contingent acreage logjam

hmmm, wonder who That Guy might be!

Horrors Today: Your efforts on the job may be thwarted now, no matter how hard you work. It's as if you're attempting to roll boulders up a steep hill and you wonder if it's worth all the effort. However, regardless of your lack of results, it's important that you keep trying since you are setting the stage for greater opportunities to come to fruition in the year ahead.

My Lesson of the Day.  sigh. 

And here's my quote for the day, applicable for you SAQA list members:

************************************

I was married by a judge. I should have asked for a jury.  Groucho Marx

************************************

Yesterday, yeah a Sunday when I'm supposed to be 'resting' and getting the Christmas stuff put away (because my MIL was Armenian and left her stuff up undisturbed until Jan. 6th or the world would collapse.)  Well it looks here like it happened anyway-  boxes and bubble wrap everywhere and the (semi-permanent, weather proof, and sun resistant) wreathes won't fit into the new WalMart boxes I bought for storage.  I don't know where my head was when I got them.

Probably being held by that Armenian to continue the family tradition.

Anyway-  we were headed for a Green Market to see what there was to see, but I detoured TY to stop at Michaels to get some ink pads for my new custom stamps that should arrive today.  Then we hit the Green Market and drove around for 15 minutes with no parking place anywhere, which led us instead to Whole Foods.  Now Sunday at Whole Foods is not my idea of fun, but then neither is Michaels, or my dining room Christmas staging area.  Because I don't have a dining room, I have one big room with everything imaginable except a toilet in it so the Christmas stuff really needs to be put away and NOW.

And here is is Monday morning and yup, it's all still there piled high with the wreathes sticking out of their new plastic casket.  

Poor Brain, needs some stretching

So instead, to fill my morning with a bit of research to keep me sitting here drinking copious coffee,  I'm going to talk about pattern.  Hold on, don't leave, this could get interesting.  Or not.

What do these next two photos have in common?

The Golden ratio:  At least since the 20th century, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.  Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. Since the twentieth century, the golden ratio has been represented by the Greek letter Φ or φ (phi, after Phidias, a sculptor who is said to have employed it. The golden ratio has also been used to analyze the proportions of natural objects.  So, the building block of the Golden Ratio is this, the golden rectangle:

Sorry, this is where a tiny bit of algebra creeps in that you swore you would never use:

And this proportion goes to infinity in either direction.

Here we have the Acropolis again, showing the ratio-

So, take this red line drawing and turn it on it's edge:

And you get a Fibonacci Spiral!  Created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34

And you get examples of this in the Agave above, in this tiny little shell,

In cloud formations over the earth,

                                          in plant forms on the micro level,

And in the galaxies!

From this we get things more down to earth and of people proportions, like the Snail's Trail quilt pattern.  Here's one I made years ago- it's heavily coated in gel medium because I didn't like quilting!  Weird, but it sold out of the first and only show it was in. Just for fun, zoom in and follow the pattern-  I was in my heavy-floral period here, all linen home dec fabrics on canvas backing.

(And here's a more readable version by somebody else:)

OK, so natural and manmade forms can all be governed by the golden ratio but that isn't the whole of it-  look at this!

 After the triangle is drawn using the ratio, it fits the human body!  Thanks DaVinci, a guy who liked to find reasons for things. George Odom has given a remarkably simple construction for φ involving an equilateral triangle: if an equilateral triangle is inscribed in a circle and the line segment joining the midpoints of two sides is produced to intersect the circle in either of two points, then these three points are in golden proportion. This result is a straightforward consequence of the intersecting chords theorem and can be used to construct a regular pentagon, a construction that attracted the attention of the noted Canadian geometer H. S. M. Coxeter who published it in Odom's name as a diagram in theAmerican Mathematical Monthly accompanied by the single word "Behold!"


TO UNDERSTAND IS TO PERCEIVE PATTERNS

So, how do you like them apples (as my father used to say)?  We need a breather before we head off to test the new stamp pads.

Have a piece of cake----- I promise it wasn't governed by any golden ratios!

Yup, it IS a cake.  How disgusting a waste of cake talent!  Love that it is presented in it's aluminum pan.