I announce a competition - who will create the most interesting and beautiful portrait of the roots of two equations. I will send a hard copy of my book (2⁵ Problems for STEM Education - 1st Edition - Valery Ochkov - Rout (routledge.com)) to the winner of the contest. The end date of the competition is April 1, 2022. I will personally determine the winner. Materials explaining the essence of the task, in attachment. In the picture - a sample of a work of science and art, which should be submitted to the competition.
Our paintings will look good in a house where the wife is a designer and the husband is an architect.
@ValeryOchkov wrote:
I hope this case will be interesting (2 roots)
Maybe. Will also depend on the center position and the zoom factor, I guess.
Give it a try and show the generated art work.
BTW you were cheating in the plot you showed - lemniscate and oval aren't even touching on close look.
The scaling factor needed for the lemniscate would be 1/2* sqrt(3).
EDIT: I just notice that I already posted the picture showing exactly the case of touching oval and lemniscate -> https://community.ptc.com/t5/PTC-Mathcad/Portrait-of-roots-of-two-equations/m-p/778067/highlight/true#M199817
There is not much difference compared to the case with four points of intersection other than only two colors (plus black for "no solution") are used instead of four.
Anyway, I recreated the pic and included it in the small gallery below.
Here some more galleries. Combining multiple curves results in more points of intersection and more colorful pictures.
@ValeryOchkov wrote:
Fine!
But what is it?
What it is? I would say its off-topic because its not created by Mathcad but edited using a paint program and because it does not follow your initially stated requirement "portrait of the roots of two equations" using the effects of a numerical algorithm. 😄
But of course we could use the equation you show to create on-topic pics:
or a bit simpler:
The latter contains a lot of black (no solution) in the center and this does not change when we switch from LM to QN:
Here are a few more on-topic pics 😉
@ValeryOchkov wrote:
The best
I remember that I pressed F9 many times on the expression to change the random color until I could claim it to be the pic of a flower 😉
There are 16 point of intersection and no positions where there is no solution. So the image consists of 16 colors. Here are a few other random colorings of the same picture:
But the pictures that consist of fewer colors also have their appeal. For example the following - has something of Lost in Space.
I propose a sketch of a tattoo - one of the faces of the goddess of mathematics Athena - the face of applied mathematics. An applied mathematician or programmer can come to a tattoo salon and order such a tattoo on his body.
And speaking seriously, we can say the following.
The theme of the portrait of the roots of a system of two equations is presented in the first chapter of this book.
STEM Problems with Mathcad and Python - 1st Edition - Valery Ochkov - (routledge.com)
Go to the site and order not a tattoo, but the book itself 😉
The article on this problem
See the attach
One part of the article.
Thanks, Werner, onr more! I have a dream to be your coautor.
