Math Blog
Projective Geometry
Rays and Perspective Imagine a flat floor extending to infinity in all directions and covered with square tiles, creating a Cartesian coordinate system. A parabola, such as the graph \(y...
Projective Geometry
Rays and Perspective Imagine a flat floor extending to infinity in all directions and covered with square tiles, creating a Cartesian coordinate system. A parabola, such as the graph \(y...
Conformal Torus Knots
In this post we'll meet a staple at the Differential Geometry math art shop: Flat tori in four-space, and "conformal torus knots" lying on these surfaces. Although we generally strive...
Conformal Torus Knots
In this post we'll meet a staple at the Differential Geometry math art shop: Flat tori in four-space, and "conformal torus knots" lying on these surfaces. Although we generally strive...
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...