## “You can’t criticize geometry. It’s never wrong.”*…

In the world of mathematical tiling, news doesn’t come bigger than this. In the world of bathroom tiling – I bet they’re interested too.

If you can cover a flat surface using only identical copies of the same shape leaving neither gaps nor overlaps, then that shape is said to “tile the plane.” Every triangle can tile the plane. Every four-sided shape can also tile the plane.

Things get interesting with pentagons. The regular pentagon

cannottile the plane. (A regular pentagon has equal side lengths and equal angles between sides, like, say, a cross section of okra, or, erm, the Pentagon). But some non-regular pentagons can.The hunt to find and classify the pentagons that can tile the plane has been a century-long mathematical quest, begun by the German mathematician Karl Reinhardt, who in 1918 discovered five types of pentagon that do tile the plane…

Pentagons remain the area of most mathematical interest when it comes to tilings since it is the only of the ‘-gons’ that is not yet totally understood…

Read the whole story– and see all 15 types of pentagonal tilings discovered so far– at “Attack on the pentagon results in discovery of new mathematical tile.”

* Paul Rand

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**As we grab the grout,** we might recall that it was on this date in 1953, after a year of experimentation, that marine engineer and retired semi-pro baseball player David Mullany, Sr. invented the Wiffleball. (He patented it early the following year.) Watching his 13-year-old son play with a broomstick and a plastic golf ball ball in the confines of their backyard, Mullany worried that the effort to throw a curve would damage his young arm. So he fabricated a full- (baseball-)sized ball from the plastic used in perfume packaging, with oblong holes on one side… a ball that would naturally curve. The balls had the added advantage, given their light weight, that they’d not break windows.

David Jr. came up with the name: he was fond of saying that he had “whiffed” the batters that he struck out with his curves. The “h” was dropped, the name trademarked, and (after Woolworth’s adopted the item) a generation of young ballplayers– and their parents– converted.