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Walter Trump
Walter Trump (born 1952 or 1953 ) is a German mathematician and retired high school teacher. He is known for his work in recreational mathematics. He has made contributions working on both the square packing problem and the magic tile problem. In 1979 he discovered the optimal known packing of 11 equal squares in a larger square, and in 2003, along with Christian Boyer, developed the first known magic cube In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an ''n'' × ''n'' × ''n'' pattern such that the sums of the numbers on each row, on each co ... of order 5. In 2012, Trump ''et al.'' described a model for retention of liquid on random surfaces. In 2014, he and Francis Gaspalou were able to calculate all 8 × 8 bimagic squares. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recreational Mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject. The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics. Topics Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Packing In A Square
Square packing in a square is a packing problem where the objective is to determine how many squares of side one (unit squares) can be packed into a square of side . If is an integer, the answer is , but the precise, or even asymptotic, amount of wasted space for non-integer is an open question. Small numbers of squares The smallest value of a that allows the packing of n unit squares is known when n is a perfect square (in which case it is \sqrt), as well as for n=2, 3, 5, 6, 7, 8, 10, 13, 14, 15, 24, 34, 35, 46, 47, and 48. For most of these numbers (with the exceptions only of 5 and 10), the packing is the natural one with axis-aligned squares, and a is \lceil\sqrt\,\rceil, where \lceil\,\ \rceil is the ceiling (round up) function. The figure shows the optimal packings for 5 and 10 squares, the two smallest numbers of squares for which the optimal packing involves tilted squares.. The smallest unresolved case involves packing 11 unit squares into a larger square. 11 unit s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Boyer
Christians () are people who follow or adhere to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus Christ. The words ''Christ'' and ''Christian'' derive from the Koine Greek title ''Christós'' (Χριστός), a translation of the Biblical Hebrew term ''mashiach'' (מָשִׁיחַ) (usually rendered as ''messiah'' in English). While there are diverse interpretations of Christianity which sometimes conflict, they are united in believing that Jesus has a unique significance. The term ''Christian'' used as an adjective is descriptive of anything associated with Christianity or Christian churches, or in a proverbial sense "all that is noble, and good, and Christ-like." It does not have a meaning of 'of Christ' or 'related or pertaining to Christ'. According to a 2011 Pew Research Center survey, there were 2.2 billion Christians around the world in 2010, up from about 600 million in 1910. Today, about 37% of all Christians live in the Ameri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Cube
In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an ''n'' × ''n'' × ''n'' pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal to the same number, the so-called magic constant of the cube, denoted ''M''3(''n''). It can be shown that if a magic cube consists of the numbers 1, 2, ..., ''n''3, then it has magic constant :M_3(n) = \frac. If, in addition, the numbers on every cross section diagonal also sum up to the cube's magic number, the cube is called a perfect magic cube; otherwise, it is called a semiperfect magic cube. The number ''n'' is called the order of the magic cube. If the sums of numbers on a magic cube's broken space diagonals also equal the cube's magic number, the cube is called a pandiagonal magic cube. Alternative definition In recent years, an alternative definition f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penguin Books
Penguin Books is a British publishing, publishing house. It was co-founded in 1935 by Allen Lane with his brothers Richard and John, as a line of the publishers The Bodley Head, only becoming a separate company the following year."About Penguin – company history" , Penguin Books. Penguin revolutionised publishing in the 1930s through its inexpensive paperbacks, sold through Woolworths Group (United Kingdom), Woolworths and other stores for Sixpence (British coin), sixpence, bringing high-quality fiction and non-fiction to the mass market. Its success showed that large audiences existed for serious books. It also affected modern British popular culture significantly through its books concerning politics, the arts, and science. Penguin Books is now an imprint (trade name), imprint of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Gaspalou
Francis may refer to: People *Pope Francis, the head of the Catholic Church and sovereign of the Vatican City State and Bishop of Rome *Francis (given name), including a list of people and fictional characters *Francis (surname) Places *Rural Municipality of Francis No. 127, Saskatchewan, Canada * Francis, Saskatchewan, Canada **Francis (electoral district) *Francis, Nebraska *Francis Township, Holt County, Nebraska * Francis, Oklahoma *Francis, Utah Other uses * ''Francis'' (film), the first of a series of comedies featuring Francis the Talking Mule, voiced by Chill Wills *''Francis'', a 1983 play by Julian Mitchell *FRANCIS, a bibliographic database * ''Francis'' (1793), a colonial schooner in Australia *Francis turbine, a type of water turbine *Francis (band), a Sweden-based folk band * Francis, a character played by YouTuber Boogie2988 See also *Saint Francis (other) *Francies, a surname, including a list of people with the name *Francisco (other) *Francisc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multimagic Square
In mathematics, a ''P''-multimagic square (also known as a satanic square) is a magic square that remains magic even if all its numbers are replaced by their ''k''th powers for 1 ≤ ''k'' ≤ ''P''. squares are called bimagic, squares are called trimagic, squares tetramagic, and squares pentamagic. Constants for normal squares If the squares are normal, the constant for the power-squares can be determined as follows: Bimagic series totals for bimagic squares are also linked to the square-pyramidal number sequence is as follows :- Squares 0, 1, 4, 9, 16, 25, 36, 49, .... Sum of Squares 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ... )number of units in a square-based pyramid) The bimagic series is the 1st, 4th, 9th in this series (divided by 1, 2, 3, ''n'') etc. so values for the rows and columns in order-1, order-2, order-3 Bimagic squares would be 1, 15, 95, 374, 1105, 2701, 5775, 11180, ... The trimagic series would be related in the same way to the hyper-pyr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gymnasium (school)
''Gymnasium'' (and variations of the word) is a term in various European languages for a secondary school that prepares students for higher education at a university. It is comparable to the US English term '' preparatory high school''. Before the 20th century, the gymnasium system was a widespread feature of educational systems throughout many European countries. The word (), from Greek () 'naked' or 'nude', was first used in Ancient Greece, in the sense of a place for both physical and intellectual education of young men. The latter meaning of a place of intellectual education persisted in many European languages (including Albanian, Bulgarian, Estonian, Greek, German, Hungarian, the Scandinavian languages, Dutch, Polish, Czech, Serbo-Croatian, Macedonian, Slovak, Slovenian and Russian), whereas in other languages, like English (''gymnasium'', ''gym'') and Spanish (''gimnasio''), the former meaning of a place for physical education was retained. School structure Be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stein, Bavaria
Stein (East Franconian: ''Schdah'') is a town in the district of Fürth, in Bavaria, Germany. It is situated 7 km south of Fürth, and 7 km southwest of Nuremberg (centre). Geography Stein is located in the metropolitan area Nürnberg/Fürth/Erlangen in Middle Franconia, Bavaria and is a part of the district of Fürth. It adjoins to Nuremberg in the north-west and lies on the left bank of the river Rednitz. Neighboring municipalities are Nuremberg, Rohr, Roßtal, Zirndorf and Oberasbach. Stein is divided into 11 districts: History Stein has first been mentioned in a document dating back to 1296. The origin of the settlement is linked to the first ''Rednitzbrücke'', a bridge which first crossed the river Rednitz. It was referred to as “Steinbruke” and probably caused the town's naming. In 1498, the two famous sculptors Veit Stoss and Adam Kraft were appointed as counselors for construction works on the bridge. Between the 15th and the 17th century, Stein ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientists From Bavaria
A scientist is a person who conducts scientific research to advance knowledge in an area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosophical study of nature called natural philosophy, a precursor of natural science. Though Thales (circa 624-545 BC) was arguably the first scientist for describing how cosmic events may be seen as natural, not necessarily caused by gods,Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 it was not until the 19th century that the term ''scientist'' came into regular use after it was coined by the theologian, philosopher, and historian of science William Whewell in 1833. In modern times, many scientists have advanced degrees in an area of science and pursue careers in various sectors of the economy such as academia, industry, government, and nonprofit environments.'''' History The roles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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