Math Blog
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...
Circles, Rotations, and Groups
Circles In a Euclidean plane, fix a point \(c\) and a positive real number \(r\). The circle with center \(c\) and radius \(r\) is the set of points at distance \(r\) from \(c\). To describe a...
Circles, Rotations, and Groups
Circles In a Euclidean plane, fix a point \(c\) and a positive real number \(r\). The circle with center \(c\) and radius \(r\) is the set of points at distance \(r\) from \(c\). To describe a...
Algebra to Geometry: Functions, Cartesian Coord...
Functions In mathematics, a function represents a causal relationship between “input” and “output.” For example, the area \(A\) of a square of side length \(s\) is given by the formula...
Algebra to Geometry: Functions, Cartesian Coord...
Functions In mathematics, a function represents a causal relationship between “input” and “output.” For example, the area \(A\) of a square of side length \(s\) is given by the formula...