## These Beautiful Images Are Created By Drawing Rectangles

Mathematical formulas enable us to create an infinite number of beautiful images. Below are ten mathematical images which are made by trigonometric functions. I just used high-school level mathematics to create them. At the end of this post you can see the mathematical description of “7,000 Rectangles (2)“.

5,000 Rectangles (1)

10,000 Rectangles (1)

6,000 Rectangles (1)

6,000 Rectangles (2)

10,000 Rectangles (2)

7,000 Rectangles (1)

5,000 Rectangles (2)

10,000 Rectangles (3)

10,000 Rectangles (4)

7,000 Rectangles (2)

This image shows 7,000 rectangles. For each k=1, 2, 3, … , 7000 the vertices of the k-th rectangle are:

(X(k)-A(k), Y(k)-B(k)),

(X(k)+A(k), Y(k)-B(k)),

(X(k)+A(k), Y(k)+B(k)),

(X(k)-A(k), Y(k)+B(k)),

where

X(k)=((1/4)+(3/4)(cos(πk/700))2)sin(2πk/7000),

Y(k)=((1/4)+(3/4)(cos(πk/700))2)cos(2πk/7000),

A(k)=(1/200)+(1/7)(cos(84πk/7000))8,

B(k)=(1/200)+(1/7)(sin(82πk/7000))8.

– This feed and its contents are the property of The Huffington Post, and use is subject to our terms. It may be used for personal consumption, but may not be distributed on a website.