Posts by Tag
All tags: antiprism (5), cartography (9), complex_functions (3), cursed (3), geometry (15), jupyter (5), python (8), r (1), utica (2), vectors (7)
antiprism: 5 posts

Geodesic polyhedra are the abstract geometric version of Buckminster Fuller’s geodesic domes. Take a polyhedron with triangular faces (usually the icosahedro...

A paper from 2012, The Regular Grünbaum Polyhedron of Genus 5, includes a polyhedron of genus 5, earlier discovered by Grünbaum, that is an embedding of th...

Antitile is a Python package for manipulating polyhedra and tilings. It is largely a collection of addons and scripts to be used with for Adrian Rossiter’s ...

Often, beauty in mathematics is described as relating to simplicity or symmetry. The procedure about to be described is interesting because despite being sim...

Aside from the Platonic solids, there are no regular tilings of the sphere. You can’t, for instance, have a spherical polyhedron where the faces are all tria...
cartography: 9 posts

A consequence of the Riemann mapping theorem is that the conformal map from a given region of the sphere to a given region of the plane is essentially unique...

(The title of this post is in tribute to Moler and Van Loan’s classic paper “Nineteen Dubious Ways to Compute the Exponential of a Matrix.”)

My paper “A variation on the Chamberlin trimetric map projection” was just published in Cartography and Geographic Information Science. If you don’t have ins...

John P Snyder, author of many useful articles and books on map projections, created an equalarea projection called (in an aversion of Stigler’s Law) Snyder’...

This is the first post in a series on map projections described using unit vectors. Reference the introductory article on spherical geometry with vectors if ...

An earlier article mentioned how to find the intersection of two great circles on the sphere using vectors. Another common problem is to find the intersectio...

There are many triangle centers defined for Euclidean triangles. These triangle centers can also be defined in spherical geometry, although some Euclidean ce...

Geometric constructions on the sphere are often simpler when expressed using 3dimensional unit vectors. This method sees some use in geography, where it is ...

A local organization asked for a population density map of children aged 5 and below in Oneida County, for discussion about child care. See the images below....
complex_functions: 3 posts

Triangles in spherical and hyperbolic geometry have a property that Euclidean geometry does not: their angles determine their size. The area of a spherical t...

A few posts ago, the Schwarz triangle function came up in the discussion of conformal map projections. The Schwarz triangle function maps the upper halfplan...

(The title of this post is in tribute to Moler and Van Loan’s classic paper “Nineteen Dubious Ways to Compute the Exponential of a Matrix.”)
cursed: 3 posts

(The title of this post is in tribute to Moler and Van Loan’s classic paper “Nineteen Dubious Ways to Compute the Exponential of a Matrix.”)

A question that came up in a math chatroom (yes, I’m the kind of nerd who spends time in math chatrooms): find a “Euclidean” triangle on a nonEuclidean surf...

Often, beauty in mathematics is described as relating to simplicity or symmetry. The procedure about to be described is interesting because despite being sim...
geometry: 15 posts

An earlier post explained homogenous coordinates on the sphere, and derived some relationships between spherical triangle centers. A certain geometric proper...

Trilinear coordinates, a type of homogeneous coordinate, are very useful for the study of Euclidean triangles, especially that of triangle centers. They can ...

Triangles in spherical and hyperbolic geometry have a property that Euclidean geometry does not: their angles determine their size. The area of a spherical t...

This is the first post in a series on map projections described using unit vectors. Reference the introductory article on spherical geometry with vectors if ...

A question that came up in a math chatroom (yes, I’m the kind of nerd who spends time in math chatrooms): find a “Euclidean” triangle on a nonEuclidean surf...

An earlier article mentioned how to find the intersection of two great circles on the sphere using vectors. Another common problem is to find the intersectio...

There are many triangle centers defined for Euclidean triangles. These triangle centers can also be defined in spherical geometry, although some Euclidean ce...

Geometric constructions on the sphere are often simpler when expressed using 3dimensional unit vectors. This method sees some use in geography, where it is ...

Geodesic polyhedra are the abstract geometric version of Buckminster Fuller’s geodesic domes. Take a polyhedron with triangular faces (usually the icosahedro...

Mappings between squares and disks have applications in computer graphics, and are interesting mathematically. Mappings between triangles and disks are less ...

A paper from 2012, The Regular Grünbaum Polyhedron of Genus 5, includes a polyhedron of genus 5, earlier discovered by Grünbaum, that is an embedding of th...

Antitile is a Python package for manipulating polyhedra and tilings. It is largely a collection of addons and scripts to be used with for Adrian Rossiter’s ...

Often, beauty in mathematics is described as relating to simplicity or symmetry. The procedure about to be described is interesting because despite being sim...

Aside from the Platonic solids, there are no regular tilings of the sphere. You can’t, for instance, have a spherical polyhedron where the faces are all tria...

I was inspired by a friend’s alchemical hypergeometric function notation to see how similar drawings looked on the hyperbolic Poincaré disk. Drawing lines on...
jupyter: 5 posts

Mappings between squares and disks have applications in computer graphics, and are interesting mathematically. Mappings between triangles and disks are less ...

I did a quick analysis on using the beta distribution to approximate the binomial distribution. This was definitely done for serious statistical reasons and ...

Simple exponential decay can be manipulated to create chaos like the logistic map. There are also connections with the softplus function used in machine lear...

I was inspired by a friend’s alchemical hypergeometric function notation to see how similar drawings looked on the hyperbolic Poincaré disk. Drawing lines on...

There are two “neighborhoods” often used in cellular automata, the Von Neumann neighborhood of 4 cells and the Moore neighborhood of 8 cells. Conway’s Game o...
python: 8 posts

(The title of this post is in tribute to Moler and Van Loan’s classic paper “Nineteen Dubious Ways to Compute the Exponential of a Matrix.”)

I wrote an article for the Utica College Center of Public Affairs and Election Research blog, “Why Oneida County briefly showed the most COVID19 symptoms in...

Mappings between squares and disks have applications in computer graphics, and are interesting mathematically. Mappings between triangles and disks are less ...

Antitile is a Python package for manipulating polyhedra and tilings. It is largely a collection of addons and scripts to be used with for Adrian Rossiter’s ...

I did a quick analysis on using the beta distribution to approximate the binomial distribution. This was definitely done for serious statistical reasons and ...

Simple exponential decay can be manipulated to create chaos like the logistic map. There are also connections with the softplus function used in machine lear...

I was inspired by a friend’s alchemical hypergeometric function notation to see how similar drawings looked on the hyperbolic Poincaré disk. Drawing lines on...

There are two “neighborhoods” often used in cellular automata, the Von Neumann neighborhood of 4 cells and the Moore neighborhood of 8 cells. Conway’s Game o...
r: 1 posts

I’ve written an R package that implements the trimmed SpearmanKarber method for doseresponse curves. It’s available on Github.
utica: 2 posts

A local organization asked for a population density map of children aged 5 and below in Oneida County, for discussion about child care. See the images below....

I wrote an article for the Utica College Center of Public Affairs and Election Research blog, “Why Oneida County briefly showed the most COVID19 symptoms in...
vectors: 7 posts

An earlier post explained homogenous coordinates on the sphere, and derived some relationships between spherical triangle centers. A certain geometric proper...

Trilinear coordinates, a type of homogeneous coordinate, are very useful for the study of Euclidean triangles, especially that of triangle centers. They can ...

John P Snyder, author of many useful articles and books on map projections, created an equalarea projection called (in an aversion of Stigler’s Law) Snyder’...

This is the first post in a series on map projections described using unit vectors. Reference the introductory article on spherical geometry with vectors if ...

An earlier article mentioned how to find the intersection of two great circles on the sphere using vectors. Another common problem is to find the intersectio...

There are many triangle centers defined for Euclidean triangles. These triangle centers can also be defined in spherical geometry, although some Euclidean ce...

Geometric constructions on the sphere are often simpler when expressed using 3dimensional unit vectors. This method sees some use in geography, where it is ...