László Fejes Tóth
Encyclopedia
László Fejes Tóth was a Hungarian
mathematician
who specialised in geometry
. He proved that a honeycomb
pattern is the most efficient way to pack centrally symmetric convex set
s on the Euclidean plane (a generalization of Thue's theorem
, a 2-dimensional analog of Kepler conjecture
). He also investigated packings on the sphere. He was the first to show, in 1953, that the Kepler conjecture can be reduced to a finite case analysis.
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who specialised in geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. He proved that a honeycomb
Honeycomb
A honeycomb is a mass of hexagonal waxcells built by honey bees in their nests to contain their larvae and stores of honey and pollen.Beekeepers may remove the entire honeycomb to harvest honey...
pattern is the most efficient way to pack centrally symmetric convex set
Convex set
In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object...
s on the Euclidean plane (a generalization of Thue's theorem
Thue's theorem
Thue's theorem may refer to the following mathematical theorems named after Axel Thue:* Thue equation has finitely many solutions in integers.* Thue–Siegel–Roth theorem, also known as Roth's theorem, is a foundational result in diophantine approximation to algebraic numbers.* The 2-dimensional...
, a 2-dimensional analog of Kepler conjecture
Kepler conjecture
The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic...
). He also investigated packings on the sphere. He was the first to show, in 1953, that the Kepler conjecture can be reduced to a finite case analysis.
Works
- Reguläre Figuren (1965).