0
votes
0answers
34 views

what are the interesting geometric properties of a regular n-gon? [closed]

I want to know about the interesting geometric properties of a regular n-gon. I know there are lot of results on this subject. I am interest about simple geometric properties which are easy to ...
1
vote
1answer
33 views

Where can I find a good set of notes discussing main theorems/ideas surrounding non-orientable surfaces?

I'm currently looking at non-orientable surfaces, but know very little about them. Is there are good set of notes that will teach me the classical results surrounding non-orientable surfaces?
11
votes
2answers
228 views

Why is Volume^2 at most product of the 3 projections?

Is there a simple proof for $$ \text{Vol}^2(P)\le \prod_{i=x,y,z} \text{Area}(\text{Proj}_i(P)), $$ where $P\subset \mathbb R^3$ and $\text{Proj}_z(P)$ denotes the projection of $P$ to the $z=0$ ...
2
votes
1answer
68 views

Question about Qing Liu's Algebraic Geometry book

I was just wondering what the real prerequisites are for reading Qing Liu's 'Algebraic Geometry and Arithmetic Curves', and if it is a good first book on the subject. In his preface he states that the ...
1
vote
0answers
60 views

Undergrad Geometry Book

What is a good follow-up to Stillwell's Four Pillars of Geometry? Also Algebraic Geometry/ Topology sounds fun -- are there any good undergrad books on that?
0
votes
1answer
51 views

Good book on non-Euclidean geometry

What's a good book on non-Euclidean geometry for undergrads? Especially ones that consider hyperbolic and spherical trigonometry?
2
votes
1answer
50 views

Reference Request: Split-Complex Numbers

Does anyone have a recommendation for a good book on split-complex numbers? If it also covers dual numbers or the relation between split-complex numbers and special relativity or Minkowski 4-space or ...
0
votes
0answers
15 views

good text books for axiomatic solid geometry?

I read the book about plane geometry : Marvin Jay Greenberg Euclidean and non-euclidean but it's only for the plane geometry so I want know about axiomatic solid geometry. Can someone recommend a ...
2
votes
3answers
78 views

Reference request: algebraic methods in geometry

I am a (soon to be) third year undergraduate who has just finished courses in linear and abstract algebra. While I enjoyed the study of algebraic structures in their own right, my favorite part of the ...
0
votes
2answers
66 views

Where to learn Euclidean geometry in-depth?

I am interested in Euclidean geometry and using compass and rulers to do constructions. I took geometry in high school but I feel like it didn't go in-depth enough. Where can I learn this online? I am ...
6
votes
3answers
128 views

Beginning of Romance

I am a 17 guy from India. The fascination of maths has struck me recently, while I am in standard 12th. But all the resources I have, is some school textbooks. M.L Agrawal's of 11th and 12th. I don't ...
1
vote
1answer
67 views

Reference about Gauss-Bonnet-Chern theorem.

I would like to get some references which explains Gauss-Bonnet-Chern theorem and its original proof by Chern. I tried to read his paper published in 1944 "A Simple Intrinsic Proof of the Gauss-Bonnet ...
3
votes
2answers
71 views

Most accurate translation of Euclid's Elements

Which is the most accurate translation of the Elements by Euclid? I have found manybtranslations but there seem to be some differences in each version. I would like to know which is the closest to the ...
0
votes
2answers
41 views

Geometry basic problem

Hy! If i have a triangle with given: b-c=3 cm, a=6 cm and alpha is 30°, how do I draw this? Please help me by telling me where I can find this type of exercises online with explanations. Thank you!
1
vote
1answer
37 views

Geometry reference-request

I would like some reference regarding geometry. I'm a student of civil engineering, and I wanted some insight in general geometry, e.g, know what originated it, what is valid today, etc. In specific, ...
2
votes
1answer
39 views

Square Line Picking

The probability density function of the distance between two points chosen randomly on the unit square is given by: $ P(\ell) = \begin{cases} 2\ell\left(\ell^2 - 4\ell + \pi\right) & 0 \leq \ell ...
0
votes
0answers
34 views

Computer-aided study of elementary geometry

As a beginning student of elementary (euclidean plane) geometry, so far, I have gotten the impression that there are two major approaches to geometries: naive vs axiomatic. Being a humanities student ...
1
vote
1answer
59 views

Reference - Fractal Geometry

I am looking for textbooks or lecture notes about Fractal Geometry that reach an advance level on the topic and aren't just introductory.
2
votes
1answer
49 views

Classification of parabolic elements of a subgroup of $PSL_2(\mathbb R)$

Let $G\subset PSL_2(\mathbb R)$ be the group generated by the matrices $$a_n=\begin{pmatrix} 1 & 2\cot\frac{\pi}{n}\\0 & 1\end{pmatrix},\; c_n = \begin{pmatrix} ...
3
votes
0answers
23 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 ...
2
votes
1answer
76 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 ...
16
votes
2answers
261 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
44 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
1answer
15 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
129 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
79 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
39 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
54 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
687 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
6answers
228 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
30 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
181 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
387 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
46 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
143 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
209 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 ...
5
votes
0answers
143 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 ...
3
votes
1answer
55 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
42 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
454 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
35 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
30 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
21 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 ...
2
votes
2answers
47 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. ...
12
votes
2answers
273 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
89 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
54 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
153 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
57 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 ...