Quick Brain Teaser

[conned tractor]

Too easy

The Golden Ratio.

Congratulations hombre.

[EternalOptimist]

Too easy

The Golden Ratio.

holy mackeral - now I am frightened

[conned tractor]

Here is a harder one:

1, 2, 1.5, 1.666, 1.6...

Bonus points for additional info especially on where it converges. And yes it is a real sequence.

Not much interest in trying to solve it but here is the answer.

If you take the fibinacci series, 1, 1, 2, 3, 5, 8, 13, 21.... a natural solution to many problems, something like multiplying rabbits or something like that, can't remember an example.

Then take the ratio of consecutive numbers in this series, i.e., 1/1, 2/1, 3/2, 5/3, 8/5, 13/8....this gives the sequence shown. it converges to what is known as the golden number which is 1.618....

Now the golden number is used many times throughout history and in nature, the ancient greeks used to build important buidings to the ratio as it was considered to be the most aesthetically pleasing ratio for a rectangle. Whereby the width was, for example, 1.618 * height. Thus the height was 1/1.618 * width, 1/1.618 being 0.618.

It is also a root of the quadratic x^2 - x - 1. The other root being the exact inverse of this, i.e. 1.618 = 1/0.618 which as shown is also the reciprical.

Also, some sea shells and certain proportions of humans exhibit the proportionality from what I can remember. Anyway, there are much more details here:

http://en.wikipedia.org/wiki/Golden_ratio

Tractor.

[Churchill]

Oi fuqwit, you're too late!

I say, "You're too late!!!"

[BrollyBonce]

A slightly harder question

In the context of the first question in this thread, what is the significance of the number:

0.6180339887498949......

[conned tractor]

Oi fuqwit, you're too late!

I say, "You're too late!!!"

qué?

[Churchill]

qué?

We'd already done the "Golden Ratio" bit.

[conned tractor]

We'd already done the "Golden Ratio" bit.

Yes I know, I posted the question, just giving a more complete answer for everyone. Been on the juice?

[Churchill]

Yes I know, I posted the question, just giving a more complete answer for everyone. Been on the juice?

Nope, resting my liver before I go to Ireland for a wedding. Must be detoxing!

Btw, don't believe everything Wikipedia tells you.

[Pogle]

Nope, resting my liver before I go to Ireland for a wedding. Must be detoxing!

Btw, don't believe everything Wikipedia tells you.

Your own?