Israel is yet again in the news for a scientific accomplishment.
Zilin Jiang from Technion — Israel Institute of Technology and Alexandr Polyanskii from the Moscow Institute of Physics and Technology (MIPT) have proved László Fejes Tóth’s zone conjecture. Formulated in 1973, it says that if a unit sphere is completely covered by several zones, their combined width is at least π. The proof, published in the journal Geometric and Functional Analysis, is important for discrete geometry and enables new problems to be formulated.
Discrete geometry studies the combinatorial properties of points, lines, circles, polygons, and other geometric objects. For example, it deals with the questions: What is the largest number of equal balls that can be fitted around another ball of the same size? Or, what is the densest way to pack equal-sized circles in a plane, or balls in a containing space?
Solutions to problems like these have practical applications. Thus, the dense packing problem has helped optimize coding and correct mistakes in data transmission. A further example is the four color theorem, which says that four colors suffice to plot any map on a sphere so that no two adjacent regions have the same color. It has prompted mathematicians to introduce concepts important for graph theory, which has been crucial for many of the recent developments in chemistry, biology, and computer science, as well as logistics systems.
Ok, I can’t pretend I understood much of that. But, yay us!
In other news, I am guessing Zilin Jiang has an interesting story