**[notes on the reading, quick glance]**

.application of curve.

.mathematical expression .

.history of curvature

.light read through all the expressions .

http://www3.villanova.edu/maple/misc/history_of_curvature/k.htm

http://www.goucher.edu/documents/verge/papers6/ma002.pdf

Curvature has ultimately had a single role throughout the history of mathematics: to illustrate the natural beauty of mathematics and to describe, in best way, the mathematical aspects of nature.

.Apollonius of perga : method

.Nicole Oresme :definition of curvature

.Johannes Kelpler : using a circle to measure the general curvature

.Rene descartes and pierre de Fermat : express in geometry as equation (lack of mention of PI)

.Huygens ( evolute and involute)

.Sir Isaac Newton . Calculus .object of beauty. Elegance .properties of calculus… it is know that curves behave like straight lines near a point of inflection. calculus values without geometry.

http://www.mathpages.com/rr/s5-03/5-03.htm

A modern day application of curvature can be found in the study of modern physics.

torsion

curvature

http://mysite.du.edu/~jcalvert/

http://mysite.du.edu/~etuttle/math/curves.htm

” the locus of a moving point than a set of points, to emohasizes the connectivity and one dimensional nature of a curve.

Many pathological curves can be defined as sets, but they have no practical or physical applications.

(x,y)

(r,theta)

The Cornu spiral is a vibration curve in optics, showing the contributions to the amplitude from elements of a wavefront.

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**[ Un-edited writing of last week’s sentimental discovery]**

*(I have trouble communicating. I did not want to state that i am making art which use the black universe in my brain …**but i finally realize that i am making art, yet the way i want to make art is not as sentimental … and it requires some hard studies ….. ) *

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We drink water without the wonder of what in water that we need.

It is like a build-in function, intuitively.

J.S bach did not intend each pattern-like harmony before the composition. He felt the method in moment of composing and studying.

A CS person wants to believe a defined pattern in bach’s music. The logic is not because of the pattern so music. It is incorrect to have the result as a cause to form a statement.

To conclude my wavily point, It appears clear that my goal is to study curve in its nature. It generats my creative decision of art making. If ML questions being asked: what problem are you trying to solve? What hypothesizes are you trying to proof? I can only remain peacefully silent.

We all familiar with the modern study of the 90% “unused” brain in Human(maybe animals) and The over 90% dark matter in the universe. We have not discovered the function of such ‘90%” However, they are truly functional.

For my research, I try to understand the science in curve as much I am capable of. This study somehow generate my 90% to compose the curves. In another word, I am preventing traditional way of art making which mostly rely on personalized perceptions,judgments and etc. Of course this is arguable…

In fact, there are equation-less yet logic based “algorithms” in Music Composition, visual art and cinematography, such as 12 tone system, color theory, and 180′ rule.

**<** ———–* fin*———————————————————