#tangent

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”…

This is based on my failure of creating an optimum solution for planar polygonal subdivisions. There is a method called Tangent Plane Intersection (TPI), explained briefly here (sometimes similar algorithms are called “planar remeshing” and  “variational shape approximation”) which is effectively used in the Trada pavilion (here). I tried to implement a similar method using only native Grasshopper components and no recursion, but it quickly became much more complicated than I thought. It was based on the simple idea that…

The first-year Architectural Geometry course includes Euclidean constructions as a study of associative geometry. We have exercised the below questions to study this topic. These are three mutually tangent circles, that can be drawn using only a compass and ruler, without built-in tangency functions in Rhino. Such exercises are expected to improve students’ reasoning. We believe architectural geometry education should encourage a conception that allows students to think about what they are doing and control their process, rather than just…