Geometry Definition and 999 Threads

My friend was doing an analytical geometry problem and a shape appeared that I wanted to find the area of with my new knowledge of integrals. I found the area and I'm now working to find an equation for the nth area as the size of the shape changes for all integers. After doing the math I come...

Hi all, I am having an issue with the following problem. I just don't know how to approach it. Homework Statement Homework Equations Ax^2 + Bxy + Cy2 + Dx + Ey + F = 0 The Attempt at a Solution I am confused on how to put this problem in terms of x & y and get numerical values for both...

I was reminded of this point by a recent discussion in the "Classification of manifolds ..." thread. The question is this: As I understand it, the NCG framework requires a Riemannian manifold. Given this, at best one could hope to obtain a Euclidean theory, right? So is it fair to say...

Question: Find the point in the plane x+2y-3z=1 with minimum distance to point (1,1,1). Attempt at resolution: Well, techinically, I already have the means to solve this. I can find the distance between the point and the plane to be 1/sqrt(14) and then I can either solve for the sphere...

Question: What are the vector, parametric and symmetric equations of the angle bissector of angle ∠ABC, given that A=(1,2,3), B=(3,4,5) and C=(6,7,0). Attempt at resolution: Well, I defined some D=(d_1,d_2,d_3) to be a point in the angle bissector, and two lines r:X=(3+2a,4+2a,5+2a) and...

Does it still have a sense of Euclid-style geometry-are there still cubes and spheres, so to speak? Is it mostly about 1D curves/2D surfaces, or does it consider higher dimensions? Are the surfaces which the field concerns mostly graphs of several variables, e.g. ## x^3+y^3+z^3=1 ##, or are they...

Author: Barrett O'Neill Title: Elementary Differential Geometry Amazon Link: https://www.amazon.com/dp/0120887355/?tag=pfamazon01-20 Prerequisities: Contents:

Universe geometry article simpify? article development for the Forum on geometry suggestions, as well as any errors etc are welcome particularly on how to keep the FLRW metrics but simplify the explanation... Universe geometry The origins of the universe is unknown in cosmology. The hot...

Here's the introduction of the paper by Freidel and Hnybida. Quantum geometry is built up of chunks of geometry that contain information relating to volume, areas, angles made with neighbor chunks, etc. The Hilbert space that these chunks (called intertwiners) live in needs a set of basis...

Is it necessary to finish Spivak's little book to move on to Spivak's Differential Geometry I, or is the material on differential forms and integration on manifolds in Chapter's 4 and 5 of Spivak's little book covered in Differential Geometry I?

Homework Statement Calculate the volume of the body that is bounded by the planes: x+y-z = 0 y-z = 0 y+z = 0 x+y+z = 2 Homework Equations The Attempt at a Solution I made a variable substitution u = y+z v = y-z w = x which gave me the new boundaries u+w = 2...

I've been developing an article on universe geometry that hopefully forum members will find as a useful reference,and would like some assistance in examining the accuracy, means of simplifying and details forum members would like added. The article is on a personal website that references...

Hello, I am new very new in this subject. I have a curiosity in understanding diff.geometry. I have some questions (which might sound elementary) to ask: (1) Is diff.geometry a subject related to the study of surface, curvatures, manifolds? (2) How it is different from Euclidean geometry...

A polygon with nonnegative area cannot be formed with fewer than 3 points. A polyhedra with nonnegative volume cannot be formed with fewer than 4 points. A hyperspace with nonnegative measure cannot be formed with fewer than n points. What I mean by "3 points" is that the cardinality of the set...

Hello, I am a beginner. I am self taught in differential calculus. Can you please suggest me any book, as a beginner, to have a very basic idea and overview on Differential Calculus. Any free e-book? Kindly suggest.

Hello, Analytic geometry has provided us with such profound tools for thinking that it is hard to imagine what thinking must have been like before we had such tools. Two particular developers of these tools are Pierre de Fermat and Renee Descartes in 17th century France. I would like to...

I could not post this to the resource forums, so I am posting it here. I am looking for a Geometry textbook for pre-service teachers. The text ideally should incorporate some constructivist practices and the use of technology to help visualize geometry problems. Most of the teachers will be...

Homework Statement Solve for the flux distribution using the 1D neutron diffusion equation in a finite sphere for a uniformly distributed source emitting S0 neutrons/cc-sec. My problem right now is that I can't figure out the boundary conditions for this problem. We usually work with...

I wonder if we can have a 1st order Goemetry

Homework Statement ds^2 = g_{tt} dt^2 + g_{tx} (dt dx + dx dt) with g_{tt} = -x and g_{tx} = 3 "Show that this is indeed a spacetime, in the sense that at every point, in any coordinates, the matrix g_{\mu \nu} can be diagonalized with one positive and one negative entry. Hint: You...

Hello. I can't seem to wrap my head around the geometry of the gradient vector in ℝ3 So for F=f(x(t),y(t)), \frac{dF}{dt}=\frac{dF}{dx}\frac{dx}{dt}+\frac{dF}{dy}\frac{dy}{dt} This just boils down to \frac{dF}{dt}=∇F \cdot v Along a level set, the dot product of the gradient vector and...

Homework Statement i'm confused as to why a molecule with 3 bonding pairs and 2 lone pairs takes on a t-shape rather than a trigonal planar shape. My notes say that this is because in a t-shape, there are less 90 degree angles between the lone pairs and the bonding pairs than in a...

Homework Statement Find parameter a so that line y=ax + 11 touches ellipse 3x^2 + 2y^2 = 11 The Attempt at a Solution| I can rewrite ellipse equation like \frac{x^2}{\frac{11}{3}} + \frac{y^2}{\frac{11}{2}} = 1 And i know that line y=kx + n touches ellipse when a^2k^2 + b^2 = n^2...

My geometry is pretty weak and I want to strengthen it.. because the other day my math teacher asked me what a tetrahedron was and I didn't know ... I've been desperately looking for this book "Geometry for the Practical Man" by J.E. Thompson. I have all the other books in the series and...

These are some of the factors I brainstormed that goes into the functionality of a spotlight: 1) Light output of the light source (measured in luminous flux, if I recall correctly) 2) The reflective potential of the reflectors surrounding the light source 3) The geometry of the reflectors...

Author: Edwin Moise Title: Elementary Geometry from an Advanced Standpoint Amazon Link: https://www.amazon.com/dp/0201508672/?tag=pfamazon01-20

Hi Friends, I am getting problem in a geometry problem. Please help me to find the answer. The problem is as follows: AB, BC, CD, AD are the tangent of circle of radius 10 cm. and center O. If the length of BC = 38 cm and CD = 27 cm. Then find the length of AB. Here tangent AB and AD are...

Hello All, I have been give a particular task with packing hexagonal shapes with radius 0.105m, into different circular areas. This is not a 3D problem, and I have been trying to search for answers on the topic of "packing" but haven't seemed to find any that fit my requirements. So the idea...

Find the missing angles in each of the following:

Let sharp triangle ABC inscribed circle $(O;R)$ and $H$ is orthocenter of triangle ABC. circle $(E;r)$ tangent to $HB$, $HC$ and tangent to in circle $(O;R)$. Prove that: midpoint of $HE$ is center of the circle inscribed the triangle $HBC$

Hi, I'm a Physics undergraduate, and this semester I have the option to choose between Geometry (Axiomatic Euclidean Geometry) and other disciplines. In the next year I want to be ready to study Differential Geometry, but I don't know if I need to study Euclidean Geometry first. The teacher of...

Homework Statement Let α(t) be a regular, parametrized curve in the xy plane viewed as a subset of ℝ^3. Let p be a fixed point not on the curve. Let u be a fixed vector. Let θ(t) be the angle that α(t)-p makes with the direction u. Prove that: θ'(t)=||α'(t) X (α(t)-p)||/(||(α(t)-p)||)^2...

I heard that some physicists are trying to determine the spacial/geometric curvature of the universe by measuring the angles of distant stars (a very large triangle). Is this possible? Or is Poincare correct when he said that there is no preferred geometry and that there is no experiment...

Homework Statement I need to derive an expression for the displacement of light as a function of thickness of glass and the angles. I will post a screen shot of the formula to be derived but it can also be found here...

Geometry Question -- Modeling bolt with flange end Homework Statement Hi I attached a picture of bolt call ed hollo bolt, in which the sleeves open when the cone pushed inside,, if i Know all the dimensions, I ask an expert and he tell me that However, the difficulty is...

We recently had a long thread https://www.physicsforums.com/showthread.php?t=666861 about cases where raising and lowering indices isn't completely natural, i.e., where a vector "naturally" wants to be upper-index or lower-index. If you have a metric, then it's pretty clear to me what...

Hi, I read in Padmanabhan's book that \nabla_a J^a=0 implies that there exists an antisymetric tensor P such that J^a= \nabla_b P^{ba}. What's the name of the theorem? Any reference? Thanks

Suppose x(t) is a curve in ℝ^2 satisfying x*x'=0 where * is the dot product. Show that x(t) is a circle. The hint says find the derivative of ||x(t)||^2 which is zero and doesn't tell me much. I was hoping for x*x= r, r a constant.

Homework Statement What is the area of a right triangle whose inscribed circle has radius 3 and whose circumscribed circle has a radius 8? Homework Equations The diameter must be the hypotenuse of the circle The Attempt at a Solution The answer is 57, but I do not know the...

Hi there. I want to learn some differential geometry on my own, when I find some time. My intention is to learn the maths, so then I can get some insight, and go more deeply on the foundations of mechanics. I need to start on the basics. I had some notions on topology when I did my analysis II...

Hi I am struggling to see how the relation: (df:U)(dh:V)-(dh:V)(df:V) (1) can be rewritten as: U(fdh:v)-V(fdh:U)-fdh:[U,V] (2) I have tried expanding (1) out by making a scalar vector product of Udh:V but i don't think that is right and i am just not sure how best to proceed. It was...

What is the difference between the Euclidean Geometry and the simple plane geometry? They seems to work with flat planes.

1. Find the volume between y-10=x and y2 -6y =x, rotated around x=1. 2. R= y2 -6y -1 r= y-10 -1 ∫2 to 5 of [(\pi(y2 -6y -1)2) - \pi(y - 11)2] ∫\pi[y4 - 12y3 + 4y2 + 12y + 1] - \pi[y2 - 22y + 121]dy = \pi[y5/5 - 12y4/4 + 4y3/3 +122/2 +y] - \pi[y3/3 - 22y2/2 + 121y] |2 to 5...

Author: Robin Hartshorne Title: Algebraic Geometry Amazon Link: https://www.amazon.com/dp/1441928073/?tag=pfamazon01-20 Prerequisities: Commutive algebra, Algebraic Geometry Level: Grad Table of Contents: Introduction Varieties Affine Varieties Projective Varieties Morphisms...

We know that the spacetime of General Relativity with a single electron in otherwise empty space is hardly curved, basically zero. In Kaluza–Klein theory with a single electron in otherwise empty space is there a type curvature due to the charge of a single electron? Is the amount of...

Here's a nice geometry problem, not hard at all if you can see what's really going on. https://lh3.googleusercontent.com/-qqF-3y81rvI/UQjt7jishKI/AAAAAAAAAII/gP8G0dgKCmc/w497-h373/cercles.gif Solution (don't click if you want to work it out yourself!):

the differential geometry is so abstract to understand. All are terms and theorem. How to understand it? can someone give me some method and guidance to learn it. HELP!

Author: Serge Lang Title: Fundamentals of Differential Geometry Amazon Link: https://www.amazon.com/dp/038798593X/?tag=pfamazon01-20 Prerequisities: Grad Analysis, Differential Geometry Level: Grad Table of Contents: Foreword Acknowledgments General Differential Theory Differential...

Author: Serge Lang and Gene Murrow Title: Geometry Amazon Link: https://www.amazon.com/dp/1441930841/?tag=pfamazon01-20 Prerequisities: High-school algebra Level: High school Table of Contents: Introduction Distance and Angles Lines Distance Angles Proofs Right Angles and...

Author: William Lewis Burke Title: Spacetime, Geometry, Cosmology Amazon Link: https://www.amazon.com/dp/0935702016/?tag=pfamazon01-20 Prerequisities: Level: