Geometry Definition and 999 Threads

Hello, I started my class on geometry a couple weeks ago, and I feel that I'm struggling. I took Algebra 1 and 2 over the summer, and I never had a problem. I passed both of those expedited classes never getting less than an A on any assignment, but I got a C on my first geometry test. I'm not...

I'm studying General Relativity and Differential Geometry. In my textbook, the author has written ##x^2=d(x,.)## where d(x,y) is distance between two points ##x,y\in M##. I couldn't understand what d(x,.) means. Moreover, I am not sure if this is generally true to write ##x^2=g_{\mu\nu} x^\mu...

Homework Statement The Tensions in four cables are equal: |T1| = |T2| = |T3| = |T4| = T Determine the value of T so that the four cables exert a totl force of 12,500-lb magnitude on the support. (Inser a picture of 4 connected cables angled 9, 29, 40, 51 degrees respectively) My question...

Homework Statement Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 2.7 cm . Two of the particles have a negative charge: q1 = -6.0 nC and q2 = -12.0 nC. The remaining particle has a positive charge, q3= 8.0 nC . What is the net...

I am looking to pick up one of these texts, but I don't really want to buy all three. Is there a considered favorite? Thanks in advance. B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity T. Frankel: The Geometry of Physics B. Schutz: Geometrical Methods of Mathematical Physics

Homework Statement Two lines passing through a point Μ are tangent to a circle at the points A and B. Through a point С taken on the smaller of the arcs AB, a third tangent is drawn up to its intersection points D and Ε with MA and MB respectively. Prove that (1) the perimeter of ▲DME, and (2)...

In Euclidean geometry, the Cauchy-Schwarz inequality is ##|e\cdot f| \le |e||f|##. In a Minkowskian signature, the inequality is reversed for timelike vectors. Apparently for spacelike vectors it depends on whether the two vectors span the light cone...

The following passage has been extracted from the John Stewart's English translated version of the "Sir Issac Newton's two Treatises: Of the Quadrature of Curves, and Analysis by equations of an infinite number of terms" http://archive.org/details/sirisaacNewtons00stewgoog: Here Newton...

Homework Statement As shown in the diagram below, the shape consists of a square and a circle with centre Q. Given that QM = 3 cm, prove that MN = 6 cm. Known data: -- triangles APB and BQC are congruent -- angle BMC = 90 -- triangles BMQ and BNA are similar and right-angled 2. Homework...

I've got this project that I'm having trouble pinning down. I'm cutting a pic up into squares to make a sort of jigsaw puzzle. I want the pieces to be a pleasing shape and the number of pieces to be within a small range. - proportions of pic: 3:2 (so, say 6000 wide by 4000 high) this is...

Hello guys . Through all the analysis of theory of general relativity we used what so called Manifolds Manifolds as we know are topological spaces that resemble ( look like) euclidean space locally at tiny portion of space And an euclidean space is the pair ( real coordinate space R^n , dot...

I'm in my last semester of my undergraduate majoring in mathematics (focusing on mathematical physics I guess - I'm one subject short of having a physics major) and am wondering, largely from a physics perspective if it would be better to do a functional analysis course or a differential...

I have finished reading both books on geometry by Kiselev and now look to move on but can't find any book to let me do so. Specifically, I would like a nice comprehensive book that goes into detail on transformations, isometries, coordinate geometry, symmetry, mensuration, and vectors. Now I'll...

The problem a) find the length of AD in the figure b) Why are there two solutions in a) and what solution fits the figure? Figure The attempt I started with drawing a "help line" in the figure. The cosine formula for AC with respect to triangles ADC and CBA gives us two equations: ##...

What are some rigorous theoretical books on mathematics for each branch of it? I have devised a fantastic list of my own and would like to hear your sentiments too. Elementary Algebra: Gelfand's Algebra Gelfand's Functions & Graphs Burnside's Theory of Equations Euler's Analysis of the...

Homework Statement ABC is a triangle with I as the centre of the incircle and K as the centre of the circumcircle (I ≠ K). d(X) is the sum of the distances from a point X inside the triangle to the three sides. Verify if d(P)=d(Q) (P and Q are points inside the triangle), the lines PQ and IK...

Homework Statement http://i.imgur.com/lnk7e0D.png CDE is an equilateral triangle inside a circle, with side length 16. FGH is also an equilateral triangle and F is the mid point of DE. Find the length of the side FGH. Should be expressed as Asqrt(B)-C. Where A B and C are positive integers...

Homework Statement http://i.imgur.com/lzTN7If.png Excuse the bad drawing Point E lies on the side AC of the square ACBD. The segment EB is broken up into 4 equal parts as well as the segment ED. If JK = 3 find the area of the quadrilateral FGKJ[/B] Homework Equations Trapezoid equation to...

Hello fellow science enthusiasts! I will start by describing my problem. I am majoring in Computer Science. More importantly, I am taking a course in Single Variable Calculus I. We are using the textbook written by Stewart: Calculus Early Transcendentals. And as I continue read through it...

Hi all, I'm interested in the behavior of electric fields in a gravitational shockwave geometry. I'm specifically thinking about gravitational shockwaves due to null shells as discussed, for example, in Dray-'tHooft http://www.sciencedirect.com/science/article/pii/0550321385905255 (available...

Homework Statement Basically there are 3 plate capacitors, with a distance a between the first two and b between the last two. In between the first two plates is voltage V. A particle of charge q is released from the first plate, and when it leaves the second plate it is no longer...

I'm planning to write about analytical geometry, but I'm unsure about where to start. The course that I've taken begins with the definition of a vector, it then proceeds to develops all the vector algebra and all properties. After it reaches the cross product and triple product it begins to...

I think this will probably turn out to be one of the most important QG papers this quarter. It is based on some very interesting and groundbreaking work by Dittrich and Geiller that has come out over the past year and a half. I'll give links to that after posting the main abstract...

I neet to do a structured triangular mesh 2D of a complex geometry with FORTRAN Can someone help me!

"Then, since on the circumference of each of the circles ABDC and ACK two points A and C have been taken at random, the straight line joining the points falls within each circle, but it fell within the circle ABCD and outside ACK, which is absurd. Therefore a circle does not touch a circle...

What are the geometric shapes that you can find in daily life?

I don't fully understand hyperbolic space. I saw a numberphile video about it. I thought It would a cool idea to make a video game based around hyperbolic space. I was going make it in html5/css/javascript. I know I need to learn a lot of math. I was going to render the hyperbolic objects in a...

Hi, Just wondering. Has anyone tried Harold Jacobs Geometry first edition (1974). I've considered getting it instead of 2nd edition, but don't know how big the difference is between them.

In a trivial optimization problem, when seeking the value of x2 that minimizes y(x2)/(x2-x1), the solution is graphically given by the tangent line shown in the figure. I'm having a lot of difficulty understanding why this is true, i.e., the logical steps behind the equivalence supporting the...

Say you have a box with a round marble on it. Classically I would have no problem describing that, but how is it done in general relativity? Do one just assume that the marble is round and that the box is ... boxy... in the 3D subspace at a certain foil of time? (Foliation is the correct term...

Hi I'm looking for 2 books 1. a big geometry and trigonometry book that covers almost everything (also proofs) from basic to intermediate so i have a solid understanding of geometry trigonometry. 2. a geometry or trigonometry that gives you an appreciation for trigonometry fx how it was used...

Hello, I am studying for an analytic geometry final but I am totally lost for this problem... We didn't even cover this topic in class (my prof didn't show up for class for two weeks) and I have no clue on how to do it. If anyone could help I would appreciate it. Question: Prove that the...

Homework Statement the radius from the symmetry to center of the plasma is about 6.2 metres and the minor radius is 2 metres Homework Equations Can you guys help me to make the plasma geometry for MCNP? The Attempt at a Solution the softcode of plasma geometry

What is the relationship between the nitrogen inversion (or "flip-flop" or "turning itself inside out") and the associated microwave radiation of the ammonia molecule ?

Homework Statement Let g_{\mu\nu} be a static metric, \partial_t g_{\mu\nu}=0 where t is coordinate time. Show that the metric induced on a spacelike hypersurface t=\textrm{const} is given by \gamma_{ij} = g_{ij} - \frac{g_{ti} g_{tj}}{g_{tt}} . Homework Equations Let y^i be the coordinates...

In the euclidean plane, point A is on a circle centered at point O and point O is on a circle centered at point A. What is measure of angel BAC? So I drew a picture, and it seems that BAC is going to definitely be greater than 90 degree's. From there I am confused on what to do next. Anyone...

What is the greatest possible area of a triangle that has one vertex at the center of a circle with radius 1 and the other 2 vertices on the circumference of the circle? Can anyone give me some insight into this? I was thinking maybe make the center angel 90 degree's? If so my circle would have...

i found that in Anechoic chamber there are pyramidal structures over the walls, what are the geometries of the height and base of those pyramids? W and H on the picture:

I had vaguely read somewhere a while ago that Ed Witten was developing some sort of new geometry where the only true, fundamental objects were worldsheets. Perhaps I'm not correctly remembering the idea but I think it was something like this. Has he announced this recently? I can't seem to...

I've been quite under desperate lately. I got no clue on how to solve this (apparently easy) geometry problem: Consider a circle C of center O in a plane and a line segment AB not necessarily outside the circle C. Having no compass, just a pen and a simple ruler, construct 2 points M and N...

My understanding: When we draw a triangle on a flat piece of paper and measure the angles using a protractor, the sum of the angles is ##180^\circ##. So we conclude that the universe is locally flat. Suppose we draw a very big triangle that spans across galaxies (say, using lasers and mirrors)...

Homework Statement See attached picture Homework Equations For any rectangular prism, the formulas are the following: Surface Area = 2(lw + wh + hl); l is length, w is width, and h is height. Volume = lwh; l is length, w is width, and h is height. For a square-based prism, the formulas are...

Homework Statement I need to find optical power (reciprocal focal length) of this system with thin lens Homework Equations I tried to solve this using spherical diopter equation n1/a+n2/b=(n2-n1)/R where a is object distance and b is image distance The Attempt at a Solution equation for...

I'm performing a 3D CFD simulation in ansys fluent on a laboratory in order to verify the pressure map and overall ventilation design. During meshing, ansys is displaying the following error "The mesh file exporter does not support overlapping geometry in Contact Regions. Please resolve the...

In my textbook, its given that the equation of family of circles touching a given circle S and line L is ##S+\lambda L=0## So to find the equation of family of circles touching line L at point P(p,q), can i use the same equation taking S to be a circle of radius zero and center at P? That is...

Homework Statement a) Suppose that A,B,C,D are four "points" in a projective plane, no three of which are on a "line." Consider the "lines" AB, BC, CD, DA. Show that if AB and BC have a common point E, then E = B. b) From a) deduce that the three lines AB, BC, CD have no common point , and the...

Maybe a little bit of a fresh mathematical virgin thing to ask, but what exactly is the definition of analytical geometry? I am asking for the reason I have recently acquired a book on the subject, but I found it by accident, and I would like to comprehend the most basic concepts of it! I am...

Atyy spotted 3 potentially important LQG papers and added them to the biblio thread. The B-O approximation has proven essential in quantum chemistry and similar applications dealing with wave functions of complex systems with many components. Geometry is such a system and it seems reasonable...

Hi everyone, I have an undergrad in Physics from an Indian University. And presently I am pursuing a masters in theoretical physics in UK. Here I got a chance to explore courses in the math department. I took two courses in geometry : Differential geometry and Geometry of General Relativity. I...

Homework Statement The corners A, B and C of a triangle lies on a circle with radius 3. We say the triangle is inscribed in the circle. ∠A is 40° and ∠B is 80°. Find the length of the sides AB, BC and AC. Homework EquationsThe Attempt at a Solution I found out the arc AB is 2π, arc BC is 4π/3...