Emergent Polygons

Using a compass and straightedge enables precise geometric constructions, allowing for the creation of complex tessellations. To begin these constructions, a single starting point is sufficient. Circles, which represent a collection of points at a specific distance from the center, and straight lines, which represent a collection of points in a particular direction, are utilized for geometric constructions. In this short tutorial, we move on with the beginner-level drawing exercises. This time, I am drawing an irregular tiling with triangles…

The term “hexa” generally refers to the number six, derived from the Greek word. It is commonly used in mathematics, geometry, and other scientific fields to indicate six-sided shapes or structures. A hexagon is a polygon with six sides and six angles. It is one of the regular polygons, meaning all of its sides and angles are equal. A hexahedron is a polyhedron with six faces. The most well-known example is the cube, which has six square faces, twelve edges,…

The geometric shapes constructed using only a compass and straightedge have significantly influenced the development of reasoning and logic that underpin modern science. This non-numerical approach is also known as the Synthetic Geometry. Before René Descartes introduced Analytic Geometry, this method was widely studied and practiced. In “Elements”, Euclid explores fundamental rules, such as ‘The straight line between two points is the shortest,’ and derives all geometric truths from simple, observable principles, built up step by step through logical deduction….

The practical geometry of the ancient Egyptian “rope-stretchers” delineated land after the annual flooding of the Nile River. Thus, the term “geometry” derives from the Greek words “gaia” (earth) and “metria” (measurement). Greek mathematicians used compass and straightedge to perform similar calculations on paper. This abstract thinking allowed for insights into the underlying logic, independent of the accuracy of hand tools. So, the abstract “circle” and “line” constructed by perfect compasses and straightedges can be seen as a reflection of…

A spiral is a curve that begins at a central point and continuously moves outward, either getting larger (in an outward spiral) or smaller (in an inward spiral). It often revolves around a central point or axis. Spirals are fascinating because they appear in many aspects of nature, mathematics, and art. In this drawing exercise, I utilized several commands to draw such a system. However, this drawing is not a curved spiral but rather a segmented one. In this basic…