In this post you can see three images with their mathematical descriptions. I have defined them by trigonometric functions. In order to create such shapes, it is very useful to know the properties of the trigonometric functions. I believe these images show us an important fact:
We can draw with mathematical formulas.
In addition to the images in this post, you can see A Bird In Flight, Fish, Boat and three images in one of my previous posts: These Are Mathematical Sets.
Parrot
(x-A(k))+(y-B(k))=(R(k)),
for k=-10000, -9999, ... , 9999, 10000, where
A(k)=(3k/20000)+(cos(37πk/10000))sin((k/10000)(3π/5))+(9/7)(cos(37πk/10000))(cos(πk/20000))sin(πk/10000),
B(k)=(-5/4)(cos(37πk/10000))cos((k/10000)(3π/5))(1+3(cos(πk/20000)cos(3πk/20000)))+(2/3)(cos(3πk/200000)cos(9πk/200000)cos(9πk/100000)),
R(k)=(1/32)+(1/15)(sin(37πk/10000))((sin(πk/10000))+(3/2)(cos(πk/20000))).
Stork
(x-A(k))+(y-B(k))=(R(k)),
for k=-4000, -3999, ... , 3999, 4000, where
A(k)=(3k/4000)+(cos(32πk/4000))sin((k/4000)(π/2)),
B(k)=-(cos(32πk/4000))cos((k/4000)(π/2))(1+(cos(πk/8000)cos(3πk/8000)))+3(cos(πk/8000)cos(3πk/8000))(cos(16πk/4000)),
R(k)=(1/30)+(1/15)(cos(πk/8000)cos(5πk/8000))(1-(1/2)(cos(32πk/4000)))+(1/7)(sin(32πk/4000))(sin(πk/4000)).
Magpie
(x-A(k))+(y-B(k))=(R(k)),
for k=-10000, -9999, ... , 9999, 10000, where
A(k)=(11k/100000)+(cos(41πk/10000))sin((k/10000)(π/2)),
B(k)=-(cos(41πk/10000))cos((k/10000)(π/2))(1+(5/2)(cos(3πk/100000)cos(9πk/100000)))+(1/2)(cos(πk/40000)cos(3πk/40000)cos(3πk/20000)),
R(k)=(1/50)+(1/20)(sin(41πk/10000)sin(πk/10000)).
Support HuffPost
Our 2024 Coverage Needs You
Your Loyalty Means The World To Us
At HuffPost, we believe that everyone needs high-quality journalism, but we understand that not everyone can afford to pay for expensive news subscriptions. That is why we are committed to providing deeply reported, carefully fact-checked news that is freely accessible to everyone.
Whether you come to HuffPost for updates on the 2024 presidential race, hard-hitting investigations into critical issues facing our country today, or trending stories that make you laugh, we appreciate you. The truth is, news costs money to produce, and we are proud that we have never put our stories behind an expensive paywall.
Would you join us to help keep our stories free for all? Your contribution of as little as $2 will go a long way.
Can't afford to donate? Support HuffPost by creating a free account and log in while you read.
As Americans head to the polls in 2024, the very future of our country is at stake. At HuffPost, we believe that a free press is critical to creating well-informed voters. That's why our journalism is free for everyone, even though other newsrooms retreat behind expensive paywalls.
Our journalists will continue to cover the twists and turns during this historic presidential election. With your help, we'll bring you hard-hitting investigations, well-researched analysis and timely takes you can't find elsewhere. Reporting in this current political climate is a responsibility we do not take lightly, and we thank you for your support.
Contribute as little as $2 to keep our news free for all.
Can't afford to donate? Support HuffPost by creating a free account and log in while you read.
Dear HuffPost Reader
Thank you for your past contribution to HuffPost. We are sincerely grateful for readers like you who help us ensure that we can keep our journalism free for everyone.
The stakes are high this year, and our 2024 coverage could use continued support. Would you consider becoming a regular HuffPost contributor?
Dear HuffPost Reader
Thank you for your past contribution to HuffPost. We are sincerely grateful for readers like you who help us ensure that we can keep our journalism free for everyone.
The stakes are high this year, and our 2024 coverage could use continued support. If circumstances have changed since you last contributed, we hope you’ll consider contributing to HuffPost once more.
Already contributed? Log in to hide these messages.
