What is Fundamental: Definition and 946 Discussions

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits.
There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then tile the space. One general construction of fundamental domains uses Voronoi cells.

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  1. T

    Why the Fundamental Theorem of Algebra & Calculus are Called "Fundamental

    Can anyone explain why the Fundamental Theorem of Algebra and the Fundamental Theorem of Calculus are called "Fundamental"? The algebra theorem states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. The calculus theorem states that an...
  2. J

    Fundamental Theorem of Calculus to find Derivative

    Use the Fundamental Theorem of Calculus to find the derivative of the function g(x) = \sqrt{x}\int sinx Ln(t) \frac{cos(t)}{t} dt g'(x) = lnx cosx / x. By integrating this function, you receive the function g(x). Then by differentiating g(x) you receive g'(x) which is what is...
  3. K

    Special relativity fundamental question

    Hi, I'm very new to special relativity and have a very basic question. A and B are moving from each other at a speed of v at some instant a light flashes in the space. A records: At time t a light flashed at x B records: At time t' a light flashed at x' Here is what I...
  4. S

    You're welcome! Glad I could help.

    What's the minimum number of objects required for a force to be present? I assume it's 2, because you'd need one object to be moved and the other to apply the force. Is this correct? Thanks
  5. G

    What if Electrons are not Fundamental? Exploring the Possibilities

    Could electrons be non-fundamental particles. What if electrons are made of other matter particles. Could these particles interact with each other and exist but had not been given much thought about its existence because the electron alone explains much phenomena except wave-particle Duality...
  6. D

    Research: Applied vs. Fundamental

    I'm graduating with a B.S. in physics and I will soon be starting a Ph.D. program in nanoscale science, which is essentially an applied physics program. I chose this program because my undergraduate research was focused in this area and I've really enjoyed it. However, I'm wondering if my...
  7. C

    Energy, Time, Position, Momentum which is more fundamental?

    Is energy more fundamental than time or vice versa? Is Momentum more fundamental than position or vice versa? Is the quantization of energy, more fundamental than the quantization of charge, or vice versa?
  8. F

    Find Fundamental Frequency of Vibrating Mylar Membrane

    Alright I've been going crazy with this problem. I'm building an electrostatic loudspeaker. In order to get it right I need to find the Fundamental frequency of the vibrating membrane. This membrane will be of an elastic substance, Mylar. Approx. 5 microns think with a young's modulus of about...
  9. P

    What can be called a fundamental theory?

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  10. S

    Exploring the 4 Fundamental Forces of Nature

    gravity: Fg = GM1M2/r^2 electro-magnetic: weak force: strong force:
  11. D

    How is the area under a curve determined using the Fundamental Theorem?

    So, the area under a curve is determined by F(b) - F(a), how does that take into account the changing area between the two extremes, a and b? I mean, since F(b) and F(a) are specific values at the ends of the graph, how is the area in between figured into it, especially if the graph is really...
  12. T

    What is the speed of sound and tension in a vibrating harpsichord string?

    Homework Statement A harpsichord string of length 1.60 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450.0 Hz. (a) What is the speed of the transverse string waves? (b) What is the tension? (c) What are the wavelength and frequency of the sound wave in air...
  13. P

    Do strings have to be the most fundamental

    Is there something in string theory that requires strings to be the most fundamental structure?
  14. S

    Fundamental Theorum of Algebra an i.

    Does the Fundamental Theorum of Algebra prove that imaginery numbers have to exist for our number system to be complete?
  15. R

    Fundamental Frequency of nylon string

    Fundamental Frequency! [SOLVED] A nylon string is stretched between fixed supports 0.75m apart. Experimental plucking of the string shows that several standing waves can exist on the string. Two such standing waves have frequencies of 225Hz and 300Hz with no other frequencies in between. Q1...
  16. hananeel

    Schools MSc in Quantum Fields and Fundamental Forces at Imperial College London

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  17. O

    Representations of the Fundamental Group

    This is not important, but it's been bugging me for a while. I'm struggling to see how the locally constant sheaves of vector spaces on X give rise to representations of the fundamental group of X. The approach I've been thinking of is the following. Given a locally constant sheaf F on X...
  18. T

    Can there be more than Four Fundamental Forces?

    We used to think gravity and electromagnetism were the two fundamental forces of nature until we discovered the strong and weak nuclear forces. Can we be wrong again and discover more forces. If not, then how are we so sure?
  19. J

    Why fundamental quantization of energy is hv?

    Now this might seem to be a very stupid question. But neverthless, I don't understand why the fundamental quantization of energy must be hv? why not any value lower or higher like hv^2 or h/v^2. Is it possible to prove that this value of quantization is most favourable than any other value...
  20. K

    Force & Volume Fundamental Units

    What are the fundamental base units for Force and Volume? I think its cm3 for volume but not completely sure.
  21. fluidistic

    Is the second's law of thermodynamics fundamental?

    Is the second law of thermodynamics fundamental? Like Newton's laws for example. I'm having doubts about the increase of entropy of any system. Poincaré stated the recurrence theorem which goes against the increase of entropy of a dynamical system with respect to time. By this theorem, a...
  22. P

    Fundamental parameter probabilities

    What are the odds that any particular big bang will result in the 20(?) fundamental parameters having the values that will allow life to form?
  23. H

    The Strand Model of fundamental interactions

    The "Strand Model" of fundamental interactions [Mentor's note: This thread is a consolidation of three different threads which were started in our Beyond the Standard Model forum. They were moved to our former Independent Research forum, because in our view this represents a "new" or "personal"...
  24. D

    Electric/magnetic lines of force's fundamental property.

    Sources say if lines are parallel they will repel else try and merge which I don't agree and even see practically. Suppose we have 2 opposite charges facing each other, the lines are parallel, they should repel. Similarly if 2 equal charges are facing each other, the direction of the lines...
  25. B

    Fundamental frequency and changes to it

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  26. J

    Fundamental frequency / sound waves

    1.Calculate the fundamental frequency of a steel rod of length 2.00 m. What is the next possible standing wave frequency of this rod? Where should the rod be clamped to excite a standing wave of this frequency? first, i used the formula velocity of sound in the rod v=sqrt(Y/p) where...
  27. C

    Proving converse of fundamental theorem of cyclic groups

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  28. S

    Fundamental Solution of Laplace Equation 2d vs 3d

    When one compares the fundamental solution for Laplace's Equation one might note that in 2 dimensions this solution becomes unbounded as r goes to infinity while in 3 dimensions the solution goes to zero as r goes to infinity. Now I understand both mathematical derivations so my question is...
  29. V

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  30. M

    What is the fundamental frequency of the string?

    One of the harmonics on a string 1.4 meters long has a frequency of 18.4 Hz. The next higher harmonic frequency is 23.9 Hz. (a) What is the fundamental frequency of the string? f1 = Hz * 5.5 OK (b) What is the speed of the waves on the string? v = m/sec the...
  31. J

    What are the frequencies of the fundamental and first two overtones?

    Homework Statement A guitar string is 90.0 cm long and has a mass of 3.17 g. From the bridge to the support post is 60.0 cm and the string is under a tension of 506 N. What are the frequencies of the fundamental and first two overtones? (f1,f2,f3) Homework Equations v=sqrt(FT/m/l)...
  32. A

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  33. M

    Fundamental reasoning:Electromagnetic Wave - Visible Light

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  34. M

    The fundamental group of the disk is trivial, why?

    How do we show that the fundamental group of the disk D^2={(x,y) in RxR: x^2 +y^2< or eq. to 1} is trivial? I know how to show that the fundamental group of the circle is isomorphic to the group of the integers under addition, but for some reason, I don't see a way to show that the...
  35. G

    How fundamental is inverse square law?

    A convincing way to reason inverse square law (of classical EM and gravity) is a conservation of the field lines as one proceeds away from a source... http://hyperphysics.phy-astr.gsu.edu/HBASE/forces/isq.html It appears as a reasonable and intuitive thing to expect... but, it does NOT seem...
  36. J

    Fundamental frequency and higher harmonics

    Could someone validate if this is correct? for waves with antinode/antinode or node/node ends if the fundamental frequency is f1 then f2 = 2f1, second harmonic and f3 = 3f1, third harmonic but for waves with antinode'/node or node/antinodes at the ends then if fundamental frequency is...
  37. M

    Fundamental group of the circle S^1

    The question is to prove that the fundamental group of the circle S^1 is isomorphic to the group of integers under addition. So I think I should show that the following map Phi is an isomorphism. Phi: F(S^1, (1,0)) --> Z defined by Phi([f])= f*(1) where f* is the lifting path of f (...
  38. P

    Fundamental doubt in Thermodynamics

    in Thermodynamics, in a book i have read that during expansion of a gas(system), W(on system by surroundings)=-ve..They have proved it using W=-force(external)*displacement. They are saying as displacement is positive and force is always considered as positive, W=-ve. But, how did they determine...
  39. H

    Fundamental Solutions of Linear homogeneous equations

    Homework Statement Can y = sin(t^2) be a solution on an interval containing t = 0 of an equation y'' + p(t)y' + q(t)y = 0 with continuous coefficients? Homework Equations The Attempt at a Solution y = sin(t^2) y' = 2tcos(t^2) y'' = 2cos(t^2) - 4t^2sin(t^2) 2cos(t^2) -...
  40. R

    Fundamental frequency of a guitar string

    1. The problem is: A guitar string is 78 cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 60 cm, and the string is under a tension of 505 N. What is the frequency of the fundamental? I don't get why it gives me two distances. Which one is L? 2. The...
  41. M

    Comparing Coulombic & Gravitational Fundamental Forces

    Could some one help me understand the difference and the similarties between Coulombic fundamental force and Gravitational fundamental force?
  42. N

    Fundamental frequency of violin string

    Homework Statement A vibrating string on a violin is 330 mm long and has a fundamental frequency of 659 Hz. What is its fundamental frequency when the string is pressed against the fingerboard at a point 60 mm from its end? *The answer is 805 Hz Homework Equations f = \overline{}nv/2L...
  43. D

    Can Linearly Dependent Solutions Form a Fundamental Set?

    For a second order linear differential homogeneous equation, if the two solution y1 and y2 is a multiple of one another. It means that it is linearly dependent which mean they can not form a fundamental set of solutions to second order differential homogeneous equation. Am I correct?? or...
  44. L

    Fundamental question: why do we age?

    Cells are constantly being replaced at a high rate, but why does our skin wrinkle nonetheless? When you workout or are involved in any physical activity, and you eat enough protein, muscle tissue is being built and repaired. Why do reflexes slow? It's still the same or nerve channels being...
  45. N

    Fundamental Frequency of a string

    Homework Statement The length of a string is 1440 cm. The string is held fixed at each end. The string vibrates in eight sections; i.e., the string has eight antinodes, and the string vibrates at 150 Hz. What is the fundamental frequency? Answer in units of Hz.Homework Equations f = nv / 2L...
  46. P

    Harmonic to have an amplitude higher than the fundamental

    Is it possible for a harmonic (produced by a stringed instrument) to have an amplitude higher than the fundamental. If so how?
  47. K

    Fundamental definition of temperature

    The fundamental definition of temperature is T^{-1} = \frac{dS}{dE} How can I verify that the dimensions work in this equation?
  48. C

    Fundamental standing wave problem

    Homework Statement A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is: A) 32 Hz B) 16 Hz C) 8 Hz D) 4 Hz E) 2 Hz Homework Equations v = \lambdaf L =...
  49. Q

    Fundamental equations that are at the root of all physics?

    Hi all :D, Is there such a thing as fundamental equations that are at the root of all physics? Thanks PS If yes- then please provide a link to it if possible. Thanks
  50. T

    Fundamental reason behind Aufbau principle

    This principle states that the electron starts filling from the lowest energy up. Why?
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