Knightsbridge and magic squares

I began this page in my Book with the grid of colored squares, a collage of leftover bits from other work.

I thought it might become another "space junk" page, but once that grid was in place it seemed to want a square grid all over. I obliged.

I decided to include a magic square of nine with the numbers are represented by images. That's at the bottom center. Some years ago I did an acrylic painting with this theme (see it next in this post). On this page in my Book I also included a square with the digits.

I'm not happy with streakiness of the grays in the lower right but I wanted to try a gradation where the same gray is the dark gray in the light portion, and the light gray in the dark portion.

MAGIC SQUARE OF NINE PAINTING
During my long mandala phase, I did this acrylic painting of a magic square of nine, except instead of simply writing a number in each square I devised an image to represent the number. The centers of the half-circles at the perimeter are filigree metal pieces.

"Magic Square of Nine" - Sold
24" (60 cms.) square; acrylic mixed media

WHAT IS A MAGIC SQUARE?
A magic square is a grid of numbers such that each horizontal, vertical, and diagonal row results in the same sum. A magic square of nine is one of the simplest, comprising only nine squares. The sum of each row is 15.

There are more complicated magic squares, larger, with more squares. Here's a magic square of four and the rows add to 34. You can learn more about magic squares on wikipedia here.

Phi Day! .618

You may know that international Pi Day is March 14 each year, 3.14. (You can see my special triangular art for Pi Day 2017 here.)

I've long been interested in divine proportion (also called sacred geometry, the golden mean, etc.) and I think there should be an international Phi Day too, .618, June 18th. If it takes off, you can tell all your friends it started here!

Current page from my 2018 Tangle-a-Day calendar.

I chose Phicops for the 18th in my Tangle-a-Day calendar because the name starts with Phi and the inspiration for it is related to shells and golden proportion. Step-outs for the tangle Phicops are here. On this calendar page I actually worked backwards, beginning with the 18th, then the nautilus spiral on the 17th, and ending with part of the spiral and Paradox on the 16th.

Tangles: Phicops

.618 (or 1.618) is the number associated with sacred geometry, even though divine proportion is about relationship and proportion, not measurement. The number is the short version of the infinitely long and non-repeating decimal places.

The Golden Mean is essentially the division of a line into two unequal parts.  The ratio of the whole line to the large part is the same as the ratio of the large part to the small part. The result is an irrational number: 1:0.6180339… 

.618 is very close to two thirds.  Many art instructions recommend placing major objects approximately one-third of the way from either side, and one-third of the way up or down.  This is called the Rule of Thirds and makes the composition more pleasing to the eye.

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Saskatchewan landscape: canola field in bloom and The Tree, a prairie landmark.
The Rule of Thirds with the focal point at one intersection.

There is so much more to this once you delve into it: sunflower seeds, Greek philosophers, da Vinci, the Masonic Guild, eggs, arms and legs, Fibonacci, nautilus spirals, pine cones, piano keys, spiral galaxies, and on and on and on. (For more information and a great video on the Fibonacci number sequence see this post.)

In the meantime, have a PHIne day!

'2014' Diva challenge

Tangles: Braze, Bunzo, Crossview, Florz,
Knot Rickz, Rain, Tipple, Yew-Dee

Laura challenged us to use the new year 2014 as inspiration for this week's challenge. There are some really interesting results flowing from participants: a word for the year, Roman numerals, simple numbers, a thought or aphorism. It's going to be a wonderful slide show!

I decided to simply use the numbers 2, 0, 1, and 4 overlapping to make my string. For some reason I did this on the diagonal. Here's the string I began with:

I really quite liked it despite some rather tiny sections. I reminded myself that the string is a guideline, not a Rule and that I could ignore some or combine sections if I felt like it.

Fibonacci

LEONARDO PISANO FIBONACCI
(pronounced FIB-on-AT-chee)
Image from
http://www.gap-system.org/~history/PictDisplay/Fibonacci.html

Leonardo Pisano is better known by his nickname Fibonacci. He was born in Italy but educated in North Africa where his father held a diplomatic post. Fibonacci was taught mathematics in Bugia, an Algerian port city. He travelled widely with his father and recognised the enormous advantages of the mathematical systems used in the countries they visited. 

Fibonacci ended his travels around the year 1200 and returned to Pisa. There, he wrote a number of texts which played an important role in reviving ancient mathematical skills and made significant contributions of his own. Of his books, some no longer exist, but we still have copies of Liber abaci written in 1202. A mathematical problem in Liber abaci led to the introduction of the Fibonacci numbers and the Fibonacci sequence for which he is best remembered today:

"A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?"

Trying to figure out things like this muddles my brain and neurons go off like holiday fireworks. I generally have to draw pictures with arrows, so I'll take it from the experts that the resulting sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on. In this sequence each number is the sum of the two preceding numbers. It appears in many different areas of mathematics and science. It relates directly to the growth patterns of trees, shells, flowers and animals, the proportions of human bodies and what we perceive as visually appealing or beautiful, and so much more.

You may have noticed that the Zentangle kit contains 34 blank tiles. You can buy tiles alone in packs of 55.

Here is a beautiful video that gives an overall impression, and a bit of hard information, about the Fibonacci numbers and sacred geometry. (Go full screen. It's worth it.)