3
votes
0answers
20 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
3
votes
1answer
51 views

Geometry textbook

I am planning to take a graduate Geometry course next semester. The preliminary syllabus does not specify any textbook but has the following descriptions: Catalog Course Description: This course ...
7
votes
1answer
123 views

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
5
votes
1answer
31 views

Proof of the Barrow's Inequality?

Barrow's inequality states that if $P$ is any point inside triangle $ABC$, and $PU$, $PW$, and $PV$ are the angle bisectors, then the following inequality holds, $PA+PB+PC\geq 2(PU+PV+PW)$. I know ...
1
vote
0answers
51 views

Reference request: Cool angle-chasing problems

I'm trying to locate a geometry book (possibly a high-school level one) which included a section with a list of up to 30 angle-chasing problems (a variant of the so-called adventitious angles problem ...
1
vote
1answer
14 views

Placing a shape on a grid

I am interested in a certain kind of geometrical optimisation problems. I will illustrate it on a semi-concrete example: You are given a two-dimensional shape, say a polygon, and a rectangular ...
3
votes
2answers
110 views

Geodesic equations and christoffel symbols

I want to learn explicitly proof of the proposition 9.2.3. Which books or lecture notes I can find? Please give me a suggestion. Thank you:)
1
vote
4answers
67 views

Pre College Mathematics

During my school days I was a very keen student of mathematics. But circumstances led me to opt for commerce at the college level. Now I wish to continue learning mathematics on a self study basis. ...
0
votes
1answer
37 views

Curve in $\mathbb{P}^{n}(\mathbb{R})$, differentiable manifolds

I need a book which contains the demonstration that if $\Gamma$ is a curve in $\mathbb{P}^{n}(\mathbb{R})$ defined as $F(x_{1}, \cdots \ \ , x_{n+1}) = 0 $ , with $F$ homogeneous polynomial, then ...
4
votes
1answer
48 views

What is the Bi-affine plane

I want to know the definition of the Bi-affine plane. In an article it says that semi-symmetric plane is same as bi-affine plane. But I want to the exact definition and axioms. Also There are two ...
1
vote
4answers
272 views

What is the maximum number of pieces that a pizza can be cut into by 7 knife cuts? (NBHM 2005)

I am seeing this question very first time and do not know any formal way to solve it. Which part of mathematics it is related to? What is the maximum number of pieces that a pizza can be cut into by ...
3
votes
5answers
208 views

I want a good dictionary of mathematics/ geometry

I noticed I a made a mistake in some geometrical terminology and wanted to better my life by buying a new dictionary of mathematics or more specialised Geometry. (okay I am just a shopaholic for ...
2
votes
1answer
29 views

Embedding distance constraints in the plane

Let me first state my question somewhat vaguely. I am interested for which sets of "distance constraints" between $n$ points can be realised in the Euclidean plane. More precisely suppose you're ...
1
vote
2answers
147 views

Books on geometric transformations and/or analytic geometry?

I've been looking to expand my knowledge in geometry as it's not covered in my undergraduate curriculum. For some reason I'm repelled by the classical approach (hopefully it will pass) as I feel it's ...
2
votes
3answers
236 views

Book with lots of geometry theorems

I want to study geometry and was looking for some book that has lots of theorems and covers almost all Euclidean geometry that is needed for High School and Maths Olympiads. Thanks.
0
votes
1answer
37 views

Adding together curves or shapes to approximate something more complex

I'm looking for proper terminology / references for the following sort of problem: Say we have some one-dimensional curve like $y = 10$ defined over the real valued domain $[0,1]$, and we ask, how ...
2
votes
1answer
109 views

Pre-College Maths Textbooks

I am a high school student searching for some mathematics books covering material all the way up to, but not including, college level mathematics. I have already read Gelfand's books and Lang's Basic ...
2
votes
0answers
169 views

Good textbook on geometries

I am looking for a good textbook that thoroughly covers euclidean, affine, projective and non-euclidean geometries. I will be starting graduate school in algebraic geometry next year and I would like ...
4
votes
0answers
115 views

Obtaining a deeper understanding of lower level Mathematics

I am a college student, at a community college and I am in the process of obtaining an associates degree in general science with a specialization in mathematics in hope of transferring to a university ...
2
votes
0answers
40 views

Partial Differential Operators on Vector Bundles

can anyone suggest me a nice reference for partial differential operators on vector bundles? Thanks..
1
vote
0answers
35 views

Reference Request concerning Jet Bundles..

can anyone recommend me a nice reference concerning jet bundles? I've been looking for one for a long time but I couldn't find it...Thanks..
0
votes
2answers
292 views

What is a good book on basic high school math (algebra, geometry, trig etc.)?

What is a good book on basic high school math (algebra, geometry, trig etc.)? I want a book that presents mathematics in a rigorous manner and with emphasis on creativity rather than memorization. If ...
0
votes
0answers
31 views

Set of all affine maps as affine space

Given a two vector spaces, the set of all linear maps between them can easily be turned into a vector space again. The same if true for affine maps: Given two affine space $X$ and $Y$, the set ...
1
vote
0answers
28 views

Seeking collection of geometry problems

I'm looking for a collection of geometry problems that does not surpass high-school to first-year university geometry.. Problem that could be found sometimes in SAT/GMAT test. They should all at ...
0
votes
0answers
18 views

transversal homoclinic points on a higher-dimensional torus

In many sources (for example introduction to chaotic dynamical systems by Devaney) one can find a proof of the fact that the transversal homoclinic points (points which lay on both stable and unstable ...
1
vote
1answer
30 views

translation of Pasch “Vorlesungen über die neuere Geometrie”

Has Pasch "Vorlesungen über die neuere Geometrie" ever been translated?
0
votes
0answers
42 views

A Survey on Rota's Conjecture

I am looking for a survey on Rota's Conjecture (1970). I am more interested in geometric aspects of the conjecture and any geometric content related to the conjecture. Any reference would be helpful. ...
11
votes
2answers
246 views

Decomposable Families of Shapes

There are two types of golden triangles in the world, as shown in the following picture: Here $\varphi = \dfrac{1+\sqrt{5}}{2}$ denotes the golden ratio. Each of these golden triangles can be ...
0
votes
1answer
83 views

Good websites/books for geometry exercises?

I'm looking for exercises similar to those seen on putnam exams or olympiad exams, such as finding the area of polygons inscribed other polygons, finding certain angles, etc.
5
votes
0answers
51 views

The space of paths

Let $ (M,g) $ be a compact Riemannian manifold, and let the path space $ \Omega $ of $ M $ be the set of equivalence class of smooth maps $ \gamma : [0,1] \rightarrow M $ (equivalent under ...
5
votes
2answers
146 views

How to prove these two “obvious” facts about circles?

1) It's said that Thales proved that "a diameter divides a circle in two congruent parts". I searched a lot but did not find his proof. How can it be proved? 2) How to prove that "a circle is a ...
1
vote
1answer
49 views

Boundary Normal Coordinates

Let $ (M,g) $ be a 2D Riemannian manifold with boundary. The boundary normal coordinates $\psi $ are constructed roughly as follows: in a sufficiently small neighborhood $ U $ of $ \partial M $, for ...
0
votes
0answers
71 views

First event in a straight skeleton

Is there a simple geometric criterion to check whether the first event in (the wave propagation of) a straight skeleton is an edge event or a split event? The literature I could find is computational ...
1
vote
2answers
33 views

Learning about geometric bezier splines

I want to understand geometric Bezier splines. I have basically no advanced maths but am willing to learn. Can anybody suggest a good starting point for a complete beginner to start learning what I ...
3
votes
0answers
63 views

Distance function and Green's function

Let $ (M,g) $ be a two dimensional Riemmanian manifold, with a smooth distance function $ d(x,y) $ for all $ x, y$ in $ M$. The logarithm of the distance function then satisfies $ \Delta \left( ...
2
votes
1answer
67 views

Generalized Straight Skeleton

The straight skeleton of a polygon can be computed by having the edges of the polygon move inwards at a uniform constant speed. Is it useful to generalize this computation process by varying the ...
5
votes
0answers
103 views

Geometrical interpretation of a group action of $SU_2$ on $\mathbb S^3$

Background There're some nomenclatures from Michael Artin's Algebra to explain. 3-Sphere, or $\mathbb S^3$, is the locus of $x_0^2+x_1^2+x_2^2+x_3^2=1$, where $(x_0,x_1,x_2,x_3)\in\mathbb R^4$. ...
4
votes
2answers
132 views

Textbooks with exposition done mostly in proof outlines or exercises?

As the title indicates, I'm trying to find books where the exposition of the main course of thought is done entirely or mostly in outlines of proofs, or as exercises with or without hints. I'm trying ...
8
votes
2answers
163 views

Extending the primes

I had an idea and I'd like to find out whether it has a name or has been studied before. Imagine the natural numbers and the operations of addition and multiplication, but with the following ...
7
votes
0answers
191 views

Kakeya Needle problem video

I'm intruiged by the Kakeya Needle problem, described here on Wikipedia. Wikipedia has a nice animation of a needle turning through a hypo-cycloid: What I'm searching for is a visualisation of the ...
3
votes
2answers
126 views

Distance metric for (infinite) lines in 3D

I would like a metric $d(\;)$ between pairs of (infinite) lines in $\mathbb{R}^3$, with these properties: If two lines $L_1$ and $L_2$ are parallel and separated by distance $x$, then $d(L_1,L_2) = ...
3
votes
5answers
286 views

Geometry books with beautiful diagrams

What are some geometry books with particularly beautiful diagrams? Old or new. Could be on 'standard' material or specialised on one particular topic. Something for the connoisseur of mathematical ...
0
votes
2answers
74 views

Seeking a detailed and comprehensive book on plane geometry

I'm really tired of going through tons of wikipedia pages. Wikipedia is a good thing, but at one point one who wants to go deeper needs an ordered, comprehensive and formal treatment. Me at least. ...
1
vote
1answer
267 views

Locus of vertex of parabolas through three points

Consider all parabolas through three given points $A,B,C$. What is the locus of the vertex? Qualitatively it traces three branches with the lines through the mid-points of the sides of the triangle ...
3
votes
1answer
241 views

Book on Geometry (GRE Math Subject Test)?

I don't believe that this is a duplicate of any question that is on this site. I am currently searching for a geometry textbook which covers (at least) material for the GRE Math Subject Test. I have ...
4
votes
1answer
98 views

Book on quadric surfaces with linear algebra

Most information that I can find about quadric surfaces is written from a calculus perspective - without using any matrices or vectors. However, I would like to have a reference that tells me the ...
2
votes
3answers
135 views

On integral of a function over a simplex

Help w/the following general calculation and references would be appreciated. Let $ABC$ be a triangle in the plane. Then for any linear function of two variables $u$. $$ \int_{\triangle}|\nabla ...
3
votes
0answers
145 views

Imagining four or higher dimensions and the difference to imagining three dimensions

I’m very interested in how people envision four or higher dimensions. And I’m especially interested in how geometers and topologists who actually work in four dimensions do. Now I know of the video ...
0
votes
0answers
51 views

Reference materials on hyperspheres

Anyone have a good reference for various facts about hyperspheres, either permanent online (such as a book/paper on arXiv, or, say a trusted site such as Wolfram MathWorld) or printed (book or ...
2
votes
3answers
112 views

I'm researching about geometry non-Euclidean [closed]

I'm researching non-Euclidean geometry. Now I am looking for a good source for it. Please suggest me something.Thanks.