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Geometry & Math in art & history. Ancient Egyptians not only used mathematics and geometry (phi) but also cooked up a lot of savory & fruit pies!
Pie recipes have traveled throughout the decades with savory fillings such as cheese, meat, and vegetable-filled dinner pies as well as berry & fruit pies, all of which are covered and sealed within a variety of pastry styles. The pie was also a handy form to transport food long distances while also extending the ingredients to feed more people. I like pie for breakfast... my favorite time to eat fruit pie.
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| Geometry artwork in ink by Minaz Jantz |
The Golden Relationship: Art, Math, and Nature:
Exercises from the book 'Universal Patterns' by Martha Boles & Rochelle Newman
WHAT???... you thought this was an artist's blog so what does this 'eating and making pie' got to do with art? The starving artist has to eat sometime so why not start the day with pie!
This blog entry is a continuation of the previous blogs written about my self-study in learning from the book 'Universal Patterns' teaching the history and methods for PHI also known as; Sacred geometry, Divine Proportion, Golden Mean, Golden Ratio, (1.61803).
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| Ink drawing by Minaz Jantz |
Studying geometry is a necessary skill for serious artists to understand and utilize in their creations to give meaning to the space and objects we create. Leonardo Da Vinci studied in-depth and developed drawings, showing the human body with its Divine Proportions. This is natural math that mother nature constructs itself, using the ratio Phi (1.61803) which is in balance with all parts of itself. Here is a link to explain and demonstrate more in-depth the history of Phi. www.goldennumber.net/history.htm
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Have fun making designs from circles in ink. |
The first chapter in the book teaches how to construct lines to be perpendicular and divide them into golden ratios. What I like about drawing geometry, is using the tools; compass (http://en.wikipedia.org/wiki/Compass_(drafting)), drafting pencil, and my see-through triangle. While making my construction lines very lightly with a hard sharp lead in my drafting pencil, I accurately join the points exactly or be noticeably out in my proportions by the end of the drawing. This can be challenging for me as it requires patience and excellent lighting to SEE the finely drawn lines, dots, and dashes.
Later, I freehand with an HB softer pencil the lines and the structure design within the shapes that I want to express. I can fill those HB pencil lines in with a black felt tip pen or ballpoint pen to show a more dramatic result.
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| Designing each square unique to the other for a patchwork design. |
The above drawing is a project from the first chapter, in which I drew a series of 6 squares, divided into interesting patterns, much like quilt-makers would do before making a blanket. I took a blue pen and a black pen to cross-hatch the shapes for color and texture and also used a black felt tip marker for defined outlines. This is very fun and meditative to do once I got the hang of it.
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The second chapter is learning to make a Pentagon from a circle, a five-sided shape. http://en.wikipedia.org/wiki/Pentagon Many designs can be created just from this shape. I made a paper Pentagon ball and covered it with many designs within the shape.
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Pentagram and circle design. |
I had the most fun learning to make this shape; the pentagon shape (5 points). After figuring out this 5-sided shape, it continues to develop into a more complex and beautifully designed 10-sided shape, called a decagon. If my measuring and mark-making were off just slightly, by the time I get to the end of drawing the decagon, the whole shape will be out of kilter. Practicing using the drafting tools and sharp pencil leads help me to become more accurate. After a while, with practice, it becomes obvious sooner when I am off the mark and I can correct it before going on too far. There is lots of head-scratching and going back over the notes to make sure I got it right.
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Golden rectangles.
Chapter 3 gets me creating all kinds of triangles. One of the most famous triangular shapes is called a variety of names; Egyptian triangle, Triangle of Price, Rope Stretchers Triangle, Golden Triangle, and the 3-4-5 Triangle. These are all the same; right angle 90 degrees, with the ratio 3-4-5 for each of the three sides, totaling close to the phi measurements of (1.66666).
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Pentagram & Circle Design |
The Egyptian triangle, a simple measurement, was developed by the builders of pyramids by tying a rope with 12 evenly spaced knots on a rope then attaching the rope at one end to a stake in the ground, would use the knots to guide the measurements in sections of 3 knots-4 knots-5 knots (total 12 knots) keeping a straight edge measuring 90 degrees on the rope. With this simple tool, they could draw out harmonic proportions to build their perfectly shaped Pyramids. Check out this informative link that explains more about this particular triangle with many names...www.dartmouth.edu
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Fibonacci Circle design |
The next blog entry will include some more artwork examples using more of the course materials from the book 'Universal Patterns' by Martha Boles & Rochelle Newman....until then.....eat your pie for breakfast...Minaz
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