Tag Archives: golden ratio

Did You Know?—Perfection creates perfection

Did you know?

It’s hard to believe that my last blog post was March 26. I guess I have some splainin’ to do.

Since I have been extraordinarily bored in my third attempt at retirement (the first two were equally boring), I have been out & about looking for things to do. I found it! A long-time acquaintance, now a 3-time author, hired (uh-oh; there goes retirement) me to do the final editing and design layout of his fourth book, titled “Spiny Succulents.” Right up my alley.

Spiny Succulents, by Jeff Moore

I got his final draft on January 28. At 358 pages and over 1,300 pictures, I’m still working on it. Close to being finished. Just Index, Table of Contents, minor changes, and a final read-through, and that’s it!

After I get back from my trip to northern Utah for the 150th anniversary celebration of the driving of the Golden Spike and the completion of the nation’s first transcontinental railroad, I’ll be writing my own book. Two books, actually (that should keep me busy for a while in retirement!). The first will be Nature’s Geometry: Flora with Nature’s Geometry: Fauna being a natural follow-up.

Both will be picture books mainly, so I will be able to combine my love of nature, photography, and books. I’ll be looking at stars, circles, triangles, symmetry, and spirals.

It was spirals that got me interested in doing the books because then I can add my love of mathematics to this endeavour (I misspelled endeavour for my Canadian friends).

I have been enraptured by spirals in nature ever since I discovered my first spiral succulent back in 1973. It was an Aloe polyphylla:

They grow high up in the mountains in Lesotho in Africa. They like it cold, often being covered in snow for half the year. I grew one in a terrarium from 1978 to 1993 in Texas, adding ice to the terrarium each day to mimic it’s natural environment. I now have another one, a juvenile that is not spiraling yet, also in an “ice terrarium.”

Aloe polyphylla in an ice terrarium

Spirals in nature are quite predictable by using the golden ratio that exists in the Fibonacci sequence of numbers. The Fibonacci sequence begins with 0 and 1. Succeeding numbers are created by adding the two previous numbers. So the sequence would be:

0   1   1   2   3   5   8   13   21   34   55   89   144   233   377   …

Yesterday in my gardens, I found a mammillaria which perfectly illustrates the sequence and shows the spirals very well.

Mammillaria exhibiting Fibonacci influence

See the spirals? Very beautiful.

Since I know a lot about Fibonacci number sequencing, I’m expecting to find a total number of spirals that equals a number in the Fibonacci sequence. Look what I found:

Spiral count on a Mammillaria

There are 13 spirals (red) going counter-clockwise, and 21 spirals (black) going clockwise. Total of 34 spirals. Here is the Fibonacci number sequence again:

0   1   1   2   3   5   8   13   21   34   55   89   144   233   377   …

And there we have it!

13   21   34

As one gets into the higher numbers, problems creep up, most often related to events that interfere with how Mother & Father Nature wish to do things—extreme weather events, pests, diseases, and damage from humans. That’s where standard deviation comes in, but I won’t get into that here.

What all of this tells me about my mammillaria is that Mother & Father Nature are very happy, no extreme weather events have interfered with its growth, no pests have tried to eat it, no diseases have ravaged it, and humans (me!) have not damaged it.

So, basically, I have a perfect plant.

Well, duh.

It’s my plant growing in my gardens.My wise old grandmother

“Perfection creates perfection” my wise old grandmother used to say……………

I'm Zoey the Cool Cat, and I approve this post

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