Geometry
A defense of Tetrahedron Maps
This very unsphere shape can actually be a great globe
I have a small obsession about constant area hexagonal map. Maps can serve many purposes, but the ones I am mostly interested in education, their ability to show the world in a way that you can figure out new connections just by looking at them. Hexagonal maps have a strong association with board Games (and Video Games), and I believe it is because games, like maps, are an attempt at creating an idealized model of a piece of the world, a scenario in which from far away, a complex system looks simpler. As if you knew the basic rules, then you could figure out how the game plays out. I wanted to give an upgraded new map for the Impossible Map I've made last year, and so I started working on…
Gosper World - a novel world map made of hexagonal-like fractals (or, how I made Matt Parker’s Impossible Ball)
This is a blog format of the presentation given at the Bridges Conference of Mathematics and Art 2024 in Richmond. The original paper the presentation is based on can be found on the Bridges Website. You can also download the poster and print it in large format. Is it possible to wrap a sphere using ONLY hexagons? This is the question that started me in this journey and the one we will be exploring. The answer has some surprising implications, from the big to the fun. In the bigger side, for instance, Uber stores almost all of its geographical information on ride and traffic data using hexagons around the earth. It argues that doing it facilitates computing approximate radius and distance…
Gosperaedron: a new polyhedral for mapping purposes
While it typically falls outside my primary areas of research in crypto usability, I've recently found myself exploring a different rabbit hole. My journey began with an attempt to improve upon Uber’s H3 system, involved a phase of laser printing numerous paper rhombic dodecahedrons, and finally culminated in a novel map projection. This map not only enhances the aesthetic appeal of Buckminster Fuller’s “Dymaxion" model of a continental Earth, but also integrates a more organic, fractal-based round border. The problem with maps Beyond their practical applications, maps serve as a representation of our perception of the world. Even before Mercator introduced his infamous map projection, a…