Thursday 24 March 2011

WHAT IS A LINE?

Types of line:




line of trees



line of people



lines on the face



directional lines



border line



countour lines



line of music



the simple line of a pencil





Some examples of line being applied to create image:
Georgina Luck
 - Shows how the simple use of line can be effective when creating an image







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David Bignotti
 - Line used for simple imagery/illustraion...







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Robinsson Cravents
 - Minor lines used to build up to a larger image
 - No distinct outline to the image



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Focusing on ancient math & shapes...








I wanted to focus on harmony and order within shapes. In order to do this, a brief history of math will probably aid my progress....

"Babylonian mathematics (also known as Assyro-Babylonian mathematics[1][2][3][4][5][6]) refers to any mathematics of the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited.[7] In respect of time they fall in two distinct groups: one from the Old Babylonian period (1830-1531 BC), the other mainly Seleucid from the last three or four centuries BC. In respect of content there is scarcely any difference between the two groups of texts. Thus Babylonian mathematics remained constant, in character and content, for nearly two millennia.[7] In contrast to the scarcity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics which include fractionsalgebraquadratic and cubic equations and thePythagorean theorem. The Babylonian tablet YBC 7289 gives an approximation to \sqrt{2} accurate to five decimal places"




"While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote: "He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life."[42]

Archimedes used the method of exhaustion to approximate the value of pi.
Archimedes was able to use infinitesimals in a way that is similar to modern integral calculus. Through proof by contradiction (reductio ad absurdum), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the value of pi. He did this by drawing a larger polygon outside a circle and a smaller polygon inside the circle. As the number of sides of the polygon increases, it becomes a more accurate approximation of a circle. When the polygons had 96 sides each, he calculated the lengths of their sides and showed that the value of pi lay between 317 (approximately 3.1429) and 31071 (approximately 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the area of a circle was equal to pi multiplied by the square of the radius of the circle. In On the Sphere and Cylinder, Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. This is the Archimedean property of real numbers.[43]
In Measurement of a Circle, Archimedes gives the value of the square root of 3 as lying between 265153 (approximately 1.7320261) and 1351780 (approximately 1.7320512). The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of the method used to obtain it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results."[44]  "