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Nature's Geometry: Succulents, by Russel Ray

Nature’s Geometry: Succulents

It looks like I finally am finished doing the final editing and design layout for Jeff Moore’s fourth book, Spiny Succulents. It only took all of February, March, April, May, and June!

Now that I’m finished, I am endeavoring to write my own book. Originally I was going to title it Nature’s Geometry: Flora. However, after doing a presentation on Nature’s Geometry: Succulents on June 22 for the Palomar Cactus & Succulent Society in Escondido, California, I realized that I actually can make three books out of the Nature’s Geometry subject: Succulents, Flora, and Fauna. I could even exclude people from Fauna and do a fourth book on People & Their Creations.

I have started fifty books previously. Chapter 1 is complete in all of them. I just couldn’t decide where to go with Chapter 2, so I gave up. With Nature’s Geometry: Succulents, I don’t have that problem because my Powerpoint presentation for Palomar C&SS is my outline. So it’s just a matter of writing the text, which was my narration for the Powerpoint presentation, and formatting the text and pictures for an 8½” x 8½” square book.

I already created the cover, which I think will help me go forward. Looks like this:

Nature's Geometry: Succulents, by Russel Ray

I also have written the Dedication. Many readers probably know who I am dedicating the book to.

Dedication, Nature's Geometry: Succulents, by Russel Ray

I hope to have this book completed by August 1, which I think is possible since I have the Powerpoint presentation as my outline. I’m letting BookBaby do the publishing and printing because they can do print on demand, which means I don’t have to order many thousands of books with the subsequent shipping charge. I can order 250 softcover books with an ISBN, printing, and shipping, for just $11.76 per copy. The only reason I’m ordering that many is because I already know what my initial demand and my promotional give-away total is. One can order as few as 10 books or so, but the price per copy goes up, of course. This enterprise should keep me busy for a little while.

Of course, Olivia also is keeping me busy, or at least entertained with her photogenic antics.


Nature’s Geometry: Flora—Who is Russel Ray?

Since January 28, 2019, I have been doing the final editing and design layout on a 350-page book titled Spiny Succulents: Euphorbias, cacti, and other sculptural succulents, and (mostly) spiny xerophytic plants. I finished it yesterday. It will be on sale in late October or early November, and is the fourth book by the author, Jeff Moore, on cacti and succulents. As with his first three books, there are lots of beautiful pictures, over 1,340 of them.

Seeing how easy it is to publish a book in today’s world—one can even get an ISBN for as low as $4.95—encouraged me to do what I have always wanted to do: write a book. I actually have two books in mind, Nature’s Geometry: Flora and Nature’s Geometry: Fauna. They basically will be picture books, with a little writing thrown in for good measure, and will allow me to combine a lifelong love of photography, nature, writing, and mathematics. My first task, then, was to ask myself, “Who is Russel and why does he get to write these two books?” In other words, “About the Author.” I sat down last night while watching the movie “Silent Hill” and wrote about Russel (that’s me!), a long diatribe that obviously will be edited for brevity for the final book. Following is what I came up with, still in first person:My Heartleaf Ivy

I was born in 1955 in Kingsville, Texas. After my dad died in 1961, mom moved us to northern Utah where her family was from. It was in Brigham City, Utah, where I became fascinated by nature. Our neighbor next door was Mrs. Larson, my first grade teacher. She had beautiful plants in her yard, and one day she gave me a “heartleaf ivy,” Philodendron cordatum. That started my fascination with plants.

My paternal grandmother adopted me in December 1965 and took me home to Kingsville. In September 1966, the principal of the grade school was going around to home rooms and asking for volunteers to learn photography. The school provided Nikon cameras, a darkroom, supplies for the darkroom, adult supervisors for the darkroom, and, most importantly, free entry to all school events, including football, baseball, basketball, and tennis (my four favorite sports). I was an easy sell, and that was my start in photography.

In September 1968, my first class in eighth grade was botany. My teacher, Mrs. Bajza, presented a slide show of many beautiful plants, all growing in her gardens. When I got home that afternoon, I asked my grandmother if I could have a small garden in her yard. I was Cooling condenserexpecting a loud and definitive, “NO!”. However, granddad and I had installed central heating and cooling earlier that year, and grandma gave me the 100-ft square section where the cooling condenser was located. If you’re familiar with cooling condensers, nothing had been growing around ours for about six months because of the hot air blowing from that condenser. I was depressed and went over to visit my best friend, Richard. He and his parents listened to me complain and invited me to go with them to the Rio Grande Valley the coming weekend to visit nurseries, which turned out to be specialized cactus and succulent nurseries. I was mesmerized. Richard’s parents allowed me to pick out plants that I liked and they bought them for me. I created a rock wall surrounding the cooling condenser to force the hot air up, allowing me to plant my cacti & succulents on the other side of the rock wall, protected from the hot condenser wind. Eventually the plants grew and bloomed, and that was the start of my fascination with cacti & succulents.

My math addiction came about because I had been good with numbers from a very early age. I was quite adept using a slide rule when I was in first grade.

Slide rule

In twelfth grade, I won a math competition in South Texas for my presentation, “Tips & Tricks To Help You With Math.” That allowed me to go to a statewide competition a few weeks later, where I came in second. First place was taken by a girl in twelfth grade in Dallas for her presentation, “Fibonacci Numbers & Nature.” Her presentation resulted in me combining my three loves of math, nature, and photography.

This book will explore nature’s geometry using math, specifically the golden ratio created by the Fibonacci sequence of numbers, but also the golden angle, the reverse golden angle, the golden rectangle, and the golden spiral, all derived from the Fibonacci number sequence.

Throughout these pages are pictures, most of them my pictures of plants in my collection, showing how the Fibonacci number sequence expressed itself in our cacti & succulents as the number of ribs on a gymnocalycium, the number of spines in a cactus areole, and, of course, the spirals prominently displayed in many species, most notably in the center of the sunflower (Helianthus) and the spiral aloe (Aloe polyphylla).


Aloe polyphylla - Spiral Aloe

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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……………

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