Soma cube
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Its name is alleged to be derived from the fictitious drug soma consumed as a pastime by the establishment in Aldous Huxley's dystopic novel Brave New World. Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube; the pieces can be used to make a variety of other 3D shapes. The pieces of the Soma cube consist of all possible combinations of three or four unit cubes, joined at their faces, such that at least one inside corner is formed. There is one combination of three cubes that satisfies this condition, six combinations of four cubes that satisfy this condition, of which two are mirror images of each other. Thus, 3 + is 27, the number of cells in a 3×3×3 cube; the Soma cube was analyzed in detail by John Horton Conway on September 1958 in Mathematical Games column in Scientific American, the book Winning Ways for your Mathematical Plays contains a detailed analysis of the Soma cube problem.
There are 240 distinct solutions of the Soma cube puzzle, excluding rotations and reflections: these are generated by a simple recursive backtracking search computer program similar to that used for the eight queens puzzle. Current world record for the fastest time to solve a soma cube is 2.93 seconds and was set by Krishnam Raju Gadiraju, India. The seven Soma pieces are six polycubes of order four, one of order three: Piece 1, or "V". Piece 2, or "L": a row of three blocks with one added below the left side. Piece 3, or "T": a row of three blocks with one added below the center. Piece 4, or "Z": bent tetromino with block placed on outside of clockwise side. Piece 5, or "A": unit cube placed on top of clockwise side. Chiral in 3D. Piece 6, or "B": unit cube placed on top of anticlockwise side. Chiral in 3D. Piece 7, or "P": unit cube placed on bend. Not chiral in 3D. Piet Hein authorized a finely crafted rosewood version of the Soma cube manufactured by Theodor Skjøde Knudsen's company Skjøde Skjern.
Beginning in about 1967, it was marketed in the U. S. for several years by the game manufacturer Parker Brothers. Plastic Soma cube sets were commercially produced by Parker Brothers in several colors during the 1970s; the package for the Parker Brothers version claimed. This figure includes rotations and reflections of each solution as well as rotations of the individual pieces; the puzzle is sold as a logic game by ThinkFun under the name Block by Block. Solving the Soma cube has been used as a task to measure individuals' performance and effort in a series of psychology experiments. In these experiments, test subjects are asked to solve a soma cube as many times as possible within a set period of time. For example, In 1969, Edward Deci, a Carnegie Mellon University graduate assistant at the time, asked his research subjects to solve a soma cube under conditions with varying incentives in his dissertation work on intrinsic and extrinsic motivation establishing the social psychological theory of crowding out.
In each of the 240 solutions to the cube puzzle, there is only one place that the "T" piece can be placed. Each solved cube can be rotated such that the "T" piece is on the bottom with its long edge along the front and the "tongue" of the "T" in the bottom center cube; this can be proven as follows: If you consider all the possible ways that the "T" piece can be placed in the large cube, it will be seen that it will always fill either two corners of the large cube or zero corners. There is no way to orient the "T" piece such; the "L" piece can be oriented such that it fills zero corners. Each of the other five pieces have no orientation. Therefore, if you exclude the "T" piece, the maximum number of corners that can be filled by the remaining six pieces is seven. A cube has eight corners, but the "T" piece cannot be oriented to fill just that one remaining corner, orienting it such that it fills zero corners will not make a cube. Therefore, the "T" must always fill two corners, there is only one orientation in which it does that.
It follows from this that in all solutions, five of the remaining six pieces will fill their maximum number of corners and one piece will fill one fewer than its maximum. Similar to Soma cube is the 3D pentomino puzzle, which can fill boxes of 2×3×10, 2×5×6 and 3×4×5 units; the Bedlam cube is a 4 × 4 × 4 sided cube puzzle consisting of one tetracube. The Diabolical cube is a puzzle of six polycubes that can be assembled together to form a single 3×3×3 cube. Tangram Tetromino Tromino Snake cube Soma Cube android game Soma Cube Lite iOS game http://www.mathematik.uni-bielefeld.de/~sillke/POLYCUBE/SOMA/cube-secrets Soma Cube – from MathWorld Thorleif's SOMA page SOMA CUBE ANIMATION by TwoDoorsOpen and Friends
Système universitaire de documentation
The système universitaire de documentation or SUDOC is a system used by the libraries of French universities and higher education establishments to identify and manage the documents in their possession. The catalog, which contains more than 10 million references, allows students and researcher to search for bibliographical and location information in over 3,400 documentation centers, it is maintained by the Bibliographic Agency for Higher Education. Official website
Piet Pieterszoon Hein
Pieter Pietersen Heyn was a Dutch admiral and privateer for the Dutch Republic during the Eighty Years' War between the United Provinces and Spain. Hein was the last to capture a large part of a Spanish "silver fleet" from America. Hein was born in Delfshaven, the son of a sea captain, he became a sailor while he was still a teenager. During his first journeys he suffered from extreme motion sickness. In his twenties, he was captured by the Spanish, served as a galley slave for about four years between 1598 and 1602, when he was traded for Spanish prisoners. Between 1603 and 1607 he was again held captive by the Spanish. In 1607, he joined the Dutch East India Company and left for Asia, returning with the rank of captain five years later, he settled in Rotterdam. In 1618, when he was captain of the Neptunus, both he and his ship were pressed into service by Venice. In 1621 he traveled overland to the Netherlands. For a year in 1622 he was a member of the local government of Rotterdam, although he did not have citizenship of this city: the cousin of his wife, one of the three burgomasters, made this possible.
In 1623, he became vice-admiral of the new Dutch West India Company and sailed to the West Indies the following year. In Brazil, he captured the Portuguese settlement of Salvador leading the assault on the sea fortress of that town. In August with a small and undermanned fleet he sailed for the African west coast and attacked a Portuguese fleet in the defended bay of Luanda but failed to capture any ships, he crossed the Atlantic Ocean again to try and capture merchant ships at the city of Vitória, but was defeated by a resistance organized by the local citizenry with the assistance of the Portuguese garrison. After finding that Salvador had been recaptured by a large Spanish-Portuguese fleet Hein returned home; the Dutch West India Company, pleased with Hein's leadership qualities, placed him in command of a new squadron in 1626. In subsequent raids during 1627 at Salvador, he attacked and captured over thirty richly laden Portuguese merchant ships before returning to the United Provinces. Modern historians today classify Hein as a pirate, though he was more properly a privateer.
While many privateers behaved no better than common pirates, Hein was a strict disciplinarian who discouraged unruly conduct among his crews and had rather enlightened views for the times about "Indian" tribes and members of other religions. He never was an individual privateer but rather commanded entire fleets of warships and the fact that he was an Admiral of the Dutch Republic should dispel such views. In 1628, Admiral Hein, with Witte de With as his flag captain, sailed out to capture a Spanish treasure fleet loaded with silver from their American colonies and the Philippines. With him was Admiral Hendrick Lonck and he was joined by a squadron of Vice-Admiral Joost Banckert, as well as by the pirate Moses Cohen Henriques. Part of the Spanish fleet in Venezuela had been warned because a Dutch cabin boy had lost his way on Blanquilla island and was captured, betraying the plan, but the other half from Mexico continued its voyage, unaware of the threat. Sixteen Spanish ships were intercepted.
After some musket volleys from Dutch sloops the crews of the galleons surrendered and Hein captured 11,509,524 guilders of booty in gold and other expensive trade goods, such as indigo and cochineal, without any bloodshed. The Dutch did not take prisoners: they gave the Spanish crews ample supplies for a march to Havana; the released were surprised to hear the admiral giving them directions in fluent Spanish. The capture of the treasure fleet was the Dutch West India Company's greatest victory in the Caribbean; as a result, the money funded the Dutch army for eight months, the shareholders enjoyed a cash dividend of 50% for that year. Hein returned to the Netherlands in 1629. Watching the crowds cheering him as he stood on the balcony of the town hall of Leyden, he remarked to the burgomaster: "Now they praise me because I gained riches without the least danger. Hein was the first and the last to capture such a large part of a Spanish "silver fleet" from America, he became, after a conflict with the WIC about policy and payment, Lieutenant-Admiral of Holland and West Frisia on 26 March 1629, thus factual supreme commander of the confederate Dutch fleet, taking as flag captain Maarten Tromp.
He died the same year, in a campaign against the Dunkirkers, the effective fleet of Habsburg commerce raiders and privateers operating from Dunkirk. As it happened his flotilla intercepted three privateers from Ostend, he deliberately moved his flagship in between two enemy ships to give them both simultaneous broadsides. After half an hour he was killed instantly, he is buried in the Oude Kerk in Delft —once again dispelling enemy propaganda that he was a pirat
Out-of-print book
An out-of-print book is a book, no longer being published. The term can apply to specific editions of more popular works, which may go in and out of print or to the sole printed edition of a work, not picked up again by any future publishers for reprint. Most works that have been published are out of print at any given time, while certain popular books, such as the Bible, are always "in print". Less popular out of print books are rare and may be difficult to acquire unless scanned or electronic copies of the books are available. With the advent of book scanning, print-on-demand technology and fewer works are now considered out of print. A publisher creates a print run of a fixed number of copies of a new book. Print runs for most modern books number in the thousands; these books can be ordered in bulk by booksellers, when all the bookseller's copies are sold, the bookseller has the option to order additional copies. If the initial print run sells out and demand still exists, the publisher will have more copies printed, if possible.
When the book is no longer selling either at a rate fast enough to pay for the inventory or stock costs, or to justify another print run, the publisher will cease to print additional copies, may remainder or pulp the remaining unsold copies. When all of the books in a print run have been sold to booksellers, the book is said to be "out of print", meaning that a bookseller cannot get any further copies from the publisher. If a book sells out unexpectedly it may be considered out of print when its initial print run is exhausted, but is soon reprinted. Publishers may choose to list a book as "out of stock indefinitely", instead of declaring it out of print, as the publisher may have to give up copyright when declaring it out of print. Publishers will let a book go out of stock for long periods reprint the book with a new cover and formatting, to catch the built up demand for the book; the author or their estate may have copyright reverted to them once the publisher has declared it out of print.
The longer a book has been out of print, the more difficult it may be to obtain a copy. If there is enough demand for an out-of-print book, all copyright issues can be resolved, another publisher may republish the book in the same manner as the original publisher might have reprinted it. In some cases, an out-of-print book one that sold poorly, may be republished if the author becomes popular again. A reader who wishes to purchase an out-of-print book must either find a bookseller that still has a copy, wait for another print run, or find someone who will sell their own copy as a used book; the advent of the Internet has made this process much easier, as many websites sell used books offered by bookstores and individuals. Some publishers intentionally limit the print run of some or all titles to fewer copies than the anticipated demand, in creating limited editions marketed to collectors. In these cases, there is an implicit or explicit promise to collectors that the book will not be reprinted, at least in the same form as published.
For instance, Madonna's book Sex, with a limited edition print run, is, according to BookFinder.com, the most sought after out-of-print book in the United States. List of publishers Old Earth Books Orphan works Out of commerce Self-publishing Rebecca J. Rosen. "The Hole in Our Collective Memory: How Copyright Made Mid-Century Books Vanish". The Atlantic. Book Finder
Perpetual calendar
A perpetual calendar is a calendar valid for many years designed to allow the calculation of the day of the week for a given date in the future. For the Gregorian and Julian calendars, a perpetual calendar consists of one of two general variations: 14 one-year calendars, plus a table to show which one-year calendar is to be used for any given year; these one-year calendars divide evenly into two sets of seven calendars: seven for each common year with each of the seven starting on a different day of the week, seven for each leap year, again with each one starting on a different day of the week, totaling fourteen. Seven one-month calendars and one or more tables to show which calendar is used for any given month; some perpetual calendars' tables slide against each other, so that aligning two scales with one another reveals the specific month calendar via a pointer or window mechanism. The seven calendars may be combined into one, either with 13 columns of which only seven are revealed, or with movable day-of-week names.
Note that such a perpetual calendar fails to indicate the dates of moveable feasts such as Easter, which are calculated based on a combination of events in the Tropical year and lunar cycles. These issues are dealt with in great detail in Computus. An early example of a perpetual calendar for practical use is found in the manuscript GNM 3227a; the calendar covers the period of 1390–1495. For each year of this period, it lists the number of weeks between Quinquagesima; this is the first known instance of a tabular form of perpetual calendar allowing the calculation of the moveable feasts that became popular during the 15th century. Offices and retail establishments display devices containing a set of elements to form all possible numbers from 1 through 31, as well as the names/abbreviations for the months and the days of the week, so as to show the current date for the convenience of people who might be signing and dating documents such as checks. Establishments that serve alcoholic beverages may use a variant that shows the current month and day, but subtracting the legal age of alcohol consumption in years, indicating the latest legal birth date for alcohol purchases.
A simple device consists of two cubes in a holder. One cube carries; the other bears the numbers 0, 1, 2, 6, 7 and 8. This is perpetual because they are on both cubes. Certain calendar reforms have been labeled perpetual calendars because their dates are fixed on the same weekdays every year. Examples are the International Fixed Calendar and the Pax Calendar. Technically, these are not perpetual calendars but perennial calendars, their purpose, in part, is to eliminate the need for perpetual calendar tables and computation devices. In watchmaking, "perpetual calendar" describes a calendar mechanism that displays the date on the watch'perpetually', taking into account the different lengths of the months as well as leap days; the internal mechanism will move the dial to the next day. These meanings are beyond the scope of the remainder of this article. Perpetual calendars use algorithms to compute the day of the week for any given year and day of month. Though the individual operations in the formulas can be efficiently implemented in software, they are too complicated for most people to perform all of the arithmetic mentally.
Perpetual calendar designers hide the complexity in tables to simplify their use. A perpetual calendar employs a table for finding. A table for the Gregorian calendar expresses its 400-year grand cycle: 303 common years and 97 leap years total to 146,097 days, or 20,871 weeks; this cycle breaks down into one 100-year period with 25 leap years, making 36,525 days, or one day less than 5,218 full weeks. Within each 100-year block, the cyclic nature of the Gregorian calendar proceeds in the same fashion as its Julian predecessor: A common year begins and ends on the same day of the week, so the following year will begin on the next successive day of the week. A leap year has one more day, so the year following a leap year begins on the second day of the week after the leap year began; every four years, the starting weekday advances five days, so over a 28-year period it advances 35, returning to the same place in both the leap year progression and the starting weekday. This cycle completes three times in 84 years, leaving 16 years in the fourth, incomplete cycle of the century.
A major complicating factor in constructing a perpetual calendar algorithm is the peculiar and variable length of February, at one time the last month of the year, leaving the first 11 months March through January with a five-month repeating pattern: 31, 30, 31, 30, 31... so that the offset from March of the starting day of the week for any month could be determined. Zeller's congruence, a well-known algorithm for finding the day of week for any date, explicitly defines January and February as the "13th" and "14th" months of the previous year in order to take advantage of this regularity, but the month-dependent calculation is still complicated for mental arithmetic: ⌊ 26 10 ⌋ mod
Netherlands Institute for Art History
The Netherlands Institute for Art History or RKD is located in The Hague and is home to the largest art history center in the world. The center specializes in documentation and books on Western art from the late Middle Ages until modern times. All of this is open to the public, much of it has been digitized and is available on their website; the main goal of the bureau is to collect and make art research available, most notably in the field of Dutch Masters. Via the available databases, the visitor can gain insight into archival evidence on the lives of many artists of past centuries; the library owns 450,000 titles, of which ca. 150,000 are auction catalogs. There are ca. 3,000 magazines, of which 600 are running subscriptions. Though most of the text is in Dutch, the standard record format includes a link to library entries and images of known works, which include English as well as Dutch titles; the RKD manages the Dutch version of the Art and Architecture Thesaurus, a thesaurus of terms for management of information on art and architecture.
The original version is an initiative of the Getty Research Institute in California. The collection was started through bequests by Frits Lugt, art historian and owner of a massive collection of drawings and prints, Cornelis Hofstede de Groot, a collector, art historian and museum curator, their bequest formed the basis for both the art collection and the library, now housed in the Koninklijke Bibliotheek. Though not all of the library's holdings have been digitised, much of its metadata is accessible online; the website itself is available in both an English user interface. In the artist database RKDartists, each artist is assigned a record number. To reference an artist page directly, use the code listed at the bottom of the record of the form: https://rkd.nl/en/explore/artists/ followed by the artist's record number. For example, the artist record number for Salvador Dalí is 19752, so his RKD artist page can be referenced. In the images database RKDimages, each artwork is assigned a record number.
To reference an artwork page directly, use the code listed at the bottom of the record of the form: https://rkd.nl/en/explore/images/ followed by the artwork's record number. For example, the artwork record number for The Night Watch is 3063, so its RKD artwork page can be referenced; the Art and Architecture Thesaurus assigns a record for each term, but these can not be referenced online by record number. Rather, they are used in the databases and the databases can be searched for terms. For example, the painting called "The Night Watch" is a militia painting, all records fitting this keyword can be seen by selecting this from the image screen; the thesaurus is a set of general terms, but the RKD contains a database for an alternate form of describing artworks, that today is filled with biblical references. This is the iconclass database. To see all images that depict Miriam's dance, the associated iconclass code 71E1232 can be used as a special search term. Official website Direct link to the databases The Dutch version of the Art and Architecture Thesaurus
Martin Gardner
Martin Gardner was an American popular mathematics and popular science writer, with interests encompassing scientific skepticism, philosophy and literature—especially the writings of Lewis Carroll, L. Frank Baum, G. K. Chesterton, he is recognized as a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies, he had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century. He was considered the doyen of American puzzlers, he was a versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematics—and by extension, mathematics in general—throughout the latter half of the 20th century, principally through his "Mathematical Games" columns; these appeared for twenty-five years in Scientific American, his subsequent books collecting them. Gardner was one of the foremost anti-pseudoscience polemicists of the 20th century.
His 1957 book Fads and Fallacies in the Name of Science became a classic and seminal work of the skeptical movement. In 1976 he joined with fellow skeptics to found CSICOP, an organization promoting scientific inquiry and the use of reason in examining extraordinary claims. Gardner, son of a petroleum geologist father and an educator and artist mother, grew up in and around Tulsa, Oklahoma, his lifelong interest in puzzles started in his boyhood when his father gave him a copy of Sam Loyd's Cyclopedia of 5000 Puzzles and Conundrums. He attended the University of Chicago, where he earned his bachelor's degree in philosophy in 1936. Early jobs included reporter on the Tulsa Tribune, writer at the University of Chicago Office of Press Relations, case worker in Chicago's Black Belt for the city's Relief Administration. During World War II, he served for four years in the U. S. Navy as a yeoman on board the destroyer escort USS Pope in the Atlantic, his ship was still in the Atlantic when the war came to an end with the surrender of Japan in August 1945.
After the war, Gardner returned to the University of Chicago. He attended graduate school for a year there. In 1950 he wrote an article in the Antioch Review entitled "The Hermit Scientist", it was one of Gardner's earliest articles about junk science, in 1952 a much-expanded version became his first published book: In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science and Present. In the late 1940s, Gardner moved to New York City and became a writer and editor at Humpty Dumpty magazine where for eight years he wrote features and stories for it and several other children's magazines, his paper-folding puzzles at that magazine led to his first work at Scientific American. For many decades, his wife Charlotte, their two sons and Tom, lived in Hastings-on-Hudson, New York, where he earned his living as a freelance author, publishing books with several different publishers, publishing hundreds of magazine and newspaper articles. Appropriately enough—given his interest in logic and mathematics—they lived on Euclid Avenue.
The year 1960 saw the original edition of the best-selling book of The Annotated Alice. In 1979, Gardner retired from Scientific American and he and his wife Charlotte moved to Hendersonville, North Carolina. Gardner never retired as an author, but continued to write math articles, sending them to The Mathematical Intelligencer, Math Horizons, The College Mathematics Journal, Scientific American, he revised some of his older books such as Origami and the Soma Cube. Charlotte died in 2000 and two years Gardner returned to Norman, where his son, James Gardner, was a professor of education at the University of Oklahoma, he died there on May 22, 2010. An autobiography — Undiluted Hocus-Pocus: The Autobiography of Martin Gardner — was published posthumously. Martin Gardner had a major impact on mathematics in the second half of the 20th century, his column was called "Mathematical Games" but it was much more than that. His writing introduced many readers to real mathematics for the first time in their lives.
The column lasted for 25 years and was read avidly by the generation of mathematicians and physicists who grew up in the years 1956 to 1981. It was the original inspiration for many of them to become scientists themselves. David Auerbach wrote: A case can be made, in purely practical terms, for Martin Gardner as one of the most influential writers of the 20th century, his popularizations of science and mathematical games in Scientific American, over the 25 years he wrote for them, might have helped create more young mathematicians and computer scientists than any other single factor prior to the advent of the personal computer. Among the wide array of mathematicians, computer scientists, magicians, artists and other influential thinkers who inspired and were in turn inspired by Gardner are John Horton Conway, Bill Gosper, Ron Rivest, Richard K. Guy, Piet Hein, Ronald Graham, Donald Knuth, Robert Nozick, Lee Sallows, Scott Kim, M. C. Escher, Douglas Hofstadter, Roger Penrose, Ian Stewart, David A. Klarner, Benoit Mandelbrot, Elwyn R. Berlekamp, Solomon W. Golomb, Raymond Smullyan, James Randi, Persi Diaconis, Penn & Teller, Ray Hyman.
His admirers included such diverse people as W. H. Auden, Arthur C. Clarke, Carl Sagan, Isaac Asimov, Richard Dawkins, Stephen Jay Gould, the entire French literary group known as the Oulipo. Salvador Dali once sought him out to discuss four-dimensional hypercubes. Gardner wrote to M. C. Escher in 1961 to ask permission
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