Tim_Lou Posted May 20, 2004 Report Share Posted May 20, 2004 i've been working on the formula of the sum 4th power during these days. (found it by myself.....i spent like hours....however, it is found that there is a discovered formula for this...waste of time lol....) anyway,it is done: nsigma k^4= [n(n+1)(2n+1)(3n^2+3n-1)]/30k=1 i spend lots of time working on this.... and the relationship of sum of nth power. any comments?or do you have any math work to share? anything? i would love to discuss something about math! thx to anyone who replies! about anything!: ) Link to comment Share on other sites More sharing options...
Tormod Posted May 20, 2004 Report Share Posted May 20, 2004 Well, I am not a math wiz...so you'd have to explain this to me. What is the "n" - does it mean "integer"? And what does "k=1" stand for? Tormod...who never aced his math classes... Link to comment Share on other sites More sharing options...
Tim_Lou Posted May 20, 2004 Author Report Share Posted May 20, 2004 well an example would be this: nsigma (k)= 1+2+4+5+6.....+n (sum from 1 to n *must be integer*)k=1 (if k=0, it would be from 0 to n...) my 4th power would be: nsimga (k^4)=1^4 + 2^4 + 3^4 + 4^4 +5^4 .........+n^4k=1 (i did these works secertly in class *math class is too boring*, it took me a lot of work to find out forumla of 1^4+2^4.....n^4) (haha, finally, there are somethings that tormad doesnt know....; ) ) Link to comment Share on other sites More sharing options...
Tormod Posted May 20, 2004 Report Share Posted May 20, 2004 You know, there is actually one other thing I don't know, but I fail to remember what it is! But I *have* read lots of popularized accounts of math (or physics) history...like "E=Mc2" by David Bodanis, and "It Must be Beautiful" by Graham Farmelo. And my father-in-law makes geometric puzzles which we just recently started to sell in the spanking new Hypography store at http://www.hypography.com/sciencestore/ (shameless plug)... Tormod Link to comment Share on other sites More sharing options...
Freethinker Posted May 21, 2004 Report Share Posted May 21, 2004 Originally posted by: TormodAnd my father-in-law makes geometric puzzles which we just recently started to sell in the spanking new Hypography store at http://www.hypography.com/sciencestore/ (shameless plug)... Saw those. NEAT! And I was just thinkiing that you needed a Cafe Press T shirt. As to a math discussion. Is the concept of "even/ odd" just a philosophical one? Does "even/ odd" exist in nature? Link to comment Share on other sites More sharing options...
Tim_Lou Posted May 21, 2004 Author Report Share Posted May 21, 2004 hmmm even and odd.... even = 2xodd = 2x+or-1 well.................. hmm........lets ask, is zero odd, even or neither??............... Link to comment Share on other sites More sharing options...
Freethinker Posted May 21, 2004 Report Share Posted May 21, 2004 No Tim, not "what is even/ odd", but does the concept actually exist in nature, or is it only a human construct? And arbitrary differentiation humans invented? Link to comment Share on other sites More sharing options...
sanctus Posted May 21, 2004 Report Share Posted May 21, 2004 Sorry tim_Lou if the math toppic becomes a physics topic, but .... Yes, there is even and odd in nature a quanton is a boson if he is constituted of a even number of fermions and it stays a fermion if there is an odd number of fermions (I have to say I just read that, it's not that I know much about). But I agree if this is the only case where we find something that has to do with even/odd in nature then it is more a human concept. Link to comment Share on other sites More sharing options...
Tormod Posted May 21, 2004 Report Share Posted May 21, 2004 I am not sure if the numbers themselves are to blame for this. I think "numbers" are a human invention, especially the floating point numbers and the negative integers (to say nothing of imaginary numbers, qubits, field mechanics etc). Another thing is the type of strange phenomena like the fibonacci sequence which can be found all over the place - in sunflowers. how branches are located on a tree, the ratio of the sprial arms of a galaxy. Yet the fibonacci sequence is simply a series of number where each number is the sum of the previous two: 0 1 1 2 3 5 8 13 21 ad infintum If we hadn't invented numbers we would probably never see this sort of thing. But does that mean that mathematics is the foundation of our universe? Tormod Link to comment Share on other sites More sharing options...
Freethinker Posted May 21, 2004 Report Share Posted May 21, 2004 Originally posted by: sanctusYes, there is even and odd in nature a quanton is a boson if he is constituted of a even number of fermions and it stays a fermion if there is an odd number of fermions (I have to say I just read that, it's not that I know much about). Originally posted by: TormodI am not sure if the numbers themselves are to blame for this. I think "numbers" are a human invention,...Another thing is the type of strange phenomena like the fibonacci sequence which can be found all over the place - in sunflowers. how branches are located on a tree, the ratio of the sprial arms of a galaxy. Yet the fibonacci sequence is simply a series of number...If we hadn't invented numbers we would probably never see this sort of thing. But does that mean that mathematics is the foundation of our universe? Perhaps it does. It SEEMS that nature sets things up in "countable" groups. Even wave/ particle collapse seems oriented towards individual elements, not some continous stream. Matter seems to have a finite smallest size. there seems to be a discrete number of electrons/ protons/ ... in an atom and specific measurable quantities of atoms in different molecules, ... Or do all these things exist like this because we expect them to? Does the wave collapse into a singular particle because that is what we are measuring for? Do numbers exist because we want them to? Or did we discover numbers because nature is broken into discrete units? Link to comment Share on other sites More sharing options...
lindagarrette Posted May 23, 2004 Report Share Posted May 23, 2004 consistent sequences in nature are physical phenomenon we can visualize if we examine them numerically. There is really no such thing as a particle or an instant in time. We like to think in terms of static conditions because they are easier to work with. Pandora Link to comment Share on other sites More sharing options...
lindagarrette Posted May 23, 2004 Report Share Posted May 23, 2004 Here is a site on fascinating numbers in nature: http://www.brantacan.co.uk/fibonacci.htm "So the whole Fibonacci thing is an accident. The rule is that the leaves or florets grow for maximum space. The rest - Fibonacci numbers, spirals, pretty patterns - follows automatically. In this context, the Fibonacci numbers are like the magic numbers in nuclear physics. The difference is that if plants had never existed, the Fibonacci numbers would still have interesting properties, whereas the values of nuclear magic numbers are dependent on the properties of nuclear forces, and are not in themseleves interesting. Very far from the floor of the valley of stability the values may even be slightly different from the normal ones. Furthermore, if the universe could have been created with slightly different fundamental constants, the nuclear magic numbers could have been different, but any life-form that could grow like plants would still show the GS and Fibonacci numbers. Perhaps the whole of physics is like the plant numbers. Perhaps the many elegant laws that so many people have struggled for so many years to create are just an accidental reflection of a few deep rules that we do not know. For example, from the use of the Lagrangian function, many laws can be recovered. The laws of refraction and reflection can be deduced from the simple rule - light takes the path of least time. " Pandora Link to comment Share on other sites More sharing options...
Freethinker Posted May 23, 2004 Report Share Posted May 23, 2004 Originally posted by: lindagarretteconsistent sequences in nature are physical phenomenon we can visualize if we examine them numerically. There is really no such thing as a particle or an instant in time. We like to think in terms of static conditions because they are easier to work with. Pandora Uncertainty, just like Zeno's Arrow paradox 2500 years before, shows that we can know EITHER the instant or the motion. A solid arrow can be examined at any time. It will be the same solid arrow whether stationary or moving. We will never know it to be an object in motion. But we will know it's motion. So we think in EITHER static or motion, but not both. Link to comment Share on other sites More sharing options...
lindagarrette Posted May 23, 2004 Report Share Posted May 23, 2004 I'm trying to figure out if there is such a thing as a particle, or mass, for that matter (so to speak). Superstring theory seems to indicate there are only waves at the bottom of it all except perhaps for 'branes' which may be something solid. Any clues? Here's a brief description from a math web site. PandoraDistinction between waves and particles. It is essential that one understand the distinction between waves and particles. A classical particle is something that has: position, momentum, kinetic energy, mass and electric charge. A classical wave has the attributes of: wavelength, frequency, velocity, amplitude of the disturbance, intensity, energy and momentum. The most distinctive difference between the two is that a particle can be localized, whereas a wave is spread out and occupies a relatively large position of space. There is one important difference between photons and massive objects in the way their waves and particles are related. Because for a photon, only one rule is required to get both wavelength and frequency from a photon's particles of energy and momentum. A massive object, on the other hand, requires separate rules for its wavelength and frequency. There is some conflict between previous classical ideas and those of the theory of matter waves. For example, the concept of a classical trajectory of a particle must be discarded and replaced by a probability distribution spread over a large region of space. But, with the application of Freire's enunciated that major flaw in the development of the wave theory of matter, no need the probability to find out the particle position in a certain region. Because the wave is spread out and occupies a relatively large position of space, I would say equivalent to an expansion of (nq*Y) in the space. That is why it is need to find out the particle through the probability. http://www.jfreire.com/extend_html/extend3.htm Link to comment Share on other sites More sharing options...
Tim_Lou Posted May 23, 2004 Author Report Share Posted May 23, 2004 ........................................................... i should've realized that this forum is mainly about science....math is.....well, this topic somehow changed back to physics........anyway, keep going.... just ignore me....keep going... Link to comment Share on other sites More sharing options...
GAHD Posted May 24, 2004 Report Share Posted May 24, 2004 "Do numbers exist because we want them to? Or did we discover numbers because nature is broken into discrete units?" Would have to say discreet units. best example being the solar system; the planets, moons, sun, all are distinct (though some are amorpherous). This " odd unit" (singular meaning odd) thinks that numbers exist because we discovered them, and gave them names. Odd to discover something that doesn't exist in any physical sence. Link to comment Share on other sites More sharing options...
Freethinker Posted May 24, 2004 Report Share Posted May 24, 2004 Originally posted by: Tim_Lou........................................................... i should've realized that this forum is mainly about science.... math is..... well, this topic somehow changed back to physics........ anyway, keep going.... just ignore me....keep going... Sorry Tim. When I was around your age I also enjoyed working with equations. I remember "doscovering" quadrtic equations. I'd solve them just for kicks.... I know, I was a strange kid.... I was a teacher's aid in College, but that was primarily treaching slide rule.... ya THAT long ago. Back when you had the THINK... lol Now I seem more interested in the philosophy behind it. That math is not just about working with symbols that represent quatities and functions, but why and from where. But it will not help you to keep a topic in the area you want by promoting an inferiority complex, you just need to find an equation that catches. Link to comment Share on other sites More sharing options...
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