Geometry In Nature And Art

Many natural scenes contain elements that can each be deconstructed into combinations of basic geometric shapes. The simplest of these are the circle, triangle, and the square. Variations on the square include the rectangle, parallelogram, and the trapezoid. Expansion beyond the square to simple regular polygons include the pentagon, hexagon, heptagon and octagon. These are five, six, seven and eight-pointed structures, respectively, with the points in the same plane and with the sides all of equal length. Each can be fit within a circle, and when drawn, it can be seen that as the number of sides of such regular polygons is increased, they will more and more approximate the shape of the circle.

Many if not most simple pictures or photos can be resolved roughly into overlapping simple geometric figures–indeed mostly as a combination of circles, triangles and squares. Rectangles, parallelograms and trapezoids can be thought of as combinations of overlapping squares and triangles. Some might add the oval to the basic list of shapes, but these can be resolved into overlapping circles.

In drawings that show a three dimensional perspective you can usually see and outline, at low resolution, many cubes, cylinders and spheres. You should also see squares and triangles.These sometimes overlap and you will also be able to resolve rectangles, parallelograms or trapezoids.

Also, an interesting group of regular polygons know as the Platonic solids is worth learning about if your interests are artistically inclined. These figures are incorporated into some natural occurring complex systems in nature. Also, variations on the Platonic solids are of interest in themselves as a form that has been has been introduced into architectural design.

The basic Platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The tetrahedron is a four sided figure, each side of which is an equilateral triangle. The cube, which is well-known to most, is a six-sided figure each side of which is a perfect square. The octahedron is an eight-sided figure, each side of which is an equilateral triangle. The dodecahedron is a twelve-sided figure each side of which is a regular pentagon, and the icosahedron is a twenty-sided figure each side of which is an equilateral triangle.

It is a worthwhile exercise to 1. find basic circular shapes as well as triangles, squares within simple drawings or photographs, and 2. try to draw the Platonic solids from the descriptions given above and then look them up and then redraw them from the descriptions or from drawings shown on various sites on the Internet.


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