## Another Beautiful Desert Day

Not much to say than it has been another beautiful day on the desert. Hi temp about 99 and lows expected to be about 68. I am so glad we moved here. Both of us are. Click on the image to enlarge.

Not much to say than it has been another beautiful day on the desert. Hi temp about 99 and lows expected to be about 68. I am so glad we moved here. Both of us are. Click on the image to enlarge.

Nothing to post today but this nice view west of our house around sunset. Click on the image to enlarge.

I bought two bunches of daisies yesterday and arranged them in a vase in the great room. I guess fall is really here in Arizona, although the daytime temperatures are in the mid nineties while the nights get down to the low sixties. My Pride of Barbados flowers are mostly gone and the shrub is going dormant. I will miss them until next June when they come back for the summer. Click on the image to enlarge.

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When Damsel took this photo of one of the cacti in the patio, it reminded me of a post I did back in the dark ages (still working for a living) about the Fibonacci Series:

When Damsel snapped this picture of a seashell a couple of days ago, it reminded me of a class I took in school. One segment of this class studied the mathematics of pattern formations in nature. It was interesting to me then and has been interesting since.

The phenomenon of an expanding spiral, as in the photo, comes from a number progression known as the **Fibonacci** series. The series is formed by starting with 0 and 1 and then adding the latest two numbers to get the next number in the progression. The first Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, and so on.

If you stack squares of dimensions in the Fibonacci sequence and connect the base intersections with a smooth curve, you get a spiral that resembles that of the shell. In the diagram at the left, two squares of dimension 1 are located in the center of the spiral, and squares of 2, 3, 5, 8 and 13 are added to the rectangle stack.

A property of the Fibonacci series is that as the series progresses, the ratio of adjacent numbers converges on a quantity known as the **Golden Ratio** or **Golden Section**. Golden Ratio comes from a name given by renaissance mathematicians. It was probably Leonardo da Vinci who first called it the sectio aurea (Latin for the golden section). The Golden Ratio appears regularly in arts, in architecture and in nature.

For everything you ever wanted to know about the Fibonacci series numbers and the Golden Section, visit Dr Ron Knott’s multimedia web site.

**UPDATE** Fibonacci spirals in linear perspective: Observe the spiral staircase as it winds into the distance below. I found this picture on a website all about European architecture. I was looking for something else and noticed the Fibonacci connection.

I spotted this little guy making his way across the RV drive today while we were working in the yard. It was less than two inches long, so it must be a juvenile Regal Horned Lizard. They can grow to be up to about 5 inches in length. Click on the image to enlarge.

Of all the birds that come around to the feeders, the male cardinal has the poorest camouflage in our Sonoran desert environment. When he does show up, we ask each other, jokingly, “Where’s Waldo?” The goldfinches feeding on Nyjer seed bags in the foreground aren’t much more subtle with their bright yellow breast feathers. Click on the image to enlarge.

Sunspot 1575 is currently pointing in our direction. It looks like the class of sunspot that can disrupt things in the electrical grid and in communications satellites. Of course, sunspots can be directly traced to periods of warmer and cooler temperatures on Earth. Click on the image to enlarge.