phi

[nathan2]

can anyone explain the golden ratio in laymans terms and is it basically a thidr of the distance measured . i am aware it is 1.6
thanks

[gen2]

Imagine placing a point C somewhere along a line AB

A...........................C........................................B

If the ratio of AC to CB is the same as the ratio of CB to AB, then you have divided the line AB into the Golden Section. This ratio has been shown to be the most aesthetically pleasing. It occurs frequently in both art and architecture. The golden ratio also occurs frequently in nature. Just Google "Fibonacci" and you will get many examples. The Fibonacci series tends to a limit which is equal to phi.

[pagey]

I love the golden ratio. The A-series paper size uses it (as it is the most aesthetically pleasing as gen2 says) and it has the property that if you fold it in half you have the next size down. So fold a4 and you get a5 (with the same length to width ratio). No other paper ratio can do this.

[mibn2cweus]

Another aspect of phi 1.618 . . . I find fascinating is that
it equals 1 more than 0.618 . . . its reciprocal. One divided by phi equals phi minus one.

Using a calculator you can converge on phi by . . .
Starting with any number greater than 1, repeatedly find the reciprocal and add one . . .

{ (1/x) + 1, (1/x) + 1, (1/x) + 1, . . . }

repeat this sequence until the same numbers appear,
than your done!

Most calculators do not have a reciprocal (1/x) key (do not confuse this with a (+/-) key), but . . .

If it has a square root (sqrt looks like a check mark) key there is another way . . .

{ + 1 = sqrt, + 1 = sqrt, + 1 = sqrt . . . }

repeat this sequence until the same number appears,
than your done!

If such enterprises bore you there is always . . .
{ 5 sqrt + 1 / 2 = } phi equals the square root of five, plus one, divided by 2.

Remember there is a lot more to phi than meets the eye. Most calculators only display the first 8 or so digits.

[Space]

pagey, I'm afraid you are wrong,
the paper height/width ratio is the square root of 2, which is not the golden number. (it's 1.41something )

[pagey]

my maths teacher told me it was when I was in school. good one. who can I trust now...!

I stand corrected! Still root 2 is also an interesting number