March 2025 archive
How does a program organize a map to facilitate finding
the nearest restaurant or gas station or Uber car?
One way is to partition the earth's surface into grid cells,
which enables a graph search (check the cell you're in,
its neighbors, neighbors of neighbors, ...).
A flat surface lends itself to being partitioned into a
grid of square cells, but what about a sphere?
Uber wrote code to partition the globe into mostly hexagonal cells, where mostly means twelve pentagonal cells and all the rest hexagonal: like a soccer ball, but with a lot more hexagons. Such a grid has a roughly uniform cell-to-cell distance everywhere on Earth. The twelve pentagons are at the vertices of a regular icosahedron. Uber followed an example from R. B. Fuller that orients the icosahedron such that the twelve vertices lie in bodies of water.
Uber has shared source code for their grid system on Github. It's hierarchical: it supports a range of coarse to fine grids. An overview is here and an interactive page showing their grids on a world map is here. Below: a screenshot showing my (rectangular) house and a hexagonal grid cell.
My architect neighbor Brian didn't like pentagons. He thought it
should be possible to partition a spherical surface with only
hexagonal cells. I showed him a proof that it was impossible
but he didn't want to believe it.
Uber wrote code to partition the globe into mostly hexagonal cells, where mostly means twelve pentagonal cells and all the rest hexagonal: like a soccer ball, but with a lot more hexagons. Such a grid has a roughly uniform cell-to-cell distance everywhere on Earth. The twelve pentagons are at the vertices of a regular icosahedron. Uber followed an example from R. B. Fuller that orients the icosahedron such that the twelve vertices lie in bodies of water.
Uber has shared source code for their grid system on Github. It's hierarchical: it supports a range of coarse to fine grids. An overview is here and an interactive page showing their grids on a world map is here. Below: a screenshot showing my (rectangular) house and a hexagonal grid cell.
My architect neighbor Brian didn't like pentagons. He thought it
should be possible to partition a spherical surface with only
hexagonal cells. I showed him a proof that it was impossible
but he didn't want to believe it.
We didn't get much precip this winter and it's not
looking like we'll get a lot of flower action this spring.
A neighbor's Joshua tree is, nonetheless, getting its flower on.
Happy nineteenth, everyone.
Happy nineteenth, everyone.
from Classification theory
and the number of non‑isomorphic models
by Saharon Shelah.
One of several satirical floats in a parade
in Germany yesterday.
Many people commenting on
news
coverage thought such politically-themed displays
were out of place at a traditional yearly carnival.
We could use demonstrations like this in Washington though.
The bald eagle pair whose
live video stream
I've occasionally watched over the past few years have three eggs this year,
two of which have recently pipped (started to hatch).
From a web page summarizing recent goings-on at the nest:
From a web page summarizing recent goings-on at the nest:
Pip1 confirmed 3/2 15:09. (We have no way of knowing which egg has pipped. They are laid without numbers.)
Pip2 confirmed 3/3 7:59:45