how many web sites will tell you this ISN'T a golden spiral?

in nature

there is a lot of fiction and hype about Fibonacci Numbers and the Golden Ratio in nature.
the previous statement is an understatement.
i was very disappointed to learn this.
a lot of this hype probably stems from Luca Pacioli's 1509 De Divina Proportione, which ascribed "holy" or "magical" properties to the Golden Ratio.^{[3],[10],[11]}

misconception #1: nautilus shells

a quick Google search will yield dozens of sites claiming that the shell of a nautilus is a Golden spiral.
the authors of these sites seem to believe these claims without verifying them. (I made the same mistake for much of my life)
it is easy to verify whether or not this is true by superimposing a Golden spiral over images of nautilus shells.

In all cases, the spiral was scaled to fit the width of a rectangle formed around the outside of each shell. Pictures were chosen for being oriented at roughly right angles. Notwithstanding the possible minor alignment error due to orientation and spiral scaling issues, all of these shells have at least one thing in common: None of them are remotely close to Golden spirals.

misconception #2: flower petals

another popular myth is that flowers have numbers of petals according to the Fibonacci numbers.
Well, it's not really a myth because it's true. There are flowers that have Fibonacci-numbered numbers of petals.

There are also flowers that don't:

Dame's Rocket: 4 petals	Osteospermum: 24 petals
Lily: 6 petals	Some type of Aster: 16 petals
Starflower: 6 petals	Saffron: 6 petals
Daffodil: 6 petals	Columbine: 10 petals

(some of the flowers above technically do have Fibonacci-numbered petals. I'm not going to say which though.)

misconception #3: the human body

The Vitruvian Man

some people say the human body exhibits Golden proportions.
if you draw random rectangles all over Leonardo Da Vinci's Vitruvian Man, some of them will be Golden rectangles.
for every infinity web sites run by mystic hippies claiming the Golden Ratio pervades the human form, there are zero credible academic sources that agree.
there is too much variance in body shape from person to person to imply that the human form conforms to a precise ratio, at least without concrete evidence. this should be trivially obvious.

beauty in coincidence?

    [show 21 spirals]

    [show 34 spirals]

    [show no spirals]

A sunflower has interconnected spirals in its center. There are 34 clockwise spirals and 21 counterclockwise spirals. The flower has 21 petals. (these are Fibonacci numbers in case you were asleep!)

beauty in coincidence?

[from Dr. Ron Knott's page on Fibonacci Numbers]

spirals and Fibonacci numbers wrapped up in one package? freaky.
however, there are other plants that exhibit interconnected spirals which don't show up in Fibonacci numbers:^[2]
the cactus to the right has 11 and 18 spirals.
there is not enough evidence to say that plants, or the spirals thereon, are generally related to the Fibonacci Sequence.
but they're still beautiful!

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