Pick two numbers at random between 1 and 10 and call them a1 and a2. From the two numbers that you have randomly picked, form a series a1, a2, a3, a4, a5, … such that the next number is the sum of the previous two numbers i.e. a3= a1+ a2, a4= a2+ a3, etc. Finally, a10/a11 is 0.618 no matter what number you chose. Why is this so?
2006-07-02 16:32:39 · 14 answers · asked by Decisiveliu 1 in Science & Mathematics ➔ Mathematics
the sequence you mentioned is the Fibonacci sequence
and that .618 is Fibonacci's number, the golden ratio
they chose a10/a11 because it ask for random number between 1 and 10, since you are going need to expand it more times as the range gets larger...
so ideally, if it is a totally random number, that number .618 will be obtained at the (nth - 1 /nth) term.
2006-07-02 16:53:18 · answer #1 · answered by hdo96815 2 · 2⤊ 0⤋
2+2=4
2006-07-02 16:39:21 · answer #2 · answered by tc_an_american 7 · 0⤊ 0⤋
1 and 10
2006-07-02 16:36:07 · answer #3 · answered by badhair92 2 · 0⤊ 0⤋
hdo96815's right.
0.618 is one of the two golden section numbers or phi, a ratio that resulted from the Fibonacci series. 1.618 is the other number and can also be obtained from that random number game above. Instead of taking a10/a11 just do the inverse i.e. a11/a10.
the result of this division (whether a10/a11 or inverse) will tend towards the golden ratio as the series expands.
2006-07-05 00:20:45 · answer #4 · answered by Anonymous · 0⤊ 0⤋
you could in person-friendly words calculate a danger utilizing absolutely numbers. you won't be able to calculate a million/infinity because infinity isn't a spread. think particularly of actual numbers you employ the effective integers. if you're choosing a random integer <= N, then the prospect is a million/N. in case you're taking the decrease as N is going to infinity, the decrease is 0. that is obviously lower than any effective variety you could call, so it must be 0. when we are saying the prospect of choosing a given effective integer out of all effective integers is 0, it must be interpreted because the decrease as i have merely defined, because it may't be calculated straight away.
2016-10-14 01:53:45 · answer #5 · answered by ? 4 · 0⤊ 0⤋
I don't know about you but I fail to see as a human being how I am supposed to pick two numbers without bias. Not being able to choose numbers randomly negates your concept.
2006-07-02 16:37:45 · answer #6 · answered by StatIdiot 5 · 0⤊ 0⤋
Whee Fibonacci and phi. I just did a math project on this. But I don't really feel like thinking about it right now. Just google it, it's easy to find.
2006-07-03 12:25:13 · answer #7 · answered by I eat apples 2 · 0⤊ 0⤋
I'm also getting a headache
but it's interesting. Get to learn something new everyday :)
2006-07-02 17:11:08 · answer #8 · answered by tankee531 4 · 0⤊ 0⤋
cause its just a property of the Fibonacci sequence that results in "phi"
2006-07-02 16:36:08 · answer #9 · answered by arcomart 3 · 0⤊ 0⤋
Man you just gave me a headache.
2006-07-02 16:35:55 · answer #10 · answered by all_my_armour_falling_down 4 · 0⤊ 0⤋