The Voderberg tiling is a mathematical spiral

tiling Tiling may refer to: *The physical act of laying tiles * Tessellations Computing *The compiler optimization of loop tiling *Tiled rendering, the process of subdividing an image by regular grid *Tiling window manager People *Heinrich Sylvester T ...

, invented in 1936 by mathematician (1911-1945). It is a monohedral tiling: it consists of only one shape that tessellates the plane with congruent copies of itself. In this case, the

prototile In the mathematical theory of tessellations, a prototile is one of the shapes of a tile in a tessellation. Definition A tessellation of the plane or of any other space is a cover of the space by closed shapes, called tiles, that have disjoint in ...

is an elongated irregular

nonagon In geometry, a nonagon () or enneagon () is a nine-sided polygon or 9-gon. The name ''nonagon'' is a prefix hybrid formation, from Latin (''nonus'', "ninth" + ''gonon''), used equivalently, attested already in the 16th century in French ''nonogo ...

, or nine-sided figure. The most interesting feature of this

polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two to ...

is the fact that two copies of it can fully enclose a third one. E.g., the lowest purple nonagon is enclosed by two yellow ones, all three of identical shape. Before Voderberg's discovery, mathematicians had questioned whether this could be possible. Because it has no translational symmetries, the Voderberg tiling is technically non-periodic, even though it exhibits an obvious repeating pattern. This tiling was the first spiral tiling to be devised, preceding later work by

Branko Grünbaum Branko Grünbaum ( he, ברנקו גרונבאום; 2 October 1929 – 14 September 2018) was a Croatian-born mathematician of Jewish descentGeoffrey C. Shephard in the 1970s. A spiral tiling is depicted on the cover of Grünbaum and Shephard's 1987 book ''Tilings and Patterns''..

References

External links

* {{Tessellation Tessellation Spirals