflections? I tried to ...
In mathematics, the Dirichlet energy is a measure of how variable a function is. More abstractly, it is a quadratic functional on the Sobolev space H1. The Dirichlet energy is intimately connected to Laplace's equation and is named after the German mathematician Peter Gustav Lejeune Dirichlet.
== Definition ==
Given an open set Ω ⊆ Rn and a function u : Ω → R the Dirichlet energy of the function u is the real number
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