Quick Brain Teaser

[tino]

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

Btw, don't believe everything Wikipedia tells you.

wat?

I base my life around Wiki facts

[Churchill]

Your own?

Nope, CM's little brother.

Then back for the 29th and Richmond!

We're having far too much fun to get married!
(Another year or so according to "the plan"...)

[BrollyBonce]

A slightly harder question

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

0.6180339887498949......

Bump

[conned tractor]

Bump

I couldn't find the answer, I did give it some thought but unfortunately wasn't able to identify the relationship.

[ASB]

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.

Almost certainly bunk. The parthenon is an oft cited example. With carefully drawn rectangles round it.

In surevers (fwiw) almost nobody expresses a preference for rectagles laid out in that ratio aestetcially. Most architect don't use it - but believes other do. It happens to be useful in laying ouy leaves in nature. It is often used as an ratio in body parts.

However I could probably define the ratio of distance between the average arse and elbow as the golden ratio and find enough cases where the number appeared relevant.

[conned tractor]

Surely the so called golden ratio is an irrational number. So it will converge to the golden ratio but you can't express that in decimal notation. That's what I was trying to allude to yesterday.

decimal to confuse those, like yourself, that are cleverer. Well done btw.

[ASB]

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.

Surely the so called golden ratio is an irrational number. So it will converge to the golden ratio but you can't express that in decimal notation. That's what I was trying to allude to yesterday.

[conned tractor]

Almost certainly bunk.

However I could probably define the ratio of distance between the average arse and elbow as the golden ratio and find enough cases where the number appeared relevant.

Probably. Just trying to give it some interest. Good arse elbow analogy.

[Pogle]

Nope, CM's little brother.

Then back for the 29th and Richmond!

We're having far too much fun to get married!
(Another year or so according to "the plan"...)

Lawks! So this implies you are affianced?

[d000hg]

Easy, about 20s including firing up calculator to prove my sums right.