**1. An Old
Man by Leonardo Da Vinci**

Leonardo Da Vinci explored the human body involving in the ratios of the lengths of various body parts. He called this ratio the "divine proportion" and featured it in many of his paintings.

Leonardo da Vinci's drawing of an old man can be overlaid with a square subdivided into rectangles, some of which approximate Golden Rectangles.

We can draw many lines of the rectangles into this figure.

Then, there are three distinct sets of Golden Rectangles: Each
one set for the head area, the torso, and the legs.

This picture includes lots of Golden Rectangles. In above figure,
we can draw a rectangle whose base extends from the woman's right
wrist to her left elbow and extend the rectangle vertically until
it reaches the very top of her head. Then we will have a golden
rectangle.

Also, if we draw squares inside this Golden Rectangle, we will
discover that the edges of these new squares come to all the important
focal points of the woman: her chin, her eye, her nose, and the
upturned corner of her mysterious mouth.

It is believed that Leonardo, as a mathematician tried to incorporate
of mathematics into art. This painting seems to be made purposefully
line up with golden rectangle.

We can notice that this picture is positioned to the principal figures in alignment with a Pentagram or Golden star.

This picture is a well-known example, in which we can find
a Golden Triangle and also Pentagram. In this picture, a
golden triangle can be used to locate one of its underlying pentagrams.

We can draw three straight lines into this figure. Then, the
image of the feature is included into a triangle. Moreover, if
a perpendicular line would be dropped from the apex of the triangle
to the base, the triangle would cut the base in Golden Section.

This picture is painted inside a Golden Rectangle. Also, we
can find part of an enormous dodecahedron above the table. Since
the polyhedron consists of 12 regular Pentagons, it is closely
connected to the golden section.

The title of this work itself includes the Golden Section.
It simply means that it is cut into sections of Golden Proportion.

Seurat attached most of canvas by the Golden Section. This
picture has several golden subdivisions.

Mondrian believed that mathematics and art were closely connected.
He used the simplest geometrical shapes and primary colours (blue,
red, yellow).

His point of view lies in the fact that any shape is possible
to create with basic geometric shapes as well as any color can
be created with different combinations of red, blue, and yellow.
The golden rectangle is one of the basic shapes appear in Mondrian's
art.

We can find that the ratio of length to width for some rectangles
is Phi.