Playing with Math, Glass & Nature

Oh, so much fun working with glass on my latest project, Green Trees.  [Hey, I know it’s a funny name considering the tree is clear textured — but the sporatic use of green for the grassy hills had to be in it too. Trees with Green is too long & sounds even stupider without Trees with Green Grass — which makes it totally too long!  Thus, the simple Green Trees.  :lol:]

These windows are going to be sliders, similar to the shutters made for the living room (lrs), but will slide inside the frame — the lrs slide outside the frame over the walls.

Thus, it’s divided into four windows — the two on the outside [each with a tree] are fixed while the middle two [with ends of branches] will slide [one to the left; other to the right] in a groove over the fixed windows.

The first glass tree is in & all the framing is completed — now we’re waiting for me, of course, for the second tree.

We’ve had a few showers [nothing too major but autumn is arriving — saw the geese practicing their ‘V’ formation flying this week] soooo, for now, I’m putting a single sheet of clear glass in the sliders.

I don’t have time to design these two now & they’re mostly going to be clear glass anyway.  Later, alligator.  With a solution found, they rarely enter my mind — they don’t need thinking now, they simply need doing.

So, while I work at finishing the second tree window, I play with designs for upcoming projects.  The first up is my commission due September 30th [if possible, not a definitative date] — an 18″ x 27″ blue & yellow abstract, similar to the mosaic in my hinged porch windows.

Since introduced to my patron during our university days, I thought it would be appropriate to use some ‘university-style’ knowledge for the design.  Among the 40 or 50 courses I took [is that all?  it seemed like hundreds], I remember a math course & an art course that each mentioned Fibonacci Numbers.  Hmmm, much different disciplines, aren’t they?

I’ve always loved math & see quite a beauty when manipulating numbers so I want to explore this connection between art & math.  My middle son, also a math lover, directed me to search the internet for Leonardo de Pisa & I was off & running.

Essentially, Fibonacci Numbers are a series of number produced by adding the sum of two numbers with the last of the previous two numbers.

Thus, starting our series with the two numbers, 0 [zero] & 1 [one], we get:

0 + 1 = 1 so we have the series {0, 1, 1}; then

1 + 1 = 2 so we have series {0, 1, 1, 2}; then

1 + 2 = 3 for {0, 1, 1, 2, 3}; then

2 + 3 = 5 for {0, 1, 1, 2, 3, 5}; then

3 + 5 = 8 for {0, 1, 1, 2, 3, 5, 8}; which continues on indefinitely to produce the series:

{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, . . .}

I know, a bit dry if you’re not a math nerd — but, listen –> a cursory read of Wikipedia’s Fibonacci Numbers reveals stuff like “golden spirals” & “shallow diagonals of Pascal’s triangle” that connect this easy-to-calculate series of numbers to all sorts of amazing things in our world, including geometry & nature — whoa, two more loves of mine — bonus!


A simple use of the number series, as the length of various squares, produces a block abstract that, for some unknown reason, is quite pleasing to the human eye.

Hmmm, that’s good for an artist to know.  😎

And connecting the arcs creates a pleasing spiral — the golden spiral — for spectacular works of art.  As each number in the series increases, the spiral grows larger.

My exploration into the uses of geometry in art continues — I look forward to some exciting stuff.  [Yeah, I know I’m a bit weird]  😉


Do you know that Fibonacci numbers are found everywhere in nature?  Like the Yellow Chamomile [left], many things are known to grow in these golden fashions — pineapple fruitlets, tree branches, [hmm, wish I’d know that when I designed Green Trees], leaves on stems, artichoke flowers, pine cone seedlets,  . . .

Fibonacci numbers show up in the breeding of rabbits, bee colonies, spirals of a sea shell & in the waves of the ocean.  Cool, eh?

I realize God is the original mathematician — explaining why we find artistic beauty in nature.  😮

And simply because math is everywhere in nature, I am excited even more — the possibilities for design in my own glass work are endless.

Simply A Dawne Thought


** all Fibonacci images are from Wikipedia