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. R

    Energy: fundamental or emergent?

    what i'd like to know is simply put this way: is energy fundamental or emergent? but more importantly, this is a fact or fiction question seeing as they (fundamental and emergent) are oposites, so can we all agree on one answer? what i mean is whatever your "opinion" at the end of the day...
  2. L

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    What would be the most fundamental equations in physics? For example, I know that all of electrodynamics can be obtained from Maxwell's Equations; therefore, Maxwell's Equations would be a complete set of the most fundamental equations of EM. However, something like PV=nRT can be derived from...
  3. A

    Fundamental Theorem of Space Curves

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  4. T

    Exploring the Standard Model: Is It Truly Fundamental?

    I was asked this question by someone else and wondered if I could get better answers here: Is it fair to say that the standard model for matter is basically descriptive, without any underlying understanding of what causes its structure? Can it be compared it to the periodic table of...
  5. J

    Why is Fundamental Math Failing Me?

    My Fundamental Math Failing This should illicit a chuckle or perhaps despair in humanity. The statement "One silver piece is equivalent to two copper pieces" is not equivalent to the equation "S = 2C" (Where S = silver and C = copper). I cannot for the life of me figure out why. I can work...
  6. F

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  7. M

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  8. Saitama

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  9. X

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  10. J

    Hamilton's Variation Principle - Fundamental Questions

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  11. R

    How much of a hydrogen atom's mass is due to the mass of fundamental particles?

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  12. M

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  13. R

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  14. B

    Derive the fundamental equation from and equation of state

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  15. H

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  16. M

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  17. O

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  18. phinds

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  19. R

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  20. R

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  21. T

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  22. R

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  23. T

    Fundamental question on GR: Basis vector meaning

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  24. S

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  25. V

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  26. J

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  27. I

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  28. J

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  29. P

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  30. phinds

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  31. S

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  32. Y

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  33. A

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  34. L

    MSc in Quantum Fields and Fundamental Forces at ICL

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  35. A

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  36. J

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    Observations show that the current density of the Universe is close to the critical density: rho = 3 H_0^2 / 8 Pi G Assuming a spherical observable Universe of constant density, together with the relation c = H_0 * R, one can rearrange the above equation to give the relation: G * M / R...
  37. T

    Fundamental source of gravity?

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  38. A

    Four fundamental forces. Which one is this?

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  39. M

    Four Fundamental Forces: What Are They and How Do They Shape Our World?

    Homework Statement Could someone give me some examples of the four fundamental forces? (Not their definitions) Homework Equations None.. The Attempt at a Solution -Strong nuclear force: -Weak nuclear force: -Electromagnetic force: Starting a car? Picking up paperclips with a...
  40. W

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  41. R

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  42. X

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  43. Y

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  44. V

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  45. A

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  46. E

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  47. K

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    I have recently been reading some of the slew of additions to the genre of layman's cosmology detailing the possibility of one (if not many!) multiverse theories. The books that I have read (including Greene's and Barrowman's) have been truly informative and I highly recommend them. I am...
  48. T

    Calculate the fundamental frequency of a steel rod

    Homework Statement 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? Homework Equations Fn=nv/2L The Attempt at a Solution since the...
  49. S

    Why do people say that mass is too fundamental to know exactly what it is?

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  50. N

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