occam's razor

Plants displaying leaves spiralling around the stem in groups of 8, so that the ninth appears directly above the first, are described as having a 5/8 phyllotaxy, on the assumption that the spiral has turned through 5 circles - (1800°).

Fig 28 and Fig 29, (page 6 - spirals and stuff), show that there are two ways of looking at, and naming, this same phyllotaxy.

Here is another example...to suggest that the first one was not a fluke

In Fig 49 the leaves spiral around the stem in groups of 5, the sixth appearing directly above the first, and the phyllotaxy is described as 3/5, on the assumption that the spiral has turned through 3 circles - (1080°).

It is 216° of turn between leaves this way round.

Fig 49

Fig 50

Fig 50 looks at it the opposite way round - the same leaves appear in the same order - after turning through only 2 circles - (720°).

This way it is 144° of turn.

Fig 51

Fig 51 shows how oppositeness to a perceived angle of 36° could be used to utilize a divergence angle of 144°.

And also how oppositeness to 144°, if there were anything to be gained,could provide a divergence angle of 216°.

The philosopher William of Occam (c.1285 - c.1349), born about 35 years after Fibonacci died, is best remembered today for proposing a logical principle which became known as Occam’s razor. It can be paraphrased as “don’t make things more complicated than they need to be”. Would he rename the phyllotaxy 2/5?

More importantly, the two examples, here and on page 6, show a band, 9° wide (Fig 52), either side of 137.5°, the golden angle. For some Fibonacci numbers that is close enough.

135°.............137.5°.....................................144°

Fig 52