Drawing Koch Pentagon

This is an implementation of the famous Koch Snowflake Fractal in Grasshopper. We will be using the Anemone add-on to handle the iterations. In this fractal, we start from an equilateral triangle. Then, we form new equilateral triangles, one-third of the side. So that each repetition protrudes in the middle of all the sides. In summary; The Preparation for Koch Snowflake Fractal Now let’s follow the Grasshopper application step by step. We start Koch Snowflake Fractal by creating a triangle…

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…

Snub Square Tiling is a semi-regular tessellation of the plane, composed of two squares and three regular triangles at each vertex. The arrangement of these two regular shapes seamlessly covers the plane without any gaps or overlaps. It is one of the eight semi-regular tessellations known in geometry. The dual of Snub Square Tiling is Cairo Pentagonal Tiling, which we will explore later. In this short tutorial, I am drawing and constructing the Snub Square Tiling by using an abstract…

In geometry, “tangent” refers to a scenario where a line, curve, or surface touches another at exactly one point without crossing or leaving a gap. A tangent line to a circle is a straight line that touches the circle at only one point, and it is perpendicular to the radius at that point. Two circles can be tangent either internally or externally. Geometric constructions using a compass and straightedge can help accurately calculate tangent circles. Thus, the “constructing tangent circles”…

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….