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
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Geodesic polyhedra are the abstract geometric version of Buckminster Fuller’s geodesic domes. Take a polyhedron with triangular faces (usually the icosahedro...
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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...
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Antitile is a Python package for manipulating polyhedra and tilings. It is largely a collection of add-ons and scripts to be used with for Adrian Rossiter’s ...
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Often, beauty in mathematics is described as relating to simplicity or symmetry. The procedure about to be described is interesting because despite being sim...
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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
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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...
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(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.”)
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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...
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John P Snyder, author of many useful articles and books on map projections, created an equal-area projection called (in an aversion of Stigler’s Law) Snyder’...
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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 ...
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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...
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There are many triangle centers defined for Euclidean triangles. These triangle centers can also be defined in spherical geometry, although some Euclidean ce...
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Geometric constructions on the sphere are often simpler when expressed using 3-dimensional unit vectors. This method sees some use in geography, where it is ...
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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
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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...
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A few posts ago, the Schwarz triangle function came up in the discussion of conformal map projections. The Schwarz triangle function maps the upper half-plan...
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(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
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(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.”)
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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 non-Euclidean surf...
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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
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An earlier post explained homogenous coordinates on the sphere, and derived some relationships between spherical triangle centers. A certain geometric proper...
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Trilinear coordinates, a type of homogeneous coordinate, are very useful for the study of Euclidean triangles, especially that of triangle centers. They can ...
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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...
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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 ...
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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 non-Euclidean surf...
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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 3-dimensional unit vectors. This method sees some use in geography, where it is ...
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Geodesic polyhedra are the abstract geometric version of Buckminster Fuller’s geodesic domes. Take a polyhedron with triangular faces (usually the icosahedro...
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Mappings between squares and disks have applications in computer graphics, and are interesting mathematically. Mappings between triangles and disks are less ...
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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...
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Antitile is a Python package for manipulating polyhedra and tilings. It is largely a collection of add-ons and scripts to be used with for Adrian Rossiter’s ...
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Often, beauty in mathematics is described as relating to simplicity or symmetry. The procedure about to be described is interesting because despite being sim...
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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...
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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
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Mappings between squares and disks have applications in computer graphics, and are interesting mathematically. Mappings between triangles and disks are less ...
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I did a quick analysis on using the beta distribution to approximate the binomial distribution. This was definitely done for serious statistical reasons and ...
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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...
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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...
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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
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(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.”)
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I wrote an article for the Utica College Center of Public Affairs and Election Research blog, “Why Oneida County briefly showed the most COVID-19 symptoms in...
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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 add-ons 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...
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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
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I’ve written an R package that implements the trimmed Spearman-Karber method for dose-response curves. It’s available on Github.
utica: 2 posts
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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....
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I wrote an article for the Utica College Center of Public Affairs and Election Research blog, “Why Oneida County briefly showed the most COVID-19 symptoms in...
vectors: 7 posts
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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 equal-area 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 3-dimensional unit vectors. This method sees some use in geography, where it is ...