The golden ratio can be discovered all over the place in nature. The distance between consecutive leaves on the stem of a rose is a golden ratio, as well as the well as the distance between branches of 'veins' in leaves, and in the dimension of a chicken egg.
Perhaps the most prevalent example is that of the equiangular spiral, the sort found in galaxies, waves, and shells. The radiograph on the right side is a radiograph of a nautilus shell. The distance between any two consecutive cells within the shell is a golden ratio. The figure to the left of it is a spiral constructed from golden triangles.
 |
 |
Humans also exhibit golden ratios. On the average 'attractive' person, the ratio of the height to the navel to the distance from the navel to the top of the head.is a golden proportion. Furthermore, the distance from the navel to the center of the neck is in golden proportion with the distance from the center of the neck to the top of the head.
The shape of the head is a golden rectangle, and the distance from chin to nose is in golden proportion to the distance from nose to eyes.
The hand also posesses a golden ratio: the distance between joints on the fingers is a golden ratio. This means that when you curl your fist, the rectangle formed from the line from your index finger's knuckle to first joint and the line from your first to second join on your index finger is a golden ratio.
 |