hey, Lets start some math discussion!

[Tim_Lou]

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:

n
sigma k^4= [n(n+1)(2n+1)(3n^2+3n-1)]/30
k=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!
: )

[Tormod]

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...

[Tim_Lou]

well

an example would be this:

n
sigma (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:

n
simga (k^4)=1^4 + 2^4 + 3^4 + 4^4 +5^4 .........+n^4
k=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....; ) )

[Tormod]

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

[Freethinker]

Originally posted by: Tormod
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)...

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?

[Tim_Lou]

hmmm even and odd....

even = 2x
odd = 2x+or-1

well..................

hmm........lets ask, is zero odd, even or neither??
...............

[Freethinker]

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?

[sanctus]

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.

[Tormod]

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

[Freethinker]

Originally posted by: sanctus
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).

Originally posted by: Tormod
I 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?