Piet Hein (16 December 1905 – 17 April 1996) was a

Danish Danish may refer to: * Something of, from, or related to the country of Denmark People * A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark * Culture of Denmark * Danish people or Danes, people with a Danish ance ...

polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...

(mathematician, inventor, designer, writer and poet), often writing under the

Old Norse Old Norse, Old Nordic, or Old Scandinavian, is a stage of development of North Germanic languages, North Germanic dialects before their final divergence into separate Nordic languages. Old Norse was spoken by inhabitants of Scandinavia and t ...

pseudonym Kumbel, meaning " tombstone". His short poems, known as '' gruks'' or grooks ( da, gruk), first started to appear in the daily newspaper ''

Politiken ''Politiken'' is a leading Danish daily broadsheet newspaper, published by JP/Politikens Hus in Copenhagen, Denmark. It was founded in 1884 and played a role in the formation of the Danish Social Liberal Party. Since 1970 it has been indep ...

'' shortly after the German

occupation of Denmark At the outset of World War II in September 1939, Denmark declared itself neutral. For most of the war, the country was a protectorate and then an occupied territory of Germany. The decision to occupy Denmark was taken in Berlin on 17 Decemb ...

in April 1940 under the pseudonym "Kumbel Kumbell". He also invented the

Soma cube The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pie ...

and the board game

Hex Hex or HEX may refer to: Magic * Hex, a curse or supposed real and potentially supernaturally realized malicious wish * Hex sign, a barn decoration originating in Pennsylvania Dutch regions of the United States * Hex work, a Pennsylvania Dutch ...

Biography

Hein, a direct descendant of

Piet Pieterszoon Hein Piet Pieterszoon Hein (25 November 1577 – 18 June 1629) was a Dutch admiral and privateer for the Dutch Republic during the Eighty Years' War. Hein was the first and the last to capture a large part of a Spanish treasure fleet which ...

, the 17th century Dutch naval hero, was born in

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

Denmark ) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of Denmark , establishe ...

. He studied at the Institute for Theoretical Physics (later to become the

Niels Bohr Institute The Niels Bohr Institute (Danish: ''Niels Bohr Institutet'') is a research institute of the University of Copenhagen. The research of the institute spans astronomy Astronomy () is a natural science that studies astronomical object, cele ...

) of the

University of Copenhagen The University of Copenhagen ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in ...

, and

Technical University of Denmark The Technical University of Denmark ( da, Danmarks Tekniske Universitet), often simply referred to as DTU, is a polytechnic university and school of engineering. It was founded in 1829 at the initiative of Hans Christian Ørsted as Denmark's fir ...

Yale Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

awarded him an honorary doctorate in 1972. He died in his home on

Funen Funen ( da, Fyn, ), with an area of , is the third-largest island of Denmark, after Zealand and Vendsyssel-Thy. It is the 165th-largest island in the world. It is located in the central part of the country and has a population of 469,947 as o ...

in 1996.

Resistance

Piet Hein, who, in his own words, "played mental ping-pong" with

Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922 ...

in the inter-War period, found himself confronted with a dilemma when the Germans occupied Denmark. He felt that he had three choices: Do nothing, flee to neutral Sweden or join the Danish resistance movement. As he explained in 1968, "Sweden was out because I am not Swedish, but Danish. I could not remain at home because, if I had, every knock at the door would have sent shivers up my spine. So, I joined the Resistance." Taking as his first weapon the instrument with which he was most familiar, the pen, he wrote and had published his first "

grook A grook ( da, gruk) is a form of short aphoristic poem or rhyming aphorism, created by the Danish poet, designer, inventor and scientist Piet Hein, who wrote over 10,000 of them, mostly in Danish. They have been published in Danish in 20 volumes ...

" ( da, gruk). It passed the censors who did not grasp its real meaning. The Danes, however, understood its importance and soon it was found as graffiti all around the country. The deeper meaning of the grook was that even if you lose your freedom ("losing one glove"), do not lose your patriotism and self-respect by collaborating with the Nazis ("throwing away the other"), because that sense of having betrayed your country will be more painful when freedom has been found again someday.

Recreational mathematics

In 1959, city planners in Stockholm, Sweden announced a design challenge for a

roundabout A roundabout is a type of circular intersection or junction in which road traffic is permitted to flow in one direction around a central island, and priority is typically given to traffic already in the junction.''The New Shorter Oxford E ...

in their city square

Sergels Torg Sergels torg ("Sergel's Square") is a major public square in Stockholm, Sweden, constructed in the 1960s and named after 18th-century sculptor Johan Tobias Sergel, whose workshop was once located north of the square. Overview Sergels torg h ...

. Piet Hein's winning proposal was based on a

superellipse A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape. In the C ...

. He went on to use the superellipse in the design of furniture and other artifacts. He also invented a

perpetual calendar A perpetual calendar is a calendar valid for many years, usually designed to look up the day of the week for a given date in the past or future. For the Gregorian and Julian calendars, a perpetual calendar typically consists of one of three ...

called the Astro Calendar and marketed

houseware Household goods are goods and products used within households. They are the tangible and movable personal property placed in the rooms of a house, such as a bed or refrigerator. Economic role Businesses that produce household goods are categor ...

s based on the superellipse and its three-dimensional analog, the

superegg In geometry, a superegg is a solid of revolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis. It is a special case of superellipsoid. Unlike an elongated ellipsoid, an elongated su ...

. He invented the

and devised the games of

Tangloids Tangloids is a mathematical game for two players created by Piet Hein to model the calculus of spinors. A description of the game appeared in the book ''"Martin Gardner's New Mathematical Diversions from Scientific American"'' by Martin Gardner ...

, Tower, Polytaire,

TacTix TacTix is a two-player strategy game invented by Piet Hein, a poet well known for dabbling in math and science, best known for his game Hex. TacTix is essentially a two-dimension version of Nim; players alternate moves, removing one or more to ...

, Nimbi, Qrazy Qube, and Pyramystery. Hein was a close associate of

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of L ...

and his work was frequently featured in Gardner's

Mathematical Games column Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for ''Scientific American'' magazine. During the next years, through June 1986, Gardner wrote 9 more columns, ...

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

. At the age of 95 Gardner wrote his autobiography and titled it ''Undiluted Hocus-Pocus''. Both the title and the dedication of this book come from one of Hein's grooks.

Personal

Piet Hein was married four times and had five sons from his last three marriages. # (1937) married Gunver Holck, divorced # (1942) married Gerda Ruth (Nena) Conheim, divorced #: Sons: Juan Alvaro Hein, born 9 January 1943; Andrés Humberto Hein, born 30 December 1943 # (1947) married Anne Cathrina (Trine) Krøyer Pedersen, divorced #: Son: Lars Hein, born 20 May 1950 # (1955) married Gerd Ericsson, who died 3 November 1968 #: Sons: Jotun Hein, born 19 July 1956; Hugo Piet Hein, born 16 November 1963

Bibliography

* ''Grooks'' – 20 volumes, originally published between 1940 and 1963, all currently

out-of-print __NOTOC__ An out-of-print (OOP) or out-of-commerce item or work is something that is no longer being published. The term applies to all types of printed matter, visual media, sound recordings, and video recordings. An out-of-print book is a boo ...

. * ''Grooks 1'', Doubleday & Co., 1969. * ''Grooks 2'', Doubleday & Co., 1968. * ''Grooks 3'', Doubleday & Co., 1970. * ''Grooks 4'', Doubleday & Co., 1973. * ''Grooks 5'', Doubleday & Co., 1973. * ''Grooks 6'', Borgens Pocketbooks 154, 1996. * ''Grooks 7'', Borgens Pocketbooks 174, 1984.

Notes

References

* Gardner, Martin: ''Piet Hein's Superellipse.'' – in Gardner, Martin: ''Mathematical Carnival. A New Round-Up of Tantalizers and Puzzles from

''. New York: Vintage, 1977, pp. 240–254. * Johan Gielis: ''Inventing the circle. The geometry of nature''. – Antwerpen : Geniaal Press, 2003. – * "A Poet with a Slide Rule: Piet Hein Bestrides Art and Science," by Jim Hicks, ''

Life Magazine ''Life'' was an American magazine published weekly from 1883 to 1972, as an intermittent "special" until 1978, and as a monthly from 1978 until 2000. During its golden age from 1936 to 1972, ''Life'' was a wide-ranging weekly general-interest ma ...

'', Vol. 61 No. 16, 10/14/66, pp. 55–66 *"Piet Hein Biographical Details", by Nils Aas, tr. by Roger Stevenson. ''The Papers of the Medford Educational Institute 3''. *"To and by Piet Hein on the Occasion of Piet Hein's Election as the Student Organization's Twelfth Honorary Member", tr. by Roger Stevenson. ''The Papers of the Medford Educational Institute 2''.

External links

* *, including several sample grooks
Superellipse
at

MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science ...

Grooks
at My Poetic Side

at Archimedes' Lab {{DEFAULTSORT:Hein, Piet 1905 births 1996 deaths 20th-century Danish inventors 20th-century Danish poets Danish male poets Recreational mathematicians Danish furniture designers 20th-century Danish mathematicians Puzzle designers University of Copenhagen alumni Yale University alumni Designers from Copenhagen Writers from Copenhagen Danish people of Dutch descent 20th-century Danish male writers Grut Hansen family