Max Brückner catalogued star-shaped polyhedra, and one shape later inspired an Escher print
the gist
A stellated polyhedron is made by extending the faces of a regular solid until they meet again, which creates spikes on each face. Max Brückner, a German geometer, documented a large collection of these stellated and uniform polyhedra in his 1900 book Polygons and Polyhedra. One shape in his collection is a compound of three octahedra, which are eight-faced solids, interlocked around a shared centre. M. C. Escher made that shape the subject of his 1948 print Stars, which shows it as a cage floating in space with two chameleons inside.
how it works
Extending the faces of a solid until they intersect again produces new points, so a shape with spikes emerges. Compound shapes are made when several identical solids share the same centre and interpenetrate.
so what
Brückner's catalogue is a key reference that shows how geometers explore shapes beyond everyday solids. Escher's use of the shape shows how pure mathematics can become visual art.
In 1909 D. W. Griffith made a 14-minute film about a speculator who corners the wheat market and doubles the price of bread. A farmer sows his field while a 'Wheat King' gambles in the Chicago wheat pit; bakers raise the loaf from five cents to ten and the poor line up for bread. Griffith cut back and forth between the farm, the feast and the breadline, a technique called parallel editing, so audiences saw both ends of the economy at once. The film drew on Frank Norris's stories and on a real scheme: months earlier Chicago financier James Patten had cornered wheat, sent bread prices up and made about $5 million, roughly $185 million today.
how it works
To corner a market, a trader buys up most of the available supply and the futures contracts that promise more. Anyone who has to deliver the commodity must then buy from the cornerer at whatever price is demanded. The trader profits until the stock is released or the scheme collapses.
so what
A century on, it still shows how markets can be rigged by someone who controls supply, and how the people at either end, farmers and eaters, pay for it. It also helped establish editing as a way to argue a point, not just tell a story.
the bigger pattern
Corners have recurred whenever supply could be locked up, from the Hunt brothers' attempt on silver in 1979 to 1980 to the 'Black Friday' gold panic of 1869. Many such schemes end by collapsing, and the response is often new rules on speculation.
fun fact
In the film the Wheat King dies by falling into a grain elevator and being buried in the wheat he hoarded, an ending borrowed from Norris's novel The Octopus.
more on this
background
A Corner in Wheat is a 1909 American short silent film which tells of a greedy tycoon who tries to corner the market in wheat, destroying the lives of the people who can no longer afford to buy bread. It was directed by D. W. Griffith and adapted by Griffith and Frank E. Woods from a novel and a short story by Frank Norris, titled The Pit and "A Deal in Wheat". Griffith may have had a real-life inspiration: six months earlier, James A. Patten had actually cornered the market in wheat, and in some cities, the price of bread doubled from five cents to ten, just as in the movie.
In 1994, A Corner in Wheat was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".
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