21. MacMahon's Coloured Cubes Torsten Sillke macmahon s cubes (Multiple Cubes, Probabilities, References).University of St Andrews - percy Alexander macmahon http://www.mathematische-basteleien.de/macmahon.htm

MacMahon's Coloured Cubes Contents of this Page What are Mac Mahon's Coloured Cubes? There are 30 Mac Mahon Cubes Making of the Cubes Figures with Cubes Mac Mahon's Problem ... To the Main Page "Mathematische Basteleien" What are Mac Mahon's Coloured Cubes? MacMahon's cubes are the cubes which develop if you give the six sides six different colours in all possible combinations. The colours are not determined. You can choose any colour. I chose red(1), light blue(2), dark blue(3), dark green(4), light green(5), and pink(6). A cube is drawn on the left as a net and in perspective with three turned square sides. P.A. Mac Mahon was an English mathematician and major. He lived from 1854 to 1929. There are 30 Mac Mahon Cubes top If you give the squares of a cube the numbers 1, 2, 3, 4, 5, 6 and form all permutations of the six numbers, you get 1*2*3*4*5*6=6!=720 cubes. Many among the cubes are the same. They can be transferred by turns around one of the 13 axles into one another. There are 24 turns and thus only 720:24 = 30 different cubes. The following picture illustrates these facts. The numbers below the cubes mean the number of the turns.

22. MacMahons Farbwürfel University of St Andrews - percy Alexander macmahon http://www.mathematische-basteleien.de/macmahons.htm

Inhalt dieser Seite Das MacMahon Problem Das Mayblox-Problem Das Kowalewski-Problem Instant Insanity ... Zur Hauptseite "Mathematische Basteleien" P.A. MacMahon war ein englischer Mathematiker und Major. Er lebte von 1854 bis 1929. top top Die Bezeichnungen wie Ab stammen von Conway (s.u.) top Das MacMahon Problem top Das zentrale Puzzle ist das MacMahon-Problem. unten, links, vorne Ca unten, rechts, vorne kommen Bd, Cf, Da, Ec und Fe in Frage. Bd unten, links, hinten kommen Bf und Ce in Frage. Bf unten, rechts, hinten kommt nur Ea in Frage. oben, links, vorne kommen Be und Cd in Frage. Be oben, rechts, vorne kommt nur Fa in Frage. oben, links, hinten kommt nur Da in Frage. oben, rechts, hinten kommt nur Bc in Frage. Die Spalten werden a,b,c,d,e,f genannt, die Zeilen A,B,C,D,E,F. Noch eine Besonderheit: Das Mayblox-Problem top Das Kowalewski - Problem top Er verlangte rechts und links bzw. vorne und hinten gleiche Farben, oben eine dritte und unten eine vierte Farbe. Innen sollten gleiche Farben zusammentreffen. Instant Insanity top top Englisch: Jaap 's Puzzle Page - Instant Insanity Ivars Peterson 's MathTrek - Averting Instant Insanity Kadon Enterprises Inc.

23. Kadon Enterprises, More About Edgematching when the British mathematician Major percy macmahon invented and macmahon divided squares and triangles into triangles to give each edge of a piece http://www.gamepuzzles.com/moredge.htm

More about edgematching The idea of fitting matching or complementary tiles together is as old as dominoes, movable picture blocks, and jigsaw puzzles. The concept of colormatching tiles based on all the permutations of colors on their edges dates from 1926, when the British mathematician Major Percy MacMahon invented and introduced Three-Color Squares and Four-Color Triangles as "mathematical pastimes." MacMahon divided squares and triangles into triangles to give each edge of a piece its own color (see Kadon's Multimatch I and III), in all possible combinations. Each set contains 24 different tiles, and MacMahon discovered that they could form a single figure with all adjacent edges matching and just one color all around the outside border. Other adjacency conditions can also be explored. 4 Cube Puzzle , now sadly out of print. The most extensive research into these sets, over three decades, was done by Wade Philpott of Lima, OH, who identified all the possible symmetrical shapes that MacMahon squares and triangles could solve with both matching edge colors and uniform border color, and who calculated all the numbers of solutions for the MacMahon squares' 4x6 rectangle. Here's a hidden solution . These findings are included in the rule books for Kadon's Multimatch I and Multimatch III. Another extensive researcher is Toby Gottfried , whose pioneering work in computer-derived solutions for the corner-colored squares (Multimatch II) won him an honors degree in computer science in 1972. Toby's program back then took 500 hours to accomplish what his 1999 computer can whip out in 2 minutes. You can see his results and play some puzzles and games on his joyous website. His latest research explores wrap-around solutions for Multimatch II's 3x8 and 4x6 rectangles. For the latter he has found 180 cylindrical solutions. One is shown at right.

24. Kadon Enterprises, Inc., Wade Philpott Profile originally proposed by the British mathematician, percy macmahon. Another puzzle set that Wade investigated exhaustively was macmahon s FourColor http://www.gamepuzzles.com/wade.htm

Puzzle explorer: Wade Philpott Wade Philpott (1918-1985) was born in Sunnyside, Washington, as Chester Wade Edwards. He was adopted by his aunt and uncle, Viola and George Philpott, in 1921, and his name was changed to Wade Edward Philpott. He graduated from Ohio Northern University with a degree in engineering and became a Registered Engineer in Ohio. His work included design of printing calculators and business machines. Multimatch and Sweep Multimatch I Multimatch was a name Wade chose for the set of 24 square tiles based on MacMahon's Three-Color Squares, originally proposed by the British mathematician, Percy MacMahon. Wade's research broke new ground in identifying all the symmetrical shapes that could be solved according to MacMahon's twin criteria of matching edge colors and forming a uniform border color. Wade also pioneered the use of computer search programs for identifying all possible solutions to a given puzzle shape. In 1982 Philpott arranged with Kadon to market his original cardboard version of Multimatch. Later, Kadon also produced the set in handcrafted, lasercut acrylic as Multimatch I , the first in a series of four edgematching puzzles bearing the name "Multimatch."

25. Furman Mathematics: Andrews Abstracts ABSTRACT In the late 1890 s, Major percy Alexander macmahon developed hisPartition Analysis with the object of proving his conjectures on plane partitions http://math.furman.edu/activities/clanton/andrews.html

Furman Mathematics Department People Resources Activities ... Advice Abstracts for George Andrews, Clanton Visiting Mathematician, 2001-2002 AN OLD ALGORITHM IN A NEW ERA (Major McMahon, you were born too soon!) ABSTRACT: In the late 1890's, Major Percy Alexander MacMahon developed his Partition Analysis with the object of proving his conjectures on plane partitions. While writing at length on this topic and clearly indicating it's power, MacMahon eventually admitted that he was unable to apply his new tool to solve any of his conjectures on plane partitions. In this talk, we shall examine MacMahon's method from a purely elementary point of view and shall illustrate its power by considering questions of general interest. First we turn to Question B3 from the 1999 Putnam exam (see the October 2000 Monthly). Second we ask how many triangles are there with integer sides and perimeter n . Our object will be to illustrate the utility of a 19th century idea that is only now coming into its own in the era of computer algebra. RAMANUJAN, FIBONACCI NUMBERS AND CONTINUED FRACTIONS

26. DML: Digital Mathematics Library: Retrodigitized Mathematics Journals And Monogr 18, Michigan Combinatory analysis, by percy A. macmahon. (by macmahon, percyAlexander), 191516. book. 19, GDZ Commentarii mathematici Helvetici, 30804 http://www.mathematik.uni-bielefeld.de/~rehmann/DML/dml_links_title_C.html

DML: Digital Mathematics Library Also: WDML: World Digital Mathematics Library Retrodigitized Mathematics Journals and Monographs Contains links to 1874 digitized books (> 385236 pages ) and to 145 digitized journals (> 2942143 pages). (Numbers of pages are preliminary; not all informations are already available.) Includes all the links mentioned on page 920 of: Allyn Jackson, "The Digital Mathematics Libary", Notices Amer. Math. Soc., vol. 50 (8), 2003 Local Copy A similar list is offered at http://www.wdml.org The database for this table is an ASCII based (ISO Latin 8859-1 extended) list , which may be parsed by this PERL script If you want items to be added here, please send me the necessary data. Lists ordered by "Journal", "Repository" (Journals only) or by "Author name", "Title" are provided, as well as an overview of the repositories Author: A B C D ... Z Title: A B C D ... Z Nr. Repository: Title, Author: Pages: Year(s): Type: Michigan C. G. J. Jacobi's Gesammelte werke. (by Jacobi, C. G. J. (Carl Gustav Jakob)) book Michigan C. G. J. Jacobi's Vorlesungen über Dynamik. Gehalten an der Universität zu Königsberg im Wintersemester 1842-1843 und nach einem von C. W. Borchart ausgearbeiteten Hefte.

27. MacMahon S Cubes A Cube Has Six Faces, And If Six Colours Are National Research Institute for Mathematical Sciences, Pretoria, South Africa,Technical Report, TWISK 40, August 1978 percy Alexander macmahon; http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/macmahon-cubes

28. RAS LETTERS Lamont—Rutherford - Royal Astronomical Society macmahon, percy Alexander 98,1. MAEDLER, Johann Heinrich 46,1. MAIN, Robert 39,1;41,1; 43,5; 44,6; 45,10; 48,2; 50,1; 51,3; 55,1; 56,5; 57,5; 58,12; 59,7; http://www.ras.org.uk/index.php?option=content&task=view&id=108

29. RAS LETTERS Lamont—Rutherford macmahon, percy AlexanderÊÊÊÊ98,1. MAEDLER, Johann HeinrichÊÊÊÊ46,1. MAIN,RobertÊÊÊÊ39,1; 41,1; 43,5; 44,6; 45,10; 48,2; 50,1; 51,3; 55,1; 56,5; 57,5; http://www.ras.org.uk/html/library/ArchiveMS/letters3.html

LAMONT, Johann vonÊÊÊÊ37,1; 38,1; 39,1; 76,1. LAMP, Ernst AugustÊÊÊÊ94,1. LANGLEY, Samuel PierpontÊÊÊÊ68,1; 83,2; 84,1. LARMOR, Sir JosephÊÊÊÊ99,1. LARTIGUE, JosephÊÊÊÊ55,1. LASSELL, WilliamÊÊÊÊ40,1; 41,2; 43,1; 44,2; 45,3; 47,1; 48,3; 49,1; 51,1; 52,1; 53,1; 54,1; 56,2; 57,3; 58,1; 62,2; 66,1; 67,1; 68,3; 71,4; 72,1; 73,1; 74,2; 76,3; 79,2. LAUGHTON, John KnoxÊÊÊÊ66,1; 69,1; 70,2; 71,4; 72,1; 73,1; 74,1; 77,4; 80,1; 83,1; 85,1. LAUGIER, Paul August ErnestÊÊÊÊ64,1. LAWSON, HenryÊÊÊÊ44,1; 47,1; 53,1; 55,1. LEAVENWORTH, Francis, P.ÊÊÊÊ1900,2. LEE, JohnÊÊÊÊ32,3; 34,2; 35,1; 39,1; 40,1; 43,2; 44,9; 45,6; 46,2; 47,6; 48,5; 49,5; 50,5; 51,2; 52,2; 53,3; 54,6; 56,1; 57,3; 58,6; 59,1; 60,6; 61,11; 62,8; 63,9; 64,1; 65,2; 66,1. LETTS, Edmund AlbertÊÊÊÊ98,3. LE VERRIER, Urbain Jean JosephÊÊÊÊ56,1. LEWIS, William JamesÊÊÊÊ73,1; 74,2; 75,2; 76,1; 77,1; 80,2; 81,1; 89,1; 99,1. LIAIS, EmmanuelÊÊÊÊ60,1; 67,1.

30. Combinatory Analysis - Percy Alexander Macmahon This volume offers an account of the theorems employed in combinatory analysis,showing their connections and uniting them as parts of a general doctrine. http://www.libreriauniversitaria.it/BUS/0486495868/Combinatory_Analysis.htm

PowerSearch: Libri Italiani English Books DVD Combinatory Analysis Percy Alexander Macmahon Clicca per ingrandire Prezzo Disponibilità Normalmente disponibile in 6/8 giorni lavorativi Metti nel carrello (Puoi sempre toglierlo dopo) Dettagli del libro Titolo: Combinatory Analysis Autore: Percy Alexander Macmahon Editore: Dover Publications Data di Pubblicazione: July 2004 ISBN: Reparto: Mathematical Analysis Descrizione This volume offers an account of the theorems employed in combinatory analysis, showing their connections and uniting them as parts of a general doctrine. The first section shows the involvement of the general theory in the algebra of monomial symmetric functions. The following section extends the simple theory of symmetric functions, enabling the intuitive derivation of theorems of algebraical reciprocity, and the third section is devoted to certain points in the theory of permutations. The final sections deal with the perfect partitions of numbers as a necessary preliminary to the discussion of arrangements on a chessboard, and with the direct application of the theory of distributions to the enumeration of the partitions of multipartite numbers. 1915-16 and 1920 eds.

31. Percy Alexander Macmahon - Www.libreriauniversitaria.it Translate this page Autore percy Alexander macmahon Tarquin, September 2004 Visualizza dettagli edisponibilità, € 25.01. Combinatory Analysis Autore percy Alexander macmahon http://www.libreriauniversitaria.it/goto/author_Percy Alexander Macmahon/shelf_B

PowerSearch: Libri Italiani English Books DVD Risultati della ricerca Libri in Inglese Nuova ricerca New Mathematical Pastimes Autore: Percy Alexander Macmahon Tarquin, September 2004 Combinatory Analysis Autore: Percy Alexander Macmahon Dover Publications, July 2004

32. Bibliography macmahon, percy Alexander, 18541929, percy Alexander macmahon collected papers /edited by George E. Andrews, Cambridge, Mass. MIT Press, 1978- http://www.library.cornell.edu/math/bibliography/display.cgi?start=M&

33. Untitled Document percy ALEXANDER macmahon. 150th Birthday Celebration. A meeting to celebratepercy Alexander macmahon’s 150th birthday will be held on Thursday 23 September http://www.lms.ac.uk/newsletter/322/322_05.html

INTERNATIONAL MEETINGS Contents LMS Mary Cartwright Lecture LMS Invited Lectures Percy Alexander MacMahon SMS-NATO Advanced Summer Institute ... Maths Takes Shape LONDON MATHEMATICAL SOCIETY MARY CARTWRIGHT LECTURE Friday 20 February 2004, University College London Professor Dierk Schleicher (Bremen) Understanding Complex Dynamical Systems and their Parameter Spaces Tea Mary Cartwright Lecture Professor Mary Rees (Liverpool) The Topographer’s View of Parameter Spaces The two talks by Mary Rees and Dierk Schleicher will discuss parameter spaces which arise in complex dynamical systems: each point in such a parameter space represents a different dynamical system, and different parameters are distinguished by the different features which the corresponding dynamical systems might have. This gives interesting structure to parameter spaces. One often finds that a relatively small class of dynamical features yields a good understanding of the entire parameter space. The first talk

34. Untitled Document percy Alexander macmahon s 150th Birthday Celebration percy Alexander macmahonwas President of the London Mathematical Society from 18941896, http://www.lms.ac.uk/newsletter/327/327_04.html

INTERNATIONAL MEETINGS Contents LMS Meeting, London: Hardy Lecture LMS Northern Regional Meeting LMS Popular Lectures 2004 LMS Spitalfields Day ... Yorkshire Differential Geometry Day LONDON MATHEMATICAL SOCIETY Friday 18 June 2004 J.C. Rickard (Bristol University) Senior Berwick Prizewinner 2002 will speak at 3.30 pm on The stable module category of a finite group algebra T. Tao (UCLA) will give the Hardy Lecture at 5.00 pm on Long arithmetic progressions in the primes The meeting will be held at the Chemistry Auditorium, Christopher Ingold Building, University College London, 20 Gordon Street, London WC1. Tea will be served at 4.30 pm. Tuesday 15 June There are limited funds available to contribute in part to the expenses of members of the Society or research students to attend the meeting. Requests for support, including an estimate of expenses, may be addressed to the Programme Secretary at the Society (web: www.lms.ac.uk

35. Universal Book Of Mathematics: List Of Entries macmahon, percy Alexander (18541929) macmahon squares Madachy, Joseph S.magic cube magic square magic tour main diagonal major axis Malfatti circles http://www.daviddarling.info/works/Mathematics/mathematics_entries.html

WORLDS OF DAVID DARLING ENCYCLOPEDIA NEWS ARCHIVE ... E-MAIL THE UNIVERSAL BOOK OF MATHEMATICS From Abracadabra to Zeno's Paradoxes More details on the book Alphabetical List of Entries abacus Abbott, Edwin Abbott (1838-1926) ABC conjecture Abel, Niels Henrik (1802-1829) Abelian group abracadabra abscissa absolute absolute value absolute zero abstract algebra Abu’l Wafa (A.D. 940-998) abundant number Achilles and the Tortoise paradox. See Zeno's paradoxes Ackermann function acre acute adjacent affine geometry age puzzles and tricks Agnesi, Maria Gaetana (1718-1799) Ahmes papyrus. See Rhind papyrus Ahrens, Wilhelm Ernst Martin Georg (1872-1927) Alcuin (735-804) aleph Alexander’s horned sphere algebra algebraic curve algebraic fallacies algebraic geometry algebraic number algebraic number theory algebraic topology algorithm algorithmic complexity Alhambra aliquot part al-Khowarizmi (c.780-850) Allais paradox almost perfect number alphamagic square alphametic Altekruse puzzle alternate altitude ambiguous figure ambiguous connectivity.

36. Collected Works In Mathematics And Statistics macmahon, percy Alexander, 18541929, percy Alexander macmahon collected papers,2, QA 3 M27 1978, Killam. Magnus, Wilhelm, 1907-1990, Wilhelm Magnus, http://www.mathstat.dal.ca/~dilcher/collwks.html

Collected Works in Mathematics and Statistics This is a list of Mathematics and Statistics collected works that can be found at Dalhousie University and at other Halifax universities. The vast majority of these works are located in the Killam Library on the Dalhousie campus. A guide to other locations is given at the end of this list. If a title is owned by both Dalhousie and another university, only the Dalhousie site is listed. For all locations, and for full bibliographic details, see the NOVANET library catalogue This list was compiled, and the collection is being enlarged, with the invaluable help of the Bibliography of Collected Works maintained by the Cornell University Mathematics Library. The thumbnail sketches of mathematicians were taken from the MacTutor History of Mathematics Archive at the University of St. Andrews. For correction, comments, or questions, write to Karl Dilcher ( dilcher@mscs.dal.ca You can scroll through this list, or jump to the beginning of the letter: A B C D ... X-Y-Z A [On to B] [Back to Top] N.H. Abel

37. Royal Society | About The Society | History Of Science | Biographies Of Fellows macmahon, percy Alexander. Proceedings A 1930 vol 127 pp xxvii, plate. McMichael,Sir John. Biographical Memoirs 1995 vol 41 pp 281-296, plate, http://www.royalsoc.ac.uk/page.asp?id=2376

38. Lib. Cong. Title Author Publisher Year Notes 66013992 Symmetry QA165 M16, Combinatory Analysis, macmahon, percy A. Chelsea Publishing Company,1960, Volumes I II. QA165 N47, Lehrbuch der Combinatorik, Netto, http://www.phy.ohiou.edu/~asmith/library/card_catalog_central.htm

Lib. Cong. # Title Author Publisher Year Notes Symmetry Groups in Nuclear and Particle Physics F.J. Dyson W.A. Benjamin LCCN code The Two Cultures and a Second Look Snow, C. P. The New American Library Philosophical Problems of Space and Time "Grunbaum, Adolf" "Reichenbach, Hans" "Dover Publications, Inc." "Of Time, Passion, and Knowledge" "Fraser, J. T." Doubleday BD638 V. 59 The Voices of Time "Fraser, J.T." The University of Massachussettes Press Mathematics and Optimal Form "Hildebrandt, Stefan and Tromba, Anthony" "Scientific American Books, Inc." Superior Beings "Brams, Steven J." "Springer-Verlag New York, Inc." Precision Measurement and Fundamental Constants II U. S. Department of Commerce/ National Bureau of Standards U. S. Government Printing Office World Atlas McGraw-Hill Book Company The Tides Pulse of the Earth "Clancy, Edward P." Anchor Books Doubleday The Encyclopedia of Oceanography "Fairbridge, Rhodes W."

39. Fine's Equation -- From MathWorld Andrews, GE (Ed.) percy Alexander macmahon Collected Papers, Vol. 2. Cambridge,MA MIT Press, p. 260, 1986. Andrews, GE Nathan Fine, 19161994. Not. http://mathworld.wolfram.com/FinesEquation.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Special Functions q-Series ... Somos Fine's Equation The q -series identity where is the number of divisors of that are congruent to 1, 5, 7, and 11 (mod 24) minus the number of divisors of congruent to -1, -5, -7, and -11 (mod 24) and is a Kronecker symbol The first few powers of starting with , 1, ... are 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, ... (Sloane's SEE ALSO: q -Series [Pages Linking Here] REFERENCES: Andrews, G. E. (Ed.) Percy Alexander MacMahon: Collected Papers, Vol. 2. Cambridge, MA: MIT Press, p. 260, 1986. Andrews, G. E. "Nathan Fine, 1916-1994." Not. Amer. Math. Soc. Sloane, N. J. A. Sequences in "The On-Line Encyclopedia of Integer Sequences." CITE THIS AS: Eric W. Weisstein. "Fine's Equation." From MathWorld A Wolfram Web Resource.

40. COLLECTED PAPERS macmahon, percy Alexander, 18541929. Collected Papers, 2, QA3/M23 1978. Manin, Yu,Selected Papers, 1, QA3/M3413 1996. Matsushima, Yozo 1921-1983. http://www.matmor.unam.mx/acervo/OBRAS_COMPLETAS_EN_MATEMATICAS.html

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