Using Math. Formulae to create works of art
25 year Iranian student Hamid Naderi Yeganeh uses
cosines and sines to create fantastic and intricate mathworks. The
images are defined by basic mathematical concepts. Yeganeh studied math.
at the university of Qom in 2012 and at the same time hedeveloped
a love for the art. At first, he was interested in beautiful symmetrical
shapes. So he started to create mathematical figures using trigonometric
functions to define the end points of line segments. After a while, he
realised that he could find interesting shapes that looked like real
life things such as animals. Math and Art have long been linked. Artists in ancient Greece used concepts such as ratio and symmetry to sculpt the human form. Leonardo Da Vinci's work was also greately influenced by math. His Vitruvian Man, is an illustration based on the writings of the Roman architect Vitruvius, sought to capture the exact proportions of the human body. In his native Iran, Yeganeh points to Iranian tiling as a good example of the use of tessellations, or repeating pattern of polygons. He applies this concept to his work. 

This image shows 7000 circles. For k=1,2,3,.....7000, the center of the kth circle is (cos(2PIk/7000)), (sin(18PIk/7000))^3) and the radius of the kth circle is (1/4)(cos(42PIk/7000))^2 

This image shows 8000 circles. For k=1,2,3,.....8000, the center of the kth circle is (cos(6PIk/8000)), (sin(22PIk/8000))^3) and the radius of the kth circle is (1/5)(sin(58PIk/8000))^2 

This image shows 8000 circles. For k=1,2,3,.....8000, the center of the kth circle is (cos(26PIk/8000))^3, (sin(14PIk/8000)) and the radius of the kth circle is (1/4)(cos(40PIk/8000))^2  
This image shows 10000 circles. For k=1,2,3,.....10000, the center of the kth circle is (cos(14PIk/10000))^3, (sin(24PIk/10000))^3) and the radius of the kth circle is (1/3)(sin(44PIk/10000))^4  
This image shows 6000 circles. For k=1,2,3,.....6000, the center of the kth circle is (cos(6PIk/6000)), (sin(14PIk/6000))^3) and the radius of the kth circle is (1/4)(sin(66PIk/6000))^2 

This image shows 10000 line segments. For k=1,2,3,.....10000, the end point of the kth line segment is (sin(108PIk/10000)sin(4PIk/10000)), (cos(106PIk/10000)sin(4PIk/10000))and (sin(104PIk/10000)sin(4PIk/10000)), (cos(102PIk/10000)sin(4PIk/10000))  
This image shows 10000 line segments. For k=1,2,3,.....10000, the end point of the kth line segment is ((3/4)cos(86PIk/10000),(sin(84PIk/10000))^5) and ((sin(82PIk/10000)^5,(3/4) (cos(80PIk/10000))  
This fox is created using one of the most complex math formula found in his work. The image shows a subset of the complex plane that contains all complex numbers of the form λA(t) +(1λ)B(t), 0 <= t <=2PI; 0 <=λ <= 1 , where A(t) = sin(4t +(PI/4))cos(2t)+(2i/3)sin(2t+(PI/2)) and B(t) =(2/3)(sin(t+(PI/5)))^3(cos(t+(PI/3)))^2+i(sin(3t(PI/3)))^2+(i/2)sin(4t+(PI/6))  
This image is a bird in flight. It shows 500 line segments. For each i=1,2,3,.....500, the end points of theith line segment are ((3/2)(sin((2PIi/500)+(PI/3)))^7, (1/4)cos(6PI/500))^2) and ((1/5)sin((6PIi/500)+(PI/5)),(2/3)(sin(( 2PI/500)(PI/3)))^2. When different numerical values are assigned to the equation above,he end results can pictorially represent a bird in flight. 
