Geometry Definition and 999 Threads

Homework Statement Hartle, Gravity, P9.8 A spaceship is moving without power in a circular orbit about a black hole of mass M, with Schwarzschild radius 7M. (a) What is the period as measured by an observer at infinity? (b) What is the period as measured by a clock on the spaceship...

Here is my formula for the area of n layers of appolonian gasket(assuming no circles past the nth layer): $$πR^2 - (πR^2 - (\sum_{0}^{n} x_n*πr_{n}^2))$$ Here R is the radius of the outer circle, r is the radius of an inner circle, x is a function that represents the number of circles in a...

There is a graph showing n on its x-axis and its total stopping time on its y axis. From here we can see that the points on the graph are not random at all; they have some kind of geometric pattern that is due to the 3x+1 in the odd case and x/2 in the even case. I have seen many attempts to...

Homework Statement Let S be a sphere with the equation ##(x-2)^2+y^2+z^2=2 ## and let p a line which satisfies the condition ## p \in (\Pi \cap \Sigma) ## where ##\Pi## and ##\Sigma## are planes with equations: ##\Pi :x+z=2## ##\Sigma: 5x-2z=3## a) Show that S and p have exactly one common...

Homework Statement line m2-to-m is 3km longer than line m1-to-m what are lengths for ##M~~M_2## and ##M~~M_1## Homework Equations pythagorean theorem hopefully can be used The Attempt at a Solution use the picture to your advantage in hopefully creating a valid system of equations. With...

Homework Statement 23. In a ABCD quadrilateral let P,Q,R,S be midpoints of sides AB,BC,CD and DA. Let X be the intersection of BR and DQ, and let Y be the intersection of BS and DP. If ##\vec{BX}=\vec{YD} ## show that ABCD is a parallelogram . Homework Equations ## (\vec{a}\cdot\vec{b})=0##...

I was in a primary school class room the other day and the teacher asked me for help with this geometry problem, that he had set for his class as an extension challenge, but then realized he couldn't do. The known angles are marked in degrees. We have to find the angle x. I spent five minutes...

Okay, I have read on spinors here and there but I really don't understand geometrically or intuitively what it is. Can someone please explain it to me and how/when it is used? Thanks!

Homework Statement the trajectory γ: ℝ→ℝ3 of a charged particle moving in a uniform magnetic field satisfies the differential equation γ''= B x γ'(t) . where B = (B1, B2, B3) is a constant 3-vector describing the magnetic field, and × denotes the vector product. (a) Show that the particle...

Dear Physics Forum personnel, Is it possible to learn differential geometry simultaneously while learning the relativity and gravitation? I have been reading Weinberg's book (currently in Chapter 02), but I believe that modern research in relativity is heavily based on the differential...

I want to build a model of how the ecliptic interacts with the horizon. The horizon appears to be a flat circle, so I thought I'd use a CD sized shape for that. What shape would I use for the ecliptic, and how large relative to the CD? I would like it to be as close as possible to the my...

Reading the English translation of Einstein's seminal paper on GR. http://einsteinpapers.press.princeton.edu/vol6-trans/90?ajax This paragraph below on p78 doesn't make much sense to me. Could you provide a second English translation or even adding math notation. "Before Maxwell, the laws...

Hello, My 14 year-old son just started ninth grade. Last year in eighth grade in middle school, he completed a Regents ninth grade level science (living environment) class and its corresponding lab and a Regents ninth grade level advanced algebra class. He passed both Regents exams both of...

I am actually very confused on how to solve the problem. Do I just find the distance between the lines? How do I incorporate the 500 Newtons into the problem? Really confused.

Homework Statement I've been looking at examples of motion derivations for my class, and it's honestly just very confusing. I heard Dynamics should prep you for this but I must have had a very poor course because we never had to understand geometry and physics to this degree... Homework...

Homework Statement The global topology of a ##2+1##-dimensional universe is of the form ##T^{2}\times R_{+}##, where ##T^{2}## is a two-dimensional torus and ##R_{+}## is the non-compact temporal direction. What is the Fermi energy for a system of spin-##\frac{1}{2}## particles in this...

Homework Statement Given the diagram below, showing the path of a geocentric satellite S flying over a ground station G, find an expression for the geocentric semi-angle ##\phi## in terms of ##\epsilon##, the radius of the Earth ##R_E##, and the height of the orbit ##h##. Homework Equations...

This is a programming issue, but the question is really about geometry. Let me 'splain. I am making a page control in HTML/CSS/JS *no wait - come back! I swear it's not about programming!* that allows the user to play with the opacities of three overlapping images (eg. imageA = opacity 60...

can some one show me how to work this out

Homework Statement Predict the hybridization and geometry of the indicated atom. Answer all parts. Homework Equations CH3CH2 There is a ( - ) sign above the second C Hybridization = ? Geometry = ? The Attempt at a Solution I know I'm supposed to count the groups around the atom, but I'm...

I would like to begin my first exploration of the arts of differential geometry/topology with the first volume of M. Spivak's five-volume set in the different geometry. Is a thorough understanding of vector calculus must before reading his book? I read neither of his Calculus nor Calculus on...

How are those two geometries realeted? Conformal geometry is a metric geometry. Projective geometry is not. But the stereographic projection is related to the conformal geometry. Or does someone know a book/ notes where the individual geometries (affine, projective, euclidean, hyperbolic...

Simple geometry can compute the height of an object from the object's shadow length and shadow angle using the formula: tan(angleElevation) = treeHeight / shadowLength. Given the shadow length and angle of elevation, compute the tree height. What I have so far: import java.util.Scanner...

So, I'm reading a physics book, and it talks about Newton's three laws, of course, but then after that it says that if a force of f pushes on an object at angle Θ, then the force in the x direction is f ⋅ cos(Θ), and the force in the y direction is f ⋅ sin(Θ). Where did THAT come from? Do we...

How can i use F4 tally in hexagonal lattice geometry which composed of circular fuel assembly? For example one hexagonal lattice includes circle which is cell number 5 and another hexagonal lattice includes circle which is cell number 7 etc. I want to use all these cells in one f4 tally. Please...

I.e. x,y,z

So I have a rectangular section as my geometry that needs to be formed in three stages. So after 1st operation I want to take that deformed shape and perform another operation (all analysis use Explicit Dynamics). Is this possible in ANSYS? Thanks in advance

A problem on geometry proof Hi (Smile), When considering the \triangle ABM E is the midpoint of AB & EO //OM (given).I think this is the way to tell AO=OM , Help .Many Thanks (Smile)

I tried about an hour to solve this but couldn't get the ratios to work I assume there are isoseles triangles in this but that is just observation

Hi, there is a book of dg of surfaces that is also about tensor calculus ? Currently i study with Do Carmo, but i am looking for a text that there is also the tensor calculus! Thank you in advance

Hi,I have been stuck on this problem The midpoints of the sides AB and AC of the triangle ABC are P and Q respectively. BQ produced and the straight line through A drawn parallel to PQ meet at R. Draw a figure with this information marked on it and prove that, area of ABCR = 8 x area of APQ. I...

The Riemann-Christoffel Tensor (##R^{k}_{\cdot n i j}##) is defined as: $$ R^{k}_{\cdot n i j}= \frac{\delta \Gamma^{k}_{j n}}{\delta Z^{i}} - \frac{\delta \Gamma^{k}_{i n}}{\delta Z^{j}}+ \Gamma^{k}_{i l} \Gamma^{l}_{j n}- \Gamma^{k}_{j l} \Gamma^{l}_{i n} $$ My question is that it seems that...

Hi guys, I'm thinking of maybe of studying differential geometry as part of my undergraduate degree. However, it's not for physicists, it's a full on formal mathematics course specifically for mathematicians. I'm not sure whether it's a bit overkill and won't actually be useful. We don't have a...

Hello from Italy I'm switching from CS to Physics BS because i personally find it more various and interesting (and in Rome there is one of the best physics school in the world). Mathematical analysis is a common subject and my credits will be recognised but i didn't study Linear algebra yet...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused...

Projective Algebraic Geometry - the Projective Plane ... Cox et al - Section 8.1, Exs 5(a) & 5(b) I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra...

I'm trying to self-study general relativity, but I encounter a problem. I can easily understand the ideas and the results, but there are some things related to 4-d geometry that I can't find, like what are Christoffel symbols and how to solve the equation of a geodesic line. I searched for those...

As the title implies, I'm looking for books on non-euclidean geometry. I'm not looking for very advanced thing, more on some book with a good introduction to this topic.

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on...

I do not get the conceptual difference between Riemann and Ricci tensors. It's obvious for me that Riemann have more information that Ricci, but what information? The Riemann tensor contains all the informations about your space. Riemann tensor appears when you compare the change of the sabe...

This is not a homework question. School year has ended for me and I'm doing some revision on my own. I want to proof the following because in an exercise I had to find the equation of the line that passed through a given point and 2 given lines. If a line r intersects with 2 given crossing...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on Chapter...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on Chapter 8...

hi.. i want to import only the geometry defined in mechanical apdl into ansys workbench so that i want to have the freedom to change the geometry and meshing whenever i want to. thankyou

Hello, I was wondering if anyone knows about the the book "The Geometry of Spacetime: An Introduction to Special and General Relativity" by Callahan and what their opinions are. Thanks!

Hello, I would like to know if anybody here has used the book "Differential Forms and the Geometry of General Relativity" by Tevian Dray and how they found it. Thanks!

Can someone help me with this? (dA/dt)=1cm/s (cm^2 whatever...leave out trivial corrections). A=pir^2 (dA/dt)=2pir(dR/dt) Multiply through by (1/2pir) (dA/dt)/(2pir)=dR/Dt What is the rate of change of the radius for a circumfrance of 2 I just used the related rates formula that I derived for...

I have found a way to construct a pentagon using only the grid system. The internal angles are all within 99% accuracy and all the angles to the 3rd decimal add up exactly to 540 degrees. This is without the use of a compass and bearing in mind that the internal lines intersect at the ration of...

I recently decided to take a whack at this problem. Came up with an interesting approach, thought it would make a good conversation topic. Anyone else tried to do this? What were your results?