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. S

    More on fundamental frequency

    A horizontal string of length 1.5 m vibrates with a wave velocity of 1320 m/s at its fundamental freq. a. What is the fund. freq.? Do I use the formula f_1 = v/4L? b. What is the freq. of the 4th overtone and how many nodes and antinodes will it have? To find 4th's freq. use f_n =...
  2. S

    What is the Fundamental Frequency?

    Which of the following could be the fundamental freq. for a vibration that has an overtone freq. of 990 Hz? a. 330 b. 660 c. 148 d. 1980 e. 1990 (All in Hz.) The formula that I think you have to use is f_n = n*f_1, where f_1 is fud. freq. Then, I thought f_2 = 2*f_1, where f_2...
  3. Y

    Fundamental frequence of violin string

    Two identical violin strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. One of the strings is retuned by adjusting its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously. -What is the...
  4. H

    From indefinite integral to fundamental theorem of calculus, how does it all link?

    Hi there, Can someone explain to me what the following are and how each one is used as a tool for the next one: 1)Indefinite integral 2)Riemann Sum 3)Definite Integral 4)Fundamental Theorem of Calculus(The part which says that the derivative of the integral of f(t)dt from a to x is...
  5. Crumbles

    Quarks and Leptons: Fundamental or not?

    I've been trying to research this area but there doesn't seem to be much out there. Does anyone know of any evidence or theory showing that quarks and leptons are or are not fundamental? I have heard of String Theory but does string theory actually suggest that quarks and leptons are made...
  6. M

    Fundamental Counting Principle Math problem

    OK I'm unclear about how to use FCP to solve this problem: The final score in a hockey game is 5-2. How many different scores are possible at the end of the second period? :confused:
  7. P

    Help with Fundamental Frequency problem

    In order to decrease the fundamental frequency of a guitar string by 2%, by what percentage should you reduce the tension? I'm so lost can you point me in the right direction?
  8. C

    Fundamental mathematic proofs

    Fundamental mathematic proofs... I know this may seem a slightly odd question, but are there any website or pdf files, etc, floating around of proofs of the basic pricipals and "tricks" of maths? eg - adding, subtraction, multiplication, division, fractional sums and products, percentages, etc...
  9. Q

    Help with fundamental concept of calculus; limits.

    I'm a high school student and am a junior right now. I like physics, and quantum theory, perhaps because it will be our future. Therefore, in order to understand it, I need to know calculus. Since I don't have homework, I don't work out the problems. I try to understand the critical...
  10. 1

    Fundamental Thm of Arithemetic

    Wow, it has been awhile! China has been fun, but now it is time to get back to the states and also math work! Here is a problem that has been giving me some problems. It reads: \prod from i=1 to n, pi^ai for each i is the canonical representation of a, deduce a formula for the sum of...
  11. P

    Suicide THE fundamental right?

    is suicide the individuals most basic and fundamental right? is it incosiderate for individual to kill himself and deprive his family and society of himself, since it is in most cases the circumstances and inconsideration of the society that is the cause of this?
  12. R

    Experimental Determination of Fundamental EM Constants

    Can anyone provide a good reference (preferably on-line), or a decent description, of how the fundamental constants of electromagnetism are experimentally determined? I'm talking about constants like the permitivity and permeability of free space. I'm also curious how the unit of charge...
  13. tandoorichicken

    Calculating Derivative of h(x) using Fundamental Theorem

    Hello everyone, its been a while. It's been almost 4 months since I did anything calculus related so I forgot all of my skills. :bugeye: The problem is: Use the Fundamental Theorem of Calculus to find the derivative of the function h(x) = \int_{2}^{\frac{1}{x}} \arctan{t} \,dt
  14. E

    Fundamental Forces: Weak Nuclear, Electromagnetism, Strong Nuclear

    so could anyone tell me was is weak nuclear force and electromagnism force and storng nuclear forces thank you!
  15. V

    Why are the fundamental postulates of special relativity controversial?

    could someone be kind enough to explain to me why the fundamental postulates of special relativity introduced thanks
  16. A

    Fundamental therom problem

    My professer told us to think about this problem. I have the answer in my solutions manual but I want to know how I would go through the thinking process to solve it...(and others like it) The question says "Find a function f and a number a such that...
  17. D

    Confused on four fundamental forces where does color come in?

    hey, I am a bit confused about the forces. if there's four of them, where does color fit in? the hyper-physics website says that the strong force is a 'residual color fource'... but see the thing is, it also says the force-carrying boson is the pion, while the gluon carries the color force...
  18. 1

    How do you tell the difference between fundamental forces?

    I wonder how do you distinguish the fundamental forces? After all, they are each only a bunch of Newtons.
  19. O

    Number Theory ebooks: Free Fundamental Downloads

    Do you know somewhere to download ebooks on Number Theory ? (fundamental and free please :redface:
  20. F

    Fundamental Forces: Push or Pull?

    Is it known for sure that any or all of the fundamental forces produce a push or a pull affect? Thanks.
  21. F

    The Importance of Semantic Clarity in Scientific Discourse

    What is understood to be the fundamental "states" of energy? Not referring to the various "forms" of energy. Thanks for any input.
  22. E

    Fundamental particle structure table

    On http://elasticity2.tripod.com/ I have replaced all previous work with a table showing tha structural relationship between fundamental particles. (Muon and Tau will be included when I have changed the scale of current work tables). I show that there are only three fundamental particles, each...
  23. Antonio Lao

    Fundamental Nature of Space Charges

    Like quarks, space charges are also fractionally charged particles. But unlike quarks, the absolute magnitude of space charges is always 1/6 while that of quarks are 2/3 and 1/3. There are also two polarities (+/-) of space charges. The grouping of space charges forms the elementary particles...
  24. D

    Solution of my fundamental equation

    Hi Russell, New thread because I think it deserves a new thread! I think Chapter I of "Foundations" is very difficult for people to follow. Hopefully, you now understand the essence of what I was trying to communicate there. I think that, under the definitions I listed for the concepts...
  25. W

    Mathematica Reexamination of fundamental mathematical concepts

    Hi, In the attached address ( http://www.geocities.com/complementarytheory/M_E.pdf ) you can find my reexamination of fundamental mathematical concepts. Please read all of it before you air your view about it. Thank you, WWW
  26. M

    Quantum numbers of fundamental particles?

    Which are (basic?) quantum nubers of fundamental particles? I am having problems becouse a lot of expresions are used on sites on the web: el. charge, color charge, mass, taste, spin, barion & lepton number... to many :eek: :confused:
  27. S

    2nd fundamental theorem of calculus

    Can some on pleases explain this too me. I have an AP book, and i am to do a few problems out of it for class, and but can't find it in there ANY WHERE. Any help would be superb! -Jacob
  28. P

    Fundamental Particles: Definition & Properties

    Perhaps this question has been addressed before, but, allow me to ask: What consitutes the classification of a "fundamental" particle? Does a fundamental particle have ANY half-life? Seems it would not. Is a fundamental particle completely impervious to destruction?
  29. F

    Strings Most Fundamental Elements?

    Most Fundamental Elements? Science continues to discover more fundamental elements with which to govern its predictions on and to unite a wider breadth of the universe. The latest, string theory, posulates, in laymens terms, that there are even smaller elements governing all aspects of our...
  30. S

    The Fundamental Postulate Of Special Relativity Is Self-Contradictory

    Fundamental Postulate Of Special Relativity: The speed of a photon in any inertial reference frame must be measured as c, where c = 299792458 meters per second. It is provable within the framework of the special theory of relativity, that Theorem Of Special Relativity: If all...
  31. D

    Properties at the fundamental scales

    Here's one... A book has a mass of say 0.2 kg, it's red, and burns at a certain temperature. Its properties can be explained by its constituent molucular make-up. Water molecules have a pH of 7. Its enthalpy of fusion is 6 kJ/mole, etc, etc. These properties can be explained by its two...
  32. R

    String resonances and fundamental particles

    Does anyone know of any good references on the relationship between string vibrations and fundamental particles such as quarks, leptons, and the gauge bosons, containing an explicit mathematical description of said relationship? Any information would be appreciated.
  33. N

    Fundamental physical constants

    In a thread in PF's Special and General Relativity ("What if the speed of light was slower") there is a discussion on physical constants, including c. lethe pointed out that there are only 26* truly fundamental constants, and posted a link to a John Baez page with a discussion of these...
  34. J

    Bosons and Mesons - Fundamental or Compound?

    The Standard Model defines Bosons, along with Fermions, as Fundamental Particles. At the same time, Mesons, which include Bosons, are supposed to be a compound made up of a quark and an anti-quark. So, which is it? Is a Boson a fundamental particle or a compound (ie.Hadron)?
  35. M

    Is the Action Integral fundamental

    What is it about the action integral in physics? Symmetries in the action integral leads to the Euler-lagrange equations. And it seems every physical situation is described by equations that must satisfy the differential equation of the Euler-lagrange. This Euler-lagrange equation must be...
  36. P

    Fundamental Counting Principle problem

    The dial on a 3 number combination lock contains markings to represent the numbers from 0 to 59. How many combinations are possible if the first and second numbers differ by 3? What I did was: 1st number: It can be any of the 60 numbers (if we take 0 also as a #) 2nd number: I think since...
  37. E

    Only four fundamental forces in the universe?

    Are we being very naive to think that there are only four fundamental forces in the universe? I mean after all the Greeks thought that there were only four elements in the universe. How do we expect to know for sure that unification involves only those four forces?
  38. S

    Is Gravity the True Fundamental Force Behind All Others?

    theory development sure comes quick sometimes! Could our illusive Gravity be THE fundamental force and all other forces be just a variation on a theme?
  39. A

    Exploring the Possibility of a Fifth Fundamental Force

    PLease forgive my ignorance if this proves to be nothing more than a showing of how far behind I have become in the last 3 years...but here it is: I was outside mowing my lawn the other day, thinking about the universe, nature, etc., when I asked the question: "What force is causing the...
  40. Loren Booda

    Math fundamental: can linearity generate reciprocity?

    Does a nontrivial function f(cx) exist such that (d/dx)f(cx)=(1/c)f(cx) and c is constant? "Linearity" here requires that c and x in the function argument preserve their product to the first power.
  41. S

    The fundamental unit of matter

    The fundamental unit of matter is the universe itself. "Multiplication through division" -- Buckminster Fuller
  42. heusdens

    Why Is There Something Instead of Nothing?

    The Fundamental Question At the very basement of our ongoing attempt to try to understand, we might as well dig into this astonishing and fundamental question in the theory of knowledge and philosophy, which is known as the "Fundamental Question". This question is adressed as: "Why is...
  43. K

    Understanding the 4 Fundamental Forces: A Simple Explanation

    In my textbk, it says that The four fundamental forces are : a) Gravitational force b) Electric and magnetic forces c) Weak force responsible for beta decay d) Strong force which holds the nucleus together What does (c) mean? I've heard that scientists think the 4 forces were...
  44. marcus

    Baez says what if area is more fundamental than length

    This is an intriguing suggestion from John Baez in the Usenet archive at cornell http://www.lns.cornell.edu/spr/1999-12/msg0020466.html I've been fascinated by this idea and have never been sure how to take it. Is it serious or just a passing fancy? what do you think? Have you heard other...
  45. Loren Booda

    Another fundamental infinite product & summation

    Can you find the values of [oo] [pi] cos(((-1n)(2n)!)1/(2n)) n=0 and [oo] [sum] sin(((-1n+1)(2n+1)!)1/(2n+1)) n=0 ?
  46. heusdens

    What is the Fundamental Question?

    http://www.hedweb.com/witherall/existence.htm"
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