What is Symbols: Definition and 292 Discussions

A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication (and data processing) is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas, or visual images and are used to convey other ideas and beliefs. For example, a red octagon is a common symbol for "STOP"; on maps, blue lines often represent rivers; and a red rose often symbolizes love and compassion. Numerals are symbols for numbers; letters of an alphabet may be symbols for certain phonemes; and personal names are symbols representing individuals. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space.
The academic study of symbols is semiotics. In cartography, an organized collection of symbols forms a legend for a map.

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  1. M

    Is There a Downloadable Package of LaTeX Symbols Available?

    TL;DR Summary: Looking for downloadable package of symbols Hi; I am picking up on the suggestion of using LAtex. I know the symbols are mostly in Word scattered about the place. Is there a downloadable package do you know that I could access please. Thanks Martyn
  2. N

    Correct Usage of Partial Derivative Symbols in PDEs

    Some may say that ##\frac{ \partial g }{ \partial t }## is correct because it is a term in a partial differential equation, but since ##g## is a one variable function with ##t## only, I think ##\frac{ dg }{ dt }## is correct according to the original usage of the derivative and partial...
  3. Jessie24789

    I Doppler Shift & Christoffel Symbols Issues

    About a month or two ago I started doing simulations of light physics around black holes and yesterday I got a fast Christoffel symbols function for the Schwarzschild metric in cartesian coordinates, but now the photon ring appears flipped. I feel as though it is wrong. But as I am still pretty...
  4. Onyx

    B Calc. Christoffel Symbols of Hiscock Coordinates

    The Hiscock coordinates read: $$d\tau=(1+\frac{v^2(1-f)}{1-v^2(1-f)^2})dt-\frac{v(1-f)}{1-v^2(1-f)^2}dx$$ ##dr=dx-vdt## Where ##f## is a function of ##r##. Now, in terms of calculating the christoffel symbol ##\Gamma^\tau_{\tau\tau}## of the new metric, where ##g_{\tau\tau}=v^2(1-f)^2-1## and...
  5. M

    Without evaluating the Legendre symbols, prove the following....

    Since ## p=73 ## in this problem, how should I prove that ## \sum_{r=1}^{73-1}r(r|73)=0 ##? Given that ## 73=1\pmod {4} ##.
  6. DaveC426913

    What Is the Simplest Artistic Representation of Nucleotide Symbols ACGT?

    My brother is a gene scientist and wants a piece of art that contains the symbols of the four nucleotides ACGT. He described the symbols as "really nothing more than the benzene ring with a bump in certain places". What is the simplest possible way to symbolically represent them? (i.e. short...
  7. G

    I The Christoffel symbols at the origin -- Why zero?

    "the christoffel symbols are all zero at the origin of a local inertial frame" Why must it be at the origin? If it is not?Thanks!
  8. A

    I Arithmetic representation of symbols according to certain rules

    Hi, Suppose I am given a sequence of special symbols and I want to produce the next sequence of symbols according to certain rules that transform one symbol into one or more symbols. They are 10 symbols in total, say; A, B, C, D, E, F, G, H, I, J The rules are: A transformed into B and it is...
  9. W

    [EZ] I could really use some help understanding the following symbols....

    Hey guys! I'm looking at a few resources and I came across an interesting one on the Aviation Stack Exchange Page. Interestingly enough, another individual is working on implementing flight mechanics / aerodynamics using code and had similar questions to me, but to be honest, I'm not quite sure...
  10. theycallmevirgo

    Is there a good source for construction blueprint symbols?

    I've seen quite a few websites but I don't know how far to trust them. Is there a book I could use? Thanks so much Joe
  11. George Keeling

    I Contracted Christoffel symbols in terms determinant(?) of metric

    M. Blennow's book has problem 2.18: Show that the contracted Christoffel symbols ##\Gamma_{ab}^b## can be written in terms of a partial derivative of the logarithm of the square root of the metric tensor $$\Gamma_{ab}^b=\partial_a\ln{\sqrt g}$$I think that means square root of the determinant of...
  12. A

    B The difference between the symbols ##=## and ##\equiv##

    I have struggled for a long time to understand the difference between the meaning of the concept of 'equality' and 'identity' as represented by the symbols ##=## and ##\equiv##. Can someone explain it to me and give examples where ##=## does apply and ##\equiv## does not and vice versa?
  13. plum356

    Writing some ZF axioms with FOL symbols

    The axioms: My work: Extension:$$\forall x\forall y,\,(x=y)\iff(\forall z,\,(z\in x\iff z\in y))$$ Empty Set:$$\exists x|\forall y,\,\neg(y\in x)$$ Pair Set:$$\forall c\forall d,\,\exists e|(c\in e)\wedge(d\in e)\wedge[\forall f,\,\neg((f=c)\vee(f=d))\implies\neg(f\in e)]$$ If you consider any...
  14. J

    Sixty Symbols YouTube question guy

    I love the Sixty Symbols you tube videos. But I'm curious, does anyone know who the whiny-voiced guy who sometimes asks off-screen questions is? Thanks.
  15. U

    Help with Kaluza Klein Christoffel symbols

    If I want to calculate ##\tilde{\Gamma}^\lambda_{\mu 5}##, I will write \begin{align} \tilde{\Gamma}^\lambda_{\mu 5} & = \frac{1}{2} \tilde{g}^{\lambda X} \left(\partial_\mu \tilde{g}_{5 X} + \partial_5 \tilde{g}_{\mu X} - \partial_X \tilde{g}_{\mu 5}\right) \\ & =\frac{1}{2}...
  16. Arman777

    The contracting relations on the Christoffel symbols

    I am trying to find $$\Gamma^{\nu}_{\mu \nu} = \partial_{\mu} log(\sqrt{g})$$ but I cannot. by calculations, I manage to find $$\Gamma^{\nu}_{\mu \nu} = \frac{1}{2}g^{\nu \delta}\partial_{\mu}g_{\nu \delta}$$ and from research I have find that $$det(A) = e^{Tr(log(A))}$$ but still I cannot...
  17. D.S.Beyer

    I Solving GR 2-Body Problem with Summ. of Christoffel Symbols

    Can you approach the GR two body problem through summations of multiple Schwarzschild solutions? Specifically, by using the Schwarzschild metric for each body of mass, then adding the Christoffel symbols together, to arrive at a new geodesic equation. Take point C between bodies A and B...
  18. docnet

    I Covariant derivatives, connections, metrics, and Christoffel symbols

    Is a connection the same thing as a covariant derivative in differential geometry? What Is the difference between a covariant derivative and a regular derivative? If you wanted to explain these concepts to a layperson, what would you tell them?

    General Relativity: How many Christoffel symbols?

    Actually I know there would be some permutations used here. I know how to calculate the symbols but estimating is quite a new thing to me
  20. rude man

    LaTeX Finding Missing Symbols in LaTeX: An Enhanced Primer

    E very once in a while I see a post in which LaTex symbols appear that are absent from the primer offered in PF. Examples: \bf A in lieu of the awkward \mathbf A ## \ell ## for script l. There must olbviously be a list of the 28 letters that can be scripted. The font section in my LaTex...
  21. brotherbobby

    Product of two Kronecker delta symbols as a determinant

    I don't have a clue as to how to go about proving (or verifying) the equation above. It would be very hard to take individual values of i,j and k and p,q and r for each side and evaluate ##3^6## times! More than that, I'd like a proof more than a verification. Any help would be welcome.
  22. JD_PM

    Mathematica Learning how to compute Christoffel symbols using Mathematica

    I am using the code provided by Artes here, but I am missing something. The Chrisfoffel-symbol formula is $$\Gamma^{\mu}_{\phantom{\mu}\nu\sigma}=\frac{1}{2}g^{\mu\alpha}\left\{\frac{\partial g_{\alpha\nu}}{\partial x^{\sigma}}+\frac{\partial g_{\alpha\sigma}}{\partial x^{\nu}}-\frac{\partial...
  23. C

    I Trying To Calculate Christoffel Symbols

    I am trying to create a function to calculate the Christoffel Symbols of a given metric (in this case the Shwartzchild metric). Calculating the (non zero) Christoffel Symboles for the Shwartzchild connection, I am a double major in Physics and Computer Science so I decided to go the code rout...
  24. binbagsss

    A Difference of Christoffel Symbols Transforms as Tensor

    My notes seem to imply this should be obvious : If i consider the covariant deriviative then i get something like christoffel= nabla ( cov derivative ) - partial So difference of two of them will stil have the partial derivatuves present ,assuming these are labelled by a different index ...
  25. L

    How do physicists/mathematicians verbalize these symbols?

    ##\hat{r}_{\perp}## and ##\hat{r}_{\parallel}## How do "practicing" physicists and mathematicians verbalize these symbols? If they ever do? Do I say r-hat-perpendicular and r-hat-parallel?
  26. olgerm

    I Difference between 1. & 2. Kind Cristoffel Symbols

    What is difference between 1. kind Cristoffel symbol and 2. kind Cristoffel symbol? Is the Cristoffel symbol in ricci curvature tensor 1. kind or 2. kind?
  27. S

    MHB Proving Primitive Symbols with Axioms

    Given : A) primitive symbols : (1, *) and B) The axioms: 1) \forall x\forall y[x*=y*\Longrightarrow x=y] 2) \forall x[x*\neq 1] 3) [P(1)\wedge\forall x(P(x)\Longrightarrow P(x*))]\Longrightarrow\forall xP(x) Then prove: \forall x[x=1\vee \exists y(y*=x)]
  28. P

    A Christoffel Symbols in terms of a Change in Basis

    Hi All Given that the Riemann Curvature Tensor may be derived from the parallel Transport of a Vector around a closed loop, and if that vector is a covariant vector Having contravariant basis The calculation gives the result Now: Given that the Christoffel Symbols represent the...
  29. M

    I Christoffel's symbols: symmetry in the two (lower) indices

    I have a technical problem. 1. Accordingly to historical E.B. Christoffel’s work (I think year 1869), (Christoffel’s) symbols are symmetric in the two (today writing) lower indices. 2. These symbols have been introduced when studying the preservation of differential forms of degree two. The...
  30. Luke Tan

    I Transformation of the Christoffel Symbols

    In Landau Book 2 (Classical Field Theory & Relativity), he mentions that the transformation rules of the christoffel symbols can be gotten by "comparing the laws of transformation of the two sides of the equation governing the covariant derivative" I would believe that by the equations...
  31. B

    B Equal sets with different symbols?

    {1, 2 ,3} = {1, 2, 3, 3, III}? {1, 2 ,3} = {one, dos, three}? {Tom, Dick, Harry} = {Thomas, Richard, Harrison}? Seems to me, these are undetermined until the set's "type" or "category" definition of its members is defined so as to determine what elements are members of the set... whether...
  32. snoopies622

    I Equivalent paths to the Christoffel symbols

    I've noticed that for both the surface of a sphere and a paraboloid, one arrives at the same Christoffel symbols whether using \Gamma^i_{kl} = \frac {1}{2} g^{im} ( \frac {\partial g_{mk} }{\partial x^l} + \frac {\partial g_{ml}}{\partial x^k} - \frac {\partial g_{kl}} {\partial x^m} )...
  33. D

    I Christoffel Symbols: Difference, Importance & Uses

    What is the general difference or importance between using christoffel symbols of the first kind and those of the second kind in terms of geometry and their application. The christoffel symbols of the second are identical to those of the first except with the inverse metric tensor in front...
  34. P

    I Christoffel symbols and covariant derivative intuition

    So I'm trying to get sort of an intuitive, geometrical grip on the covariant derivative, and am seeking any input that someone with more experience might have. When I see ##\frac {\partial v^{\alpha}}{\partial x^{\beta}} + v^{\gamma}\Gamma^{\alpha}{}_{\gamma \beta}##, I pretty easily see a...
  35. Haorong Wu

    I Confusions about some symbols in QC

    There are some pictures in Nielsen's book that I find confusing: Why there is a line half-crossing the X-box? Similarly, why there is a line connecting to ##f \left ( x \right )##? There are two H gates between ##\left | \psi _0 \right >## and ##\left | \psi _1 \right >##. Why one of them has...
  36. nomadreid

    I Cardinality of a set of constant symbols (model theory)

    First, I want to be pedantic here and underline the distinction between a set (in the model, or interpretation) and a sentence (in the theory) which is fulfilled by that set, and also constant symbols (in the theory) versus constants (in the universe of the model) Given that, I would like to...
  37. Baibhab Bose

    How to type mathematical expressions?

    I don't know how to type mathematical symbols and equations and stuff. Like if I want to ask something here in physics forum, I need to type mathematical expressions like everyone here does. How can I do that? Do I need any software?
  38. Math Amateur

    MHB Symbols for LOWER SEGMENT and UPPER SEGMENT .... Searcoid, Definition 1.3.4 ....

    In Micheal O. Searcoid's book "Elements of Abstract Analysis" we read the following: Help will be much appreciated ...Peter ========================================================================== It may help readers of the above post to hve access to Searcoid's text of Definition 1.3.4 ...
  39. C

    I Riemann Tensor knowing Christoffel symbols (check my result)

    I need to find all the non-zero components of the Riemann Tensor in a two-dimensional geometry knowing that the only two non-zero components of the Christoffel symbols are: \Gamma^x_{xx}=\frac{1}{x} and \Gamma^y_{yy}=\frac{2}{y} knowing that: R^\alpha_{\beta\gamma\delta}=\partial_\gamma...
  40. C

    I Christoffel symbols knowing Line Element (check my result)

    Hi! I'm asked to find all the non-zero Christoffel symbols given the following line element: ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy The result I have obtained is that the only non-zero component of the Christoffel symbols is: \Gamma^x_{xx}=\frac{1}{x} Is this correct? MY PROCEDURE HAS BEEN: the...
  41. W

    A Connection 1-forms to Christoffel symbols

    Let the metric be defined as ##ds^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2## Through some calculations, we then see that our connection one forms are ##\omega_{12} = -d \theta## and ##\omega_{21}= d\theta##, ##\omega_{13} = -sin\theta d \phi## and ##\omega_{31} = sin\theta d\phi##...
  42. JuanC97

    I Issues with the variation of Christoffel symbols

    Hello everyone, I'm sure a lot of you know that the Christoffel symbols are not tensors by themselves but, their variation is a tensor. I want to revive a post that was made in 2016 about this: The Variation of Christoffel Symbol and ask again "How is that you can calculate ∇ρδgμν if δ{gμν} is...
  43. Destroxia

    Calculating Christoffel Symbols from a given line element

    Homework Statement Given some 2D line element, ## ds^2 = -dt^2 +x^2 dx^2 ##, find the Christoffel Symbols, ## \Gamma_{\beta \gamma}^{\alpha} ##. Homework Equations ## \Gamma_{\beta \gamma}^{\alpha} = \frac {1}{2} g^{\delta \alpha} (\frac{\partial g_{\alpha \beta}}{\partial x^\gamma} +...
  44. Janosh89

    LaTeX "Trouble with Vector Symbols in Drafts - What to do?"

    Can anyone help? What is the convention for inserting the vector symbol? I have a draft with -(\vec{2.5})^2 which displays correctly in preview ##-(\vec{2.5})^2\\## why is vec troublesome and underlined in red?? Should I ignore! I realize that I'm not using a variable.
  45. SemM

    B Question about the Delta and Nabla symbols

    Hi, in some books the ##\nabla## symbol is used for the Laplacian ##\frac{d}{dx^2}+\frac{d}{dy^2}+\frac{d}{dz^2}## while others use the ##\Delta## symbol for this. What is the correct custom for this usage?
  46. W

    I Manipulating Christoffel Symbols: Questions & Answers

    I have a couple of questions about how Christoffel symbols work. Why can they just be moved inside the partial derivative, as shown just beneath the first blue box here: https://einsteinrelativelyeasy.com/index.php/general-relativity/61-the-riemann-curvature-tensor And if you had the partial...
  47. Math Amateur

    MHB < Z_n> .... Symbols Like < And > But Less "Sharp" ....

    I wish to display symbols like < and > as in < z_n > but more like the symbols in the following text ... Hope someone can help ... Peter
  48. yrjosmiel

    Other symbols for rotational inertia?

    So I'm currently doing a project on motors. It just so happens that I'm dealing with both electrical current and rotational inertia. I have one small problem. The symbol for electrical current is I. But so is rotational inertia! Are there any other symbols for rotational inertia/electrical...
  49. mertcan

    A Christoffel symbols expansion for second derivatives

    Hi, I really wonder how these second derivatives can be written in terms of christofflel symbols. I have made so many search but could not find on internet What is the derivation of equations related to second derivatives in attachment?
  50. A

    How Calculate Coriolis aceleration from Christoffel Symbols?

    Homework Statement Hi, We are trying to calculate the Coriolis acceleration from the Cristoffel symbols in spherical coordinates for the flat space. I think this problem is interesting because, maybe it's a good way if we want to do the calculations with a computer. We start whit the...