Geometry Definition and 999 Threads

Today, I was at an award ceremony, where in one out of the two scientific lectures, the professor was teaching the basics of Hyperbolic Geometery. However, due to time constraints, he had to teach very fast, and there was no laser pointer, nor a chalkboard, so he couldn't explain very well...

Given a,b,c construct a trigon ABC with :BC=a,BD=b,BA=c. BD is the bisector of the angle ABC

Dear all, I would need mathematical help to solve for the temperature field in an annular geometry (you find a picture attached below the text): A copper pipe containing a boiling two-phase flow (in the stratified regime) is immersed in a liquid bath, which temperature ##T_{IY}## is assumed to...

Homework Statement Three close-packed planes of atoms are stacked to form fcc lattice. The stacking sequence of the three planes can be altered to form the hexagonal close packed structure by sliding the third plane by the vector r over the second. If the planes in the fcc structure are all...

I still have some confusion of the concept of spacetime as geometry. Specifically, what confuses me is causality related to this geometry. My understanding is that stress-energy of matter/energy curves spacetime, the curvature of spacetime tells matter/energy how to move, and dictates to...

https://www2.jpl.nasa.gov/teachers/attachments/parallax.html It's written that they find the distance by calculating from the parallax angle. But how do astronomers find the parallax angle?

I'm wondering what could happen if we remove one axiom from Euclidean geometry. What are the conseqences? For example - how would space without postulate "To describe a cicle with any centre and distance" look like?

I am trying to find out the interference condition between tool and a part. The below attached snapshot is the equation between interference and machine feed. At dy/dx = 0, I will have max. interference, which I intend to find. Except x and y every alphanumeric character in the following...

Prove that tangents to the focal cord of parabola are perpendicular using the reflection property of parabola ( A ray of light striking parallel to the focal plane goes through the focus, and a ray of light going through the focus goes parallel) I don't know whether this is solvable with just...

Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Geometry Continue reading the Original PF Insights Post.

My mother's boyfriend's son who is in 6th grade asked me a question about the math they are learning. I thought it wouldn't be too bad but I cannot for the life of me figure it out. A solution would be greatly appreciated. 1. Homework Statement https://postimg.org/image/1tsa4v4t8r/ Homework...

Hello! I started reading some differential geometry applied in physics (wedge product, Hodge duality etc.) and how you can rewrite classical theories (Hamiltonian Mechanics, Electromagnetism) in a much nicer way. Can someone point me towards some reading about how can more information be...

Could I get recommemdations for textbooks that start by defining cosine and sine using power series and then recover their geometric properties? John Roe's "Elementary Geometry" does that, but it's not in my current university's library.

Homework Statement An observer from sea level watches a ship sail away from shore. If the ships height is ##\epsilon \ll 1## after scaling with the radius of the earth, show that the distance the ship disappears will be about ##\sqrt{2\epsilon}##. Homework Equations Nothing comes to mind. The...

What is a symplectic manifold or symplectic geometry? (In intuitive terms please) I have a vague understanding that it involves some metric that assigns an area to a position and conjugate momentum that happens to be preserved. What is 'special' about Hamilton's formulation that makes it more...

Homework Statement Prove or disprove: Every translation is a product of two non-involutory rotations. Homework EquationsThe Attempt at a Solution :[/B] I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...

Currently I am face deep in three math books- my issued text for algebra, Schaum's Elementary Algebra, and Kiselev's Book I (Planimetry). I love the stuff so far and want to be as knowledgeable as possible for when I can declare my major to Physics. One thing I know for sure is that algebra...

Show that y≈∆φ×secφ in the jpeg attached. or ∆y = sec φ A and B are points on curved surface, two lines are extended through origin to a line that is tangent to the circle, these points are A' and B', change in Angle will bring a change in length between A' and B'. I need to know how is this...

I posted the following on a phone forum and got no replies, as expected. It's a bit out-of-the-way and technical. Thought this might be a better place since the question still interests me. I'm using my phone to take photos of assembly procedures on my electronics workbench. However, the focus...

Homework Statement A quadrangular pyramid OABCD with square ABCD as the bottom. OA = 1, AB = 2, BC = 2 Also, OA perpendicular to AB, OA perpendicular to AD. Question 1 : Find the inner product \overrightarrow {OA}.\overrightarrow {OB} and the size of the cross product |\overrightarrow...

In classical general relativity, gravity is simply a curvature of space-time. But, a quantum field theory for a massless spin-2 graviton has as its classical limit, general relativity. My question is about the topology of space-time in the hypothetical quantum field theory of a massless spin-2...

How much would time pass between watching the sun set from ground level and then watching it set again from the top of a sky scraper? I heard once that this could be done using one of the towers of the World Trade Center. So I assume one could also do this using the Sears / Willis Tower in...

My goal is to do research in Machine Learning (ML) and Reinforcement Learning (RL) in particular. The problem with my field is that it's hugely multidisciplinary and it's not entirely clear what one should study on the mathematical side apart from multivariable calculus, linear algebra...

In a thread that is now closed in the QM sub-forum someone wrote: Isn't spacetime supposed to be fixed, "it just is", not changing or evolving? To which I replied: These days we know the core of GR - its simply this - no prior geometry (it's dynamical) which is the exact opposite of the...

Hi, I am seeking to understand better how this well accepted idea: "...according to general relativity, gravity is a manifestation of the geometry of spacetime." (https://en.wikipedia.org/wiki/Loop_quantum_gravity) is compatible with the equally well accepted idea that gravity travels at the...

The Problem is #16 in the attached picture. Essentially, I need to find the length of BC using information about congruency and the location of the centroid. I've been able to show a whole bunch of things, but nothing that gets me close to actually finding out the missing side length. I began...

I am discussing physics with a friend and we need someone to confirm a thing that we're not agreeing on. We are discussing incident light that is passing through different geometries, and I want to know how the light behaves when it reflects inside a half sphere (of glass for example). Maybe...

1. The problem statement, all variables, and given/known data Triangle ABC has a point D on the line segment AB which cuts the segment in ratio AD : DB = 2 : 1. Another point E is on the line segment BC, cutting it in ratio BE : EC = 1 : 4. Point F is the intersection of the line segments AE and...

Hey all, I was wondering if anyone had any good tips on debugging mcnp geometry? I'm an intermediate user working on better understanding the program. Does anyone have any tips or tricks that go beyond simply reading the manual?

Henry Wrinkler who played the Fonz in the 1970s sitcom Happy Days took geometry several times in high school. Henry said that he never understood the Pythagorean Theorem. In several recent and not so recent interviews, Henry Wrinkler aka THE FONZ talked about the fact that his parents put him...

Hello! Can someone point me toward some (introductory) problems in differential geometry with solutions (preferably free)? Thank you!

Is it possible to have a magnetic field of a any geometry we want, or there are only few types of geometries that can be achieved with permanent magnets and electromagnets? If the former, how do we produce a magnetic field of specific geometry? For example, can the magnetic field be cylindrical...

Suppose if we have a cube: The volume of the cube is the product of the length, width and the height. All this time, I've been looking at it as: To get the volume, multiply the area of the cross section of the cube by how many "layers" it has. To elaborate with the diagram given, one can see...

I was wondering if I read Kiselev's geometry books, would it count as a whole high school geometry curriculum? Currently, I am reading his first book, Planimetry, which is coming out as promising. I am planning to self-study geometry.

Homework Statement Prove that any chord perpendicular to the diameter of a circle is bisected by the diameter. Homework EquationsThe Attempt at a Solution I was thinking that maybe I could form two triangles, show that these triangles are congruent, and then conclude that the two lengths of...

Homework Statement It is not ordinary problem, it is connected to it. I don't understand a figure and how is described. The problem is here http://www.pmaweb.caltech.edu/Courses/ph136/yr2011/1102.2.K.pdf How did equation 2.4 from figure 2.3 arise? Why disappear ##\Delta t^2## from the right...

I am trying to make a spirally fluted pipe in ANSYS. I made the cross section as in the attached figure and sweeped on a straight line perpendicular to plane of the cross section. However I get a sort of a drill bit instead of the required spirally fluted pipe. Is there an issue with the cross...

Thought this was fascinating.. http://google.com/newsstand/s/CBIw4N3PyjU All the need to do now is make them compulsory.

Hi, all. I would like to read books about the topics - Geometry, Real Analysis and Electricity and Magnetism. And I find the followings. Are they decent and rigorous? Geometry The Real Numbers and Real Analysis Introduction to Electrodynamics Classical Electricity and Magnetism Electricity...

Hi, the question is from Serge Lang - Basic mathematics, Page 171 exercise 6. Thing to prove: Let ΔPQM and ΔP'Q'M' be right triangles whose right angles are at Q and Q', respectively. Assume that the corresponding legs have the same length: d(P,Q)=d(P',Q') d(Q,M)=d(Q',M') Then the right...

I have a body in 3D-space and I would like to calculate the rotation axis when the body moves from A to B. I know the location (x, y and z) and the orientation (rx, ry and rz (axis angles)) at both A and B. The difference between A and B is small. The time instant during a dynamics simulation...

Hello Everybody! Concept of Solid Angle was pretty much straight forward until they were on surface patches were taken into account which were visualized as base of cone. I am having difficult when 3d Objects like Sphere/Cylinder . We can very easily calculate the respective area and plugin the...

Connections between algebraic structures and geometries are mentioned in almost any course of modern geometry or algebra. There are monographs dedicated to the subject. Unfortunately, the books, I managed to find, are written for professional mathematicians. I am looking for a book that focuses...

Hi all, According to the sunrise equation, the hour angle of the sun at sunset is: cos H = -tan(a)tan(d) where H = the hour angle, a = latitude and d = solar declination angle. This equation says that H at sunset = -H at sunrise. Now, I have a few questions concerning that: 1) I was...

I came across this paper on the Geometry of M.C. Eschers work, thought I'd share the link. :smile: http://www.math.cornell.edu/~mec/Winter2009/Mihai/section1.html

Homework Statement Recall that in hyperbolic geometry the interior angle sum for any triangle is less than 180◦. Using this fact prove that it is impossible to have a rectangle in hyperbolic geometry. Homework EquationsThe Attempt at a Solution - I wanted to use the idea that rectangles are...

Hello, the name's Mike and I'm a newbie here, I have a question pertaining to solar angles required to calculate a solar panel's hourly generation over one year. Total solar irradiance on a tilted surface equals the sum of the direct, diffuse and reflected component. In my case, reflection is...

Homework Statement Question: An ant starts at one vertex of a solid cube with side of unity length. Calculate the distance of the shortest route the ant can take to the furthest vertex from the starting point. Now, in the answer, the cuboid is unfolded and a rectangle of side 1 and 2 is...

1. Is GR about fixed curved background or dynamical...When Einstein first proposed GR.. did he mean it to have fixed curved background or dynamical? 2. As I understand it. At present. We treat GR as fixed curved background.. so that when we do QFT in curved spacetime, we fix the stress-energy...

Hi all, I'm stuck on progressing a problem i have received some feedback around as detailed below. I would greatly appreciate some assistance, and thank you in advance for your time and contributions. So i have a linear system: Which is row reduced to: I have identified that the system has...