A guilloche-like trigonometric tangle

mAnasa-taraMgiNI

Coprimality, i.e., the situation where the GCD of 2 integers is 1 is one of the fundamental expressions of complexity. In that situation, two numbers can never contain the other within themselves or in multiples of them by numbers smaller than the other. In other words, their LCM is the product of the 2 numbers. There are numerous geometric expressions of this complexity inherent in coprime numbers. One way to illustrate it is by the below class of parametric curves defined by trigonometric functions:

$latex x=a_1cos(c_1t+k_1)+a_2cos(c_2t+k_2)[5pt]
y=b_1sin(c_3t+k_3)+b_2sin(c_4t+k_4)$

The human mind perceives symmetry and certain optimal complexity as the hallmarks of aesthetics. Hence, we adopt the following conditions:
1) $latex a_1, a_2, b_1, b_2$ are in the range $latex tfrac{3}{14}$..1 for purely aesthetic considerations.
2) $latex k_1, k_2, k_3, k_4$ are orthogonal rotation angles that are in the range $latex [0, 2pi]$
3) $latex c_1$, for aesthetic purposes relating to optimal…

View original post 112 more words

Published by

sudhasarathi61

It is absolutely clear that this world and its contents are purely mental and nothing solid in it. To come out of suffering entirely you should know your mind thoroughly.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s