Latest Posts

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

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

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...
Tags: complex_functions
,
geometry

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...
Tags: complex_functions

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...
Tags: cartography

(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.”)
Tags: cartography
,
cursed
,
python
,
complex_functions

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...
Tags: cartography

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’...
Tags: vectors
,
cartography

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 ...
Tags: geometry
,
vectors
,
cartography

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...
Tags: geometry
,
cursed

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...
Tags: geometry
,
vectors
,
cartography

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

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

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

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....
Tags: cartography
,
utica

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...
Tags: python
,
utica

Mappings between squares and disks have applications in computer graphics, and are interesting mathematically. Mappings between triangles and disks are less ...
Tags: python
,
jupyter
,
geometry

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...
Tags: geometry
,
antiprism

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 ...
Tags: geometry
,
python
,
antiprism

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

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...
Tags: geometry
,
antiprism

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

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...
Tags: python
,
jupyter

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...
Tags: python
,
jupyter
,
geometry

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...
Tags: python
,
jupyter

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