Geometry Definition and 999 Threads

What books should I read as prerequisites for Spivak's Differential Geometry Series? Trying to pick up Diff Geom for graduate physics but right now it is pretty daunting. I've got single variable calculus and linear algebra under my belt. Just looking for bare minimum requirements here to...

Homework Statement Find the radius of a circle inscribed in a quadrant of a circle with radius 5 Homework Equations The Attempt at a Solution I worked this but I'm not sure if its correct. I looked at the first quadrant so a quarter of a circle with radius 5. I drew the radius...

Hello all I work in transport engineering. i have come across what seems to be a simple maths problem but i do not understand it. The problem relates to geometry i.e. calculating the radius of a curve using a chord and a versine. The problem is this:- " a general rule of thumb is as...

please suggest the books 'must do' in eucleodian geometry for elementary and pre college level. Is doing 'Advanced Eucleodian Geometry' by Roger A.johnson enough?

please suggest what books should I do to strong my concepts in eucleodian geometry (ELEMENTARY & PRE COLLEGE LEVEL)? ( in case for more than 1 book please refer the order in which they should be done) Also tell me , whether doing only ADVANCED EUCLEODIAN GEOMETRY by Roger A. JOHNSON IS ENOUGH...

Geometry - Topology; "What is the difference?" It is certainly important for a good understanding of a lot of modern problems. So I think it could be important to explain clearly the difference(s) between these two notions. Can you help me?

\stackrel{\rightarrow}{PQ} bisects \angle{ABC}. If m\angle{ABD} can be represented by 3a + 10 and m\angle{DBC} can be represented by 5a - 6, what is m\angle{ABC}? What I did was add the two representations together and multiplied by two, which would give me 16a + 8. Does that sound correct?

Hey guys, Well, it's the end of the academic year. I just had my last biweekly geometry class yesterday. I hope I did well on the chapter test I took yesterday. Anyways, as the title suggests I'll be going into Algebra II next year. Based on my experience in geometry class, I can...

[b]1. The area of a parallelogram is 60 square units. A segment is drawn from one vertex to the midpoint of an opposite side. The diagonal is drawn between the other two other vertices. Find the area of the four regions formed. Homework Equations [b]3. I found that two of the...

Hi! I stumbled upon something I need to implement my problem in a computer. Because I think its actually fun to puzzle on, I thought it might be nice to post it here. The problem is this: If you have a 4D hypercube, (a_1,b_1)\times(a_2,b_2)\times(a_3,b_3)\times(a_4,b_4), what is an easy...

Homework Statement . 1. a hall that is 10 ft. wide has a ceiling that is a semi-ellipse. the ceiling is 10 ft high at the sides and 12 ft high in the center find its equation with the x-axis horizontal and the origin at the center of the ellipse. Homework Equations x^2/a^2 + y^2/b^2 = 1...

Here is a spreadsheet I made to solve projectile motion problems. It uses only euclidean geometry to solve for the answers, but it gives the answers as slopes, not angles. All variables entered also must be in slopes and not angles. I added a section that does the conversion between the two...

Dear all, I am a medical doctor stuck with a mathematics problem. I have taken a project to map the 3D movement of a particular bone and describe its motion. My maths knowledge is a bit lacking. However using logic I felt that I would need to track 3 constant markers on the particular bone...

Homework Statement Find the Mass of the Schwarzschild geometry by calculating, \frac{1}{4\pi}\int_{S}n^{\alpha}\sigma_{\beta}\nabla_{\alpha}\xi^{\beta}dA in a Schwarzschild spacetime and for S a large sphere of coordinate radius R. Here ζ is the Killing vector corresponding to time...

Hello! I'm looking for a good analytic geometry textbook. I'm studying circumferences and sphere and I'm using the book Analytic Geometry: A vector approach from Wexler but I find this book quite bad. I want some suggestions! Thank you.

I was trying to think of natural physical reasons to want to study noncommutative geometry, and it seems to me that it should be relevant even in a classical scenario. Let me know what you think of this as I am no expert. I'm not being terribly precise, either, so let me know if I should...

I think this a map of the Klein four-group geometry. Comments? http://dl.dropbox.com/u/13155084/prime-%20square-klein%20four%20group.png

I have to choose which math course I'm going to take next term. I want to take both but I'm already taking two physics courses and my college's distribution requirements require that I take an English next term... bleh... I could audit one of the physics and then take both math courses, but that...

According to the Inflation Theory our Observable Universe is but a small part of the total universe created in the Big Bang. Our observable universe appears to be flat (just like Earth at sea level may appear flat), while the total universe may be shaped like a balloon. If we assume our...

I want to find x for (1) and x and y for (2). I am not sure how to put the images directly into the thread so I apologize if you do not like having to click on them. On the first one, I do not know how we can find this without knowing that XW is a diameter (it is not given as one in the...

I'm taking general relativity and I understand how things work mathematically, but I'm trying to find ways of describing black holes to a general audience. Would it be fair to say that inside a black hole, space is curved in such a way that all possible paths lead to the singularity? Or, put...

New thread continuing a topic raised in https://www.physicsforums.com/newreply.php?do=newreply&p=3865854 Okay, so I saw on wikipedia that you can have a 'flat torus' --- at least a 2 dimensional torus inbedded in 4-space. So you can also have a 3-torus, that's flat? And would time just be...

Homework Statement Hey guys. As you can see, there are 5 questions to answer regarding this question. I'm working through it and need some help regarding a few of the questions. I have A.) The electric potential at the center of the circle is Zero. B.) The value of the electric...

Homework Statement A cylindrical tank of gas with a radius is viewed from the side (so that it looks like a circle, not a rectangle) and has a radius of 1m. Through a hole in the top, a vertical rod is lowered to touch the bottom of the tank. When the rod is removed, the gasoline level in the...

Homework Statement I have a piece of a plane in 3 dimensions (imagine holding an enevelope in the air), and two orthognal projections which form quadrilaterals, one on the xy plane (i.e. looking at the enevelope from above) and one on the xz plane (looking at it from the side). We know the...

Kisielowski Lewandowski Puchta have made a significant advance in calculating the transition amplitudes between quantum states of geometry. They have found a systematic algorithm that enumerates the (generalized) spinfoam-like histories by which one state evolves into another. And in this case...

I am reading Kane's book on Reflections and Reflection Groups and am having difficulties with some basic geometric notions - see attachment Kane paes 6-7. On page 6 in section 1-1 Reflections and Reflection Groups (see attachment) we read: " We can define reflections either with respect to...

I am completely lost with this question... for example for 2 electrons coupling that results in a singlet state with a spin momentum of 0 or a triplet state with spin momentum √2h-bar. How would you go to find the geometry of these states?

http://www.flickr.com/photos/66943862@N06/6868453382/in/photostream/lightbox/ http://www.flickr.com/photos/66943862@N06/6868453382/in/photostream/lightbox/ I was looking at a robotics kinematics analysis & there is one geometric equation assumed in the analysis which I can't seem to...

Which do you think are the main quantum geometry (QG) lines recently appearing to rival Loop? Do any look especially promising to you? Any favorites? Here are some to consider. The authors shown aren't a complete list! Just enough for an arxiv search: [Colored] tensor models (e.g. Gurau, Ryan...

Hello all I was hoping someone could help me with the following problem. I work on the railroads and my task is to improve the alignment of a curve. I have surveyed the existing geometry by going along the track and recording x, y, z co-ordinates at approx 1m intervals. I have...

Given the complete classification of finite simple groups, can one say that the number of all conceivable 2D/3D symmetrical geometric objects/arrangement is limited? Is spatial symmetry limited in our 3D world? IH

no gut? well, from GR or LQG as well, gravity is not force but geometry right? When einstein knew gravity is geometry and not force, why did he try to unify them? Will we have 3 fundamental forces. Is gut ruled out?

I need to find the total surface area of the hollowed out hemisphere (picture attached), with an inner diameter of 1.86 cm and what looks like an outer radius (also what I am assuming as height) of 1.25 cm. Surface area of a sphere is 4∏r2, so half the sphere is 2∏r2. Since the outer...

Homework Statement Points S and T lie on the line 2x+y=3. If the length ST is 13 units, and the coordinates of S are (2, -1), determine all possible coordinate pairs for T, correct to two decimal places. For simplicity, determine the coordinates for T, relative to S from the left.Homework...

A problem I should be able to solve :( (geometry) This is a random problem I discovered on the internet: If the area of a rectangle is diminished by 36%, what are the sides of the original rectangle if the sides of the diminished one are 36mm and 48mm? My answer: Let a and b be the...

I'm not sure why but I can't seem to figure this problem out at all... You have a slice of a banked circular track... Find the angle theta. See attachment, My first guess was to use the pythagorean theorem + the fact that the two lengths are both equal to angle/360* 2 * pi * r where r is...

Hi all, I've been wondering about this for some time. While I am only familiar with the basics of differential geometry, I have come across the Lie bracket commutator in a few places. Firstly, what is the intuitive explanation of the Lie bracket [X,Y] of two vectors, if there is one? In...

I do not understnad how x+y+z=0 can be a plane, I thought a plane has 2 dimensions, this is all :) thanks.

So I'm currently a sophomore math/CS major. I'm interesting in taking the algebraic geometry sequence next year; however I don't have the formal prereqs for the class, first year graduate algebra, which I would be taking simultaneously with the algebraic geometry class. I'm wondering if this...

Homework Statement Let A, B, C be three points on a plane and O be the origin point on this plane. Put a = OA and b = OB, and c = OC, (a,b and c are vectors). P is a point inside the triangle ABC. Suppose that the ratio of the areas of the triangles PAB, PBC and PCA is 2:3:5 (i) The...

Homework Statement I have 2 parametric vector equations (of a line) r(t) = (2,-4,4) + t(1,-3,4) s(t) = (1,-1,0) + t(2,-1,1) how do i find the coordinates for which they intersect each other? The answers is (1,-1,0) Homework Equations x=a+λv, for some λ in ℝ (parametric vector...

I am trying to figure out what size eaves we need for our house extension. I've tried a few calculations and now I'm posting here in the hope that a logical thinker will be able to tell me what I'm doing wrong. We live in Adelaide, Australia, and we want to put in glass double-doors on a...

Show that the ray is well defined / independent of ruler placement. Ruler placement postulate says Given two points P and Q of a line, the coordinate system can be chosen in such a way that the coordinate of P is zero and the coordinate of Q is positive. I know you can place ray AB where B can...

Hey guys, I'm looking for a good treatment (good = concise, and clear) of affine geometry. Connections, parallel transport, etc. I'm looking for this from a mathematical P.O.V. Most of the differential geometry books I have deal only with the exterior forms, and general manifolds without this...

Hello, I never took Geometry in high school, and I am currently in college studying both math and physics. Consequently, I decided to pick up a basic geometry textbook to try and learn it on my own; but I have found I have limited time due to my college studies. I am wondering, is it even...

Homework Statement Can a trapezoid ever be a kite? Can a kite be a trapezoid? 2. The attempt at a solution I believe that the answer to both is no. 1. If a trapezoid was a kite, wouldn't the pair of parallel sides, along with the congruent consecutive sides, imply that it was a...

Homework Statement The measure of the sides of an isosceles triangle are represented by x + 5, 3x +13, and 4x + 11. What are the measures of the sides? Two answers are possible. Homework Equations The Attempt at a Solution Well, I set up three different triangles, to account for the...

Homework Statement Th measure of the sides of an equilateral triangle are represented by x + 12, 3x - 8, and 2x + 2. What is the measure of each side of the triangle. Homework Equations The Attempt at a Solution Well, I know that each side of this triangle are equal, resulting...

First, let me apologize for my bad English, it's not my native language. Most areas of math for me aren't really an issue. I'm actually quite good at it. But there's one thing I absolutely despise and also something I'm very bad at: geometry. I was planning on studying theoretical physics...