14 Matching Annotations
 Feb 2020

marxdown.github.io marxdown.github.io

the area of the triangle itself is expressed by something totally different from its visible figure, namely, by half the product of the base multiplied by the altitude

In order to calculate and compare the areas of rectilinear figures, we decompose them into triangles

 Oct 2019

www.iste.co.uk www.iste.co.uk

Space and Geometry

 Jun 2019

tele.informatik.unifreiburg.de tele.informatik.unifreiburg.de

In 1953 I realized that the straight line leads to the downfall of mankind. But the straight line has become an absolute tyranny. The straight line is something cowardly drawn with a rule, without thought or feeling; it is the line which does not exist in nature. And that line is the rotten foundation of our doomed civilization. Even if there are places where it is recognized that this line is rapidly leading to perdition, its course continues to be plotted. ..Any design undertaken with the straight line will be stillborn. Today we are witnessing the triumph of rationalist knowhow and yet, at the same time, we find ourselves confronted with emptiness. An aesthetic void, dessert of uniformity, criminal sterility, loss of creative power. Even creativity is prefabricated. We are no longer able to create. That is our real illiteracy. Friedensreich Hundertwasser

 Dec 2018

www.washingtonpost.com www.washingtonpost.com

“vanishing point” geometry
More here.

 Nov 2018

iphysresearch.github.io iphysresearch.github.io

Grassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learning
就喜欢这些用微分流形讲机器学习的~！
应该写个 Paper Summary 表示尊敬~~~

Classification and Geometry of General Perceptual Manifolds
一篇Physical Review X 上的文章~ 读读看~
Paper Summary

 Mar 2018

linkspringercom.ezproxy3.library.arizona.edu linkspringercom.ezproxy3.library.arizona.edu

The Use of Projective Geometry in Computer Graphics
Chapter 2: 射影几何的一般性介绍

 Mar 2016


Letβ:V×V→Wbe a symmetric bilinear form whereVand (W,h,i) arereal vector spaces of finite dimensionnandp, respectively, equipped withinner products.Thesnullityνsofβfor any integer 1≤s≤pis defined byνs= maxUs⊂Wdim{x∈V:βUs(x, y) = 0 for ally∈V}.HereβUs=πUs◦βwhereUsis anysdimensional subspace ofWandπUs:W→Usdenotes the orthogonal projection.LetR:V×V×V×V→Rbe the multilinear map with the algebraicproperties of the curvature tensor defined byR(x, y, z, w) =hβ(x, w), β(y, z)i − hβ(x, z), β(y, w)i.Lemma 4.Assume that2p < nandνs< n−2sfor all1≤s≤p. LetV=V1⊕V2be an orthogonal splitting such thatR(x, y, z, u) =R(x, y, u, v) =R(x, u, v, w) = 0for anyx, y, z∈V1andu, v, w∈V2. Then,S=span{β(x, y) :x∈V1andy∈V2}= 0.


ac.elscdn.com ac.elscdn.com

second fundamental_form h satisfies h(TpL,xTpLj =0 forallp E M
Para o nosso caso, assumir essa hipótese com respeito a decomposição do espaço tangente ao longo do bordo.

 Dec 2015

www.mathunion.org www.mathunion.org

Let M be an rcdimensional manifold of class C°° and g any given Riemannian metric on M. We will consider the following classical problem motivated by differential geometry. Does there exist an embedding u = (w1,..., uq) : M > R9 such that the usual euclidian metric of R9 induces on the submanifold u(M) the given metric gl In other words, w must satisfy E(w) := dudu = g, (1) or in local coordinates 9 du1 du1 _ ,tîâ?â?"Qij' The dot in (1) denotes the usual scalar product of R9. The notion embedding means, that w is locally an immersion and globally a homeomorphism of M onto the subspace u(M) of R*. If an embedding w : M • R9 satisfies (1) on the whole M, we speak of an isometric embedding. If w is an immersion and a solution of (1) in a (possibly small) neighbourhood of any point of M, we speak of a local isometric embedding.

 Mar 2015

arxiv.org arxiv.org

θ dμ ≥ p 16 π  Σ 
Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por HuiskenIlmanen e Bray?

GIBBONSPENROSE INEQUALITY
Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por HuiskenIlmanen e Bray?

 Oct 2013

rhetoric.eserver.org rhetoric.eserver.org

Order, in the first place, is necessary in geometry, and is it not also necessary in eloquence?
comparison between geometry and rhetoric
