Math Blog
Compound Circular Motion
Circles and Parametrization Recall that a circle is the set of points in a plane lying at fixed radius \(r\) from a point, the center. In Cartesian coordinates, if \(c...
Compound Circular Motion
Circles and Parametrization Recall that a circle is the set of points in a plane lying at fixed radius \(r\) from a point, the center. In Cartesian coordinates, if \(c...
Square roots with a complex twist
In this post we'll build a bridge starting with the parabola familiar from plane geometry and arriving at the “Riemann surface of the complex square root,” which often mystifies complex...
Square roots with a complex twist
In this post we'll build a bridge starting with the parabola familiar from plane geometry and arriving at the “Riemann surface of the complex square root,” which often mystifies complex...
Stereographic Projection and Möbius Transformat...
Perspective “Point projection” is a simple model for representing a three-dimensional scene on a planar canvas in perspective. Fix a plane \(P\) in Euclidean three-space and a point \(p\) not on \(P\). For...
Stereographic Projection and Möbius Transformat...
Perspective “Point projection” is a simple model for representing a three-dimensional scene on a planar canvas in perspective. Fix a plane \(P\) in Euclidean three-space and a point \(p\) not on \(P\). For...
Polar Coordinates and Polar Graphs
Polar Coordinates Mathematicians translate between geometry and algebra using “coordinates”, assignments of ordered lists of numbers to geometric locations. To define Cartesian coordinates in the Euclidean plane, we fix perpendicular...
Polar Coordinates and Polar Graphs
Polar Coordinates Mathematicians translate between geometry and algebra using “coordinates”, assignments of ordered lists of numbers to geometric locations. To define Cartesian coordinates in the Euclidean plane, we fix perpendicular...
High-Dimensional Geometry
Geometry and Coordinates At the Differential Geometry math art shop we prefer shape to symbolic description. Sometimes, however, symbolic description can guide us where geometric intuition may falter. For example,...
High-Dimensional Geometry
Geometry and Coordinates At the Differential Geometry math art shop we prefer shape to symbolic description. Sometimes, however, symbolic description can guide us where geometric intuition may falter. For example,...
Complex Numbers
Formally, a complex number is an expression \(a + bi\), with \(a\) and \(b\) real numbers and \(i\) an entity satisfying \(i^{2} = -1\). The square of an arbitrary real number...
Complex Numbers
Formally, a complex number is an expression \(a + bi\), with \(a\) and \(b\) real numbers and \(i\) an entity satisfying \(i^{2} = -1\). The square of an arbitrary real number...