natural sequences mathematical?

Question

I need a real life collection of natural number sequences I already have the golden section, and fibonnaci are there any more?

Answer 1

the fibonacci sequence 1,1,2,3,5,8,13,..............

is conjectured to be related to ferns and shells,but this can only be proven by empirical evidence and it is difficult to prove either way

it is hard to imagine how the man-made number (sqrt5) can appear in nature,however, there are various geometrical methods of constructing the golden ratio (1+ sqrt 5)/2

it can be shown analytically that as the number of terms in the sequence becomes very large,the ratio of the (n+1) term to the nth term approaches (1+sqrt5)/2-but this is man-made

so i'll stick to my snails and leave the ferns to nature

i'll be convinced when it can be shown that fibonacci is directly related to natural events

Answer 2

One previous answer claims that mathematical sequences are 'linear' - they're not and don't have to be.

In fact there doesn't have to be any easily expressible relationship between the elements of a sequence, it's just that mathematics has a very hard time dealing with the sequences which don't! A sequence does not have to be increasing either.

When you say 'natural number' sequences I'm not sure if you mean 'natural number' in the mathematical sense ie non-negative integers, or simply sequences that occur in nature.

Some real-life sequences are:
- musical notes;
- distances of planets from the sun (Bode's law - not exact but close enough to count)
- the width of successive 'rings' in the spiral of snail shell
- orbitals of atoms.
- measuring up the stem of certain plants the angle at which a leaf branches off from the stem forms a regular sequence.
- the length of daylight (from sunrise to sunset) varies from day to day and forms a regular sequence
- the phases of the moon.

Answer 3

certainly you dont could comprehend the respond and then use induction, because you are able to sparkling up this kind of linear recurrence relation from its function equation. x^3-2x^2-13x-10 = (x+a million)(x^2-3x-10) = (x+a million)(x+2)(x-5) [the explanation is that (E-ok)ok^n = 0 the place is the "next" operator Ea[n] = a[n+a million] so if the roots are all diverse your 0.33 order relation could nicely be written (E-k1)(E-k2)(E-k3)a[n] = 0 right here you are able to write a[n] = A 5^n + B(-2)^n + C(-a million)^n and be certain A,B,C from the 1st values. yet for induction, assume real as much as n a[n+a million]= (2*5*5+13*5+10)5^(n-2) + 2*(2*(-2)(-2)+13(-2)+10)(-2)^(n-2) + +3*(2*(-a million)(-a million)+13(-a million)+10)(-a million)^(n-2) = one hundred twenty five*5^(n-2)+2( -8)(-2)^(n-2) +3(-a million)(-a million)^(n-2) = 5^(n+a million) +2(-2)^(n+a million) + 3(-a million)^(n+a million) a[0] = a million+2+3 = 6 a[a million] = 5-4-3 = -2 a[2] = 25+8+3 = 36 so real for all organic numbers

Answer 4

Get a large number of dominoes. Put one on the edge of the table with just under half overhanging so it almost topples over.Put the next one on top, overhanging the first by 1/3 of its length, then the next overhanging the second by 1/4 and so on. I've never tried this, but I'm reliably told that you can pile an unlimited number like this without them toppling.