The Golden Ratio

The Golden Ratio is everywhere. It's pretty ridiculous.

The Golden Ratio is defined as:
    φ = (a + b)/a = a/b
Since a = bφ, you can easily show that
    φ = (1 + 5^1/2)/2 ≈ 1.6180...

It can also be expressed as:
    φ = 1 + 1 / (1 + 1 / (1 + 1 / (1 + /(etc)))) 

Yeah, it doesn't look like much, but it's hiding in all kinds of places.

Some things that have the Golden Ratio include:

• Stonehenge (the radii on the concentric circles, not the triptychs)
• The Egyptian Pyramids (the angle between a and b below is about 51°, which makes a/h = φ)
• Acropolis of Athens
• Notre Dame de Paris

The text area of Medieval books are also designed to the Golden Ratio as well.

Pentagrams follow the ratio as well:

The colored line segments are in the Golden Ratio to eachother.

It's heavily used in architecture and design for one reason: because it looks so damn good. Seriously.