Voronoi Bubbles
Informal use of Voronoi diagrams can be traced back to Descartes in 1644 Peter Gustav Lejeune Dirichlet used two-dimensional and three-dimensional Voronoi diagrams in his study of quadratic forms in 1850. British physician John Snow used a Voronoi-like diagram in 1854 to illustrate how the majority of people who died in the Broad Street cholera outbreak lived closer to the infected Broad Street pump than to any other water pump. Voronoi diagrams are named after Georgy Feodosievych Voronoy who defined and studied the general n-dimensional case in 1908. -Wikipedia.
The dual of this subdivision is the Delaunay triangulation. Although the name Voronoi comes from a specific mathematician, as seen in the brief history above, it actually has numerous predecessors.
Dirichlet’s Age of Mathematics
Dirichlet Tessellation is essentially the exact same solution as Voronoi, and was defined for 2- and 3-dimensional spaces by the German mathematician Gustav Dirichlet about 50 years before Voronoi. Even though these systems are referred to as Voronoi in our field, the name Voronoi actually belongs to the n-dimensional generalization of this structure, whereas Dirichlet formulated the 2-dimensional definition in 1850, precisely the format used by Grasshopper. Because of this, I decided to gather some information about Dirichlet. As I mentioned on this site as well, he made contributions to Fourier Series. Beyond that, he has countless other contributions. As I looked closer, I noticed that he mentored some very interesting names (Dedekind, Riemann, Cantor, and Enneper). Each of them holds a unique place in geometry and mathematics. Dedekind surprised me in particular because, alongside Frege, he is the founder of Logicism. Riemann probably doesn’t even need to be mentioned. Cantor is the founder of set theory, and Enneper gave his name to a special surface I have used.
The relationship between Gauss and Dirichlet is a deep intellectual bond between the master who laid the foundations of number theory and his most loyal apprentice who carried that legacy to its peak. Gauss summarized his admiration for Dirichlet’s genius with the phrase, “Jewels are not weighed on a grocer’s scale,” and following Gauss’s death, Dirichlet took over his legendary chair in Göttingen, becoming the natural successor to this great mathematical heritage. Unfortunately, Dirichlet passed away only at the age of 54.
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