The Golden Ratio

[Ben Dover]

Phi. One 'H' of a lot better than Pi.

 

[earhart]

Phi. One 'H' of a lot better than Pi.

I bet you $3.14 you're wrong.

 

[Sig]

The Houston Eulers were such a hard team to bet against.

The bookies made the spread naturally, and logged it as such.

 

[PBRstreetgang]

I thought you said Golden Shower!




nevermind!
PBR

 

[Andy Neill]

If you wanted to cut a piece of sheet metal to form the floor and sloped side of a cargo bin that was 1 unit wide at the bottom, two units high, and two units wide at the top, the length of that piece would be 2 times phi. (about 3.236 units).

Consider the coorditates of the side view of the vargo bin to be (0,0), (1,0), (2,2), and (0,2).

 

[Speedtape]

Logarithmic Spirals​

The spiral shapes of a nautilus are called Equiangular or Logarithmic spirals. If P is any point on the spiral then the length of the spiral from P to the origin is finite. In fact, from the point P which is at distance d from the origin measured along a radius vector, the distance from P to the pole is d sec a.

The Fibonacci sequence relates closely to the golden ratio and to logarithmic spirals. Logarithmic spirals are simply spirals that increase at a logarithmic rate. The golden ratio, however, is a special fraction equivalent to about 0.618. A logarithmic spiral can be generated by subdividing a golden rectangle into increasingly smaller squares and golden rectangles. This subdivision begins by fitting a square within the golden rectangle. The remaining space forms a new, smaller golden rectangle. By repeating this process, the spiral form soon becomes evident. Furthermore, the subdivided sections can be thought about as Fibonacci numbers.

One reason why the logarithmic spiral appears in nature is that it is the result of very simple growth programs such as:

Grow 1 unit, bend 1 unit

Grow 2 units, bend 1 unit

Grow 3 units, bend 1 unit

And so on...
Any process which turns or twists at a constant rate but grows or moves with constant acceleration will generate a single logarithmic spiral.

 

[AceCrackshot]

Does James Brown get down?

 

[Speedtape]

Does James Brown get down?

Once upon a time!

http://www.youtube.com/watch?v=Zdz88MBWomo

then watch it to the end

http://www.youtube.com/watch?v=YSw0W8MQCxU

 

[DrewBlows]

So you're saying you should be making about 62% of what you are making?

Some days I probably shouldn't be making that much...

:laugh: