Tangent Circles Exercise

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”…

I learned this method from the open math resources website. I couldn’t help myself repeat it in Rhinoceros. It was quite fun to solve circle tangency problems in 2D, this is one of them: drawing the circle that passes three given points, not using ready-made commands but only geometric tools of the circle (compass) and ruler (line). Here is the sequence of it: First of all, we need to know that the circle we are looking for is centered somewhere…

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…

The Koch pentagon is a fractal shape that starts with a regular pentagon. Here, we divide each side of the pentagon into three equal parts. Then, we replace the middle with two sides of an outward-pointing equilateral triangle. We repeat this process for every new side in each iteration, creating a self-similar pattern. Helge von Koch (1870–1924) was a Swedish mathematician known for his analysis and number theory work. He is most famous for introducing the Koch snowflake, one of…