Geometry Definition and 999 Threads

  1. S

    A A couple of long questions on positivity bounds for UV-complete EFTs

    I had two rather long questions about the recent programe on searching for UV-completions of EFTs through positivity bounds (that is, UV completions that obey fundamental constraints given by QFTs: unitarity, locality, causality, analyticity and Lorentz invariance) Question #1: The EFT-hedron...
  2. M

    A Question about intersection of coordinate rings

    I want to prove that ##\mathcal{O}_{\mathbb{A}^n}(\mathbb{A}^n \setminus \{0\}) = k[X_1, \ldots, X_n]## for ##n \ge 2## and some user on another forum gave this proof: "We know that ##\mathcal{O}_{\mathbb{A}^n}(\mathbb{A}^n \setminus \{0\}) = \bigcap_{i = 1}^n \mathcal{O}(D(X_i))##, where...
  3. H

    Obtaining the moment of inertia of a sphere and spherical shell

    I have made an attempt, which I give below. There are two issues. The first is that I am missing a factor of 2 in the MOI of the sphere. The second issue is that the integral I am getting for the spherical shell is very complex. I have tried symbolab and it chucks out some horrible things. This...
  4. jeff einstein

    Vector addition and parallel vectors problem

    source of question: https://www.tes.com/teaching-resource/vectors-harder-gcse-practice-questions-for-edexcel-1ma1-syllabus-12621082 Found this vector question by a google search, apparently a person has made this question and it seems almost impossible to solve it without using geometry. Even...
  5. B

    I 4D Mobius strip

    if 2d = mobius strip 3d = klien bottle what could 4d be??
  6. wrong thunder

    I Exploring Interesting Mathematical Puzzles

    I thought it would be fun to start a thread where we can share and discuss interesting mathematical puzzles. Whether you have a puzzle you've been pondering or a favorite one you'd like to challenge others with, feel free to post it here. Let's see how many we can solve together! Here's one to...
  7. AnselmsApprentice

    I Modeling the Kaluza-Klein theory

    I am a retired lawyer who has been pondering tiny 5th dimensions since I first heard about them in 1986. I think I sort of understand the Kaluza-Klein theory in a geometrical sense. I'm trying to connect the dots of what I think I understand to what the standard model predicts. Does anybody here...
  8. M

    MCNP geometry error

    I've got a small geometry related error in my MCNP input deck, corresponding to cell #14 (the outer edge of my detector model). This should be a quick fix, but I'm running into issues defining that particular union of surfaces. Any assistance is appreciated.
  9. L

    I ABC triangle with integer sides

    I can find radius of incircle of ADE and incircle of ABC triangle but I don't know how them help me.
  10. P

    A Curvature with different connections on the two-sphere

    Suppose we have a 2-sphere, and an associated metric. For specificity $$d\theta^2 + \sin^2 \theta d\phi^2$$ On this 2-sphere, lets consider two different connections. The Levi-Civita connection, where geodesics are great circles, and a connection with torsion where the curves of constant...
  11. ishigg

    Need my mind refreshed on geometry

  12. Osas

    MCNP Geometry Error when I try to create a sliced geometry in a torus structure

    In a study I did in MCNP, I want to create a sliced geometry in a torus structure. But MCNP cannot calculate the volume of the geometry I created. What should I do about this issue? 2 0 -50 -12 13 3 0 #2 12 pz 34.4985 13 pz -34.4985 50...
  13. D

    I Relation between a circle and line in complex plane

    I was reading a book on complex numbers where I stumbled upon this article. I was following it when I found some error. The distance between the center of circle and line should be mod(z star - z1) right? Z0 is just any random pt on line. They have continued this fallacy in example 3.10...
  14. Q

    Courses Double Accelerating Plan in Math

    Hello All, I am an 8th grader taking honors geometry at the high school. I am accelerated in math by one year, but it quickly got boring and I wanted to do honors algebra II. I took the test for geometry (midterm and final) and failed to pass. This was about 4 months ago. I am trying to double...
  15. murshid_islam

    B Which conditions should I check to see if a quadrilateral is a square?

    If I'm given the coordinates (edit: in a plane) of 4 vertices of a quadrilateral, which conditions should I check to see if it is a square? Will it be sufficient if I check if - all 4 sides are equal all 4 angles are right angles (or even 2 angles are right angles?) or are there other...
  16. M

    MCNP TR Transform Card Question

    I'm trying to rotate an RPP 45 degrees around the y axis (BUT NOT THE ORIGIN Y AXIS, rather the y axis at x=a, z=b). Is there a way to do this in MCNP? I've tried every single possible combination of angles and inputs to no avail. Again, I have an RPP that is not centered at the origin and I...
  17. M

    Help debugging a geometry-related error in my MCNP input deck

    I'm looking for someone to help troubleshoot my MCNP input deck. I'm getting a geometry related error most likely due to some sort of surface overlap. Haven't been able to identify the issue myself, so I'd appreciate a secondary check. Thanks!
  18. D

    B A tilted container with water inside - how to calculate the distance A?

    We are trying to control a container with water inside. The container has two phases of operation. In one phase, the container is tilted. In this tilted state, the distance from the observation point (red dot) to the surface of the water (distance B) is known from a measurement device. However...
  19. paulb203

    Locus of all points -- Imprecise question?

    TL;DR Summary: When asked to show the LOCUS OF ALL POINTS how precise should the questioner be? I was asked to draw THE LOCUS OF ALL POINTS 3cm from a line. I measured 3cm above and below the line, and drew two parallel lines there. Then drew two semi-circles with radii 3cm out from either...
  20. adf89812

    When do cyanide ligands form a tetrahedral geometry with Co2+ ?

    Is there something about the repulsion of the lone pair on thenitrogen that prevents the cyanides being all on the same plane?
  21. barryj

    I What is the name of this geometry theorem?

    In geometry, there is a theorem pertaining to whether given an angle, side, and side gives 0, 1, or 2 triangles. See figure. In the figure, if x = 10sin(30) then there is exactly 1 triangle, if x > 10sin(30) then 2 triangles if x < 10sin(30) then no triangles. I think this has a theorem name or...
  22. A

    MCNP: Help constructing the geometry for this pinpoint chamber please

    I try to build this geometry in mcnp, but I'm having difficulties. Can anyone help me? I'm having a lot of trouble defining these curves. A small introduction will help me a lot.
  23. lauripro56

    Python Help solving a geometrical matching issue with Graph Neural Networks

    Hello! I wish to understand which lines and vertices in different 2D orthographic views of a 3D object correspond to each other. This information would also later be used to construct a 3D model from the 2D orthographic views. Blue shows matched edges/lines. Orange shows matched...
  24. tellmesomething

    Find the limit of the sum of the areas of all these triangles

    Firstly im not sure if the new triangle that we make of height 3 times the original height of an equilateral triangle of side a, will be an equilateral triangle as well or not. I assumed it would be, please let me know if I interpreted the question wrongly. Continuing this train of thought I...
  25. G

    Placing a pole with maximal radius subject to constraints

    I have a problem that I imagine does not have a closed-form solution and requires the use of some kind of optimization solver. I am not an engineer myself, so forgive me if the question seems stupid. The problem is as follows: I have a circle bound in a square, and an arm going from the center...
  26. S

    Correct statement related to common tangents of circles

    Let R = radius of big circle and r = radius of small circle. I worked out that ##R \times r=144## but then not sure how to proceed. I also know AB = CD = 24 cm. Thanks
  27. H

    Triangle of centroids

    Here is my sketch: The triangle ##abc## is arbitrary, the triangles ##acp##, ##abq##, and ##bcr## are equilateral with centroids ##m##, ##n##, and ##k##. I suspect that the triangle ##mnk## is equilateral. Here is my proof. By the equation for centroids, ##3m=a+c+p## ##3n=a+q+b## ##3k=b+c+r##...
  28. H

    B Clever Geometry in this Video

    Something I never would have suspected.
  29. W

    I A way to comprehend the geometry of a hypercube

    It's extremely hard, if not outright impossible, for our limited brain to visualize 4D objects. 3D objects are fine, but 4D is just impossible (except, maybe, to some people). However, at one point I figured out a way to comprehend (in some ways "visualize") the 4-dimensional hypercube, which...
  30. BadgerBadger92

    B What do people mean when they say “space is flat?”

    Please excuse my ignorance I hear some people say that space is flat. What exactly do they mean by this?
  31. U

    B Do we 100% know what the geometry of the Universe is?

    If big bang existed, than universe must be sphere, because explosion expand in all direction.. I read that universe is maybe flat so how this is possible? Why can we with telescope determine shape of universe?
  32. S

    B What would need to be possible to make a cube of circles?

    in what geometry would a cube of circles be possible
  33. Anachronist

    B Circle tangent to two lines and another circle

    I'm trying to solve this for a model I'm making in OpenSCAD. Given a circle of radius r centered on the origin, and two perpendicular lines at x=a and y=b, where is the center (x1,y1) of a circle that is tangent to both lines and the centered circle? Here's a picture: I thought it would be...
  34. N

    B Confused about dot product multiplication

    I'm confused about what we are really measuring when taking the dot product of two vectors. When we say we are measure "how much one vector points in the direction of the other", that description is not clear. At first I thought it meant how much of a shadow one vector casts on another and I...
  35. P

    I On a proof of the converse of the supporting hyperplane theorem

    The converse of the supporting hyperplane theorem states Here's the "proof": I've been told that any proof that does not use the fact that ##C## has non-empty interior will not work, because it easy to construct counterexamples of sets that will fail if they have empty interior. I'm not sure...
  36. A

    I Converse of focus-directrix property of conic sections

    In my recent study of Conic Sections, I have come across several proofs (many of those comprise Dandelin spheres) showing that the cross-section of a cone indeed follows the focus-directrix property: "For a section of a cone, the distance from a fixed point (the focus) is proportional to the...
  37. AndreasC

    I Geometry of Cherenkov radiation

    As an explanation to the Cherenkov angle, images such as this are offered: This is used to explain the Cherenkov angle θ at which the Cherenkov radiation appears to be propagating. To figure this angle out however one has to assume that the wavefronts are tangent to each of these circles, so...
  38. M

    Struggling with a geometry puzzle - area of garden path

    Could you please help me understand why the answer picture says the length of the two sides of the triangle are 1.33 yard each? Thanks
  39. I

    1st year high school geometry proof

    I have proved that triangles around the equilateral triangle are congruent, but I don't know how to prove that they are arranged in such a way that they actually do form an equilateral triangle. Like, do I write that they do form an equilateral because it's given in the problem that triangles...
  40. DaveC426913

    B Deceptively simple geometry question on SAT test

    Fascinating, and utterly unintuitive. This is a question that appeared on the American SAT test until it was recently removed. (citation: Veritasium, to which I will not link at this time.) Every student ever has gotten it wrong, and that's because the SAT writers got it wrong too. The...
  41. Lotto

    What is a focal length of a thin convex lens?

    I think that there might be several solutions. I drawed one possible situation: I think that this is just geometry, but I don't know how to solve it simply. I had an idea that if the beam was going through the black axis, then it would be easy to calculate, and that would be aslo solution for...
  42. Mohmmad Maaitah

    Engineering Improving Geometry Skills for Mechanical Engineers: A Recommended Book List

    I can't find the angle between F(Big arrow in my drawing) and the y-axis! I am terrible in geometry, what book do you suggest to me as Mechanical Engineer to get better at geometry?? This is my attempt to solution and the figure:
  43. deuteron

    Why does the given conserved quantity mean the motion is on a cone?

    TL;DR Summary: . An electrone moves in a magnetic field ##B(\vec r)=g \frac {\vec r}{|\vec r|^3}##. Why does the conservation of the quantity $$\vec J=\vec r \times\vec p +eg\frac {\vec r}{|\vec r|}$$ mean that the motion is on the surface of a cone?
  44. S

    I All possible QFTs from geometry?

    Physicist Nima Arkani-Hamed has taken an approach to understand fundamental physics based on geometry (specifically, positive geometry). This started with his work with Jaroslav Trnka in the amplituhedron [1] and later it was generalised to the associahedron [2],the EFT-hedron [3]... I was...
  45. A

    A What is the geometry of a gauge potential in the A-B experiment?

    Hi, this is a question about an article in the Scientific American magazine. In 1981 Bernstein and Phillips wrote an article about fiber bundles and quantum fields, and I believe it's still a useful reference, the kind of thing lecturers would use at university. Anyway, my question is, how do...
  46. resurgance2001

    How does Rotating an Ellipse change its equation?

  47. DaveC426913

    B How does one draw a logarithmic scale?

    So I'm playing with this visualization from this other thread and I'm brute-forcing the "days" scale because don't really know how to place the marks. (by brute-forcing, I mean I am using SUVAT to calculate the distance one can travel in one day, then redoing it to calc the distance in two...
  48. wrobel

    B A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints

    I actually do not understand where to place this thread. Hope that it is a high school level problem. There are two triangles ABC and PQR. The vertex A is a middle of the side QR. The vertex P is a middle of the side BC. The line QR is a bisector of the angle BAC. The line BC is a bisector of...
  49. Mr X

    I Resource help for co-ordinate geometry

    Can someone provide me with some free resources (classes, books, notes, sites anything) for co-ordinator geometry? I want to study it from the basics while understanding the logic of every step and build upto start of collage level. Note ; non free resources are welcome too, but free resources...
  50. S

    Run MCNP 5 input file of certain geometry for flux calculation

    Can any one please explain if I want to run mcnp 5 input file of certain geometry for flux calculation on different surfaces. So far as I know If I increase the NPS (number of particles) it wll give more accurate result but when I increase NPS from 10e9, input file do not run and close within a...
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