I want to research curves .

equation of curves

visualization of the equations

analyzing the visualization + equations

explore and experiment with the equation generated visualizations

( that involves cutting pasting equations through code  ...etc)

Books {

Henri Poincare --[the value of science] [science and hypothesis]

[book of curves]

[standard curves and plane ]

[exploration of strange curves]

[computational beauty of nature]

}

Nouns {

(focused on) :

curve

mathematics visualization

cartesian coordinate system

polar coordinate system

coordinate curves and surfaces

complex numbers

(lightly reading on)

Aperiodic tilling

Topology

geometry processing

}

My notes{

I would like to try not to cover too many filed of mathematics, too complex system and theories. All the filed i have been researching  seems from really old baroque time. Therefore, i am aware of the fact that some of the statement might not be true or relevant anymore. I am not sure what is it that fascinating me so much .

I am interested in the theory of how mathematically number sets form the plane and generate motions to "clam" the plane and dimensions. as i find computer graphic is such an wonderful platform to jiggle all the numbers and viewable.

Also, I wish my researching progress will  improve my computer science and programming knowledge.

I have not enough skill to test out complex number system and differential geometry  in programming at this stage , however i am really interested in getting into the general information. I have already read some books and papers about complex numbers and differential geometry both in mathematical terms and also in philosophy meanings. I did not completely understand them, however they are readable.  

}

Excuse for my not appropriate format, I will improve once it gets on the path!

I do not mind rewrite it  into a proper  format and writing style once allows me more time.