. KNIGHT'S TOUR NOTES 12 Chronology & Bibliography of Tours by G. P. Jelliss 3 20 47 38 5 10 45 40 48 51 4 19 46 39 8 11 21 2 37 50 9 6 41 44 52 49 32 1 18 43 12 7 63 22 53 36 31 16 59 42 54 33 64 17 60 13 30 27 23 62 35 56 25 28 15 58 34 55 24 61 14 57 26 29 2019 1 . KNIGHT'S TOUR NOTES ======================================================================== Title Page Illustrations: A selection of the author's own work. Shaped and Holey Board Tours of 6, 44 and 64 cells, showing biaxial and octonary symmetry. Figured tour with square numbers delineating a cube. A 12×14 rectangular magic knight tour. A 10×10 symmetric tour without right angles. An 8×8 symmetric tour with each angle occurring a multiple of 4 times. An 8×8 approximately axial tour with no lateral-acute or diagonal-obtuse angles. --------------------------------------------------------------------------------------------------------------------------------- Contents Chronology 3. to 1759 4. to 1824 5. to 1847 6. to 1861 7. to 1873 8. to 1884 9. to 1900 10. to 1917 11. to 1929 12. to 1935 13. to 1944 14. to 1959 15. to 1978 16. to 1985 17. to 1994 18. to 2000 19. to 2008 20. to 2019 Bibliography 21. A 23. B 29. C 32. D 35. E 36. F 39. G 41. H 44. I J 49. K 51. L 55 M 61. N 62. O P 64. Q R 66. S 70. T 71. U V 73. W 76. X Y Z Knight's Tour Notes 77. Acknowledgments and Outline 78. The Volumes in the Series --------------------------------------------------------------------------------------------------------------------------------- © George Peter.Jelliss 2019 http://www.mayhematics.com/ Knight's Tour Notes, Volume 12, Chronology & Bibliography of Tours. If cited in other works please give due acknowledgment of the source as for a normal book. 2 . KNIGHT'S TOUR NOTES ======================================================================== A Concise Chronology ======================================================================== −3500: Plough used in Mesopotamia. The ploughing of a field is in effect a rook tour. −2200: Traditional date when the 3×3 magic square was known in China. −1600 The legendary labyrinth at Knossos, as represented on Minoan coins . −1000: Wazir paths of Castellar, Maeander and Key types used as border patterns in Greek art. ------------------------------------------------------------------------------------------------------------------------- 840~ al-Adli ar Rumi (flourished 840) One closed knight tour survives. 900~ Abu-Bakr Muhammad ben Yahya as Suli (c.880 - 946). Four tours inc. 900 ~ The Kavyalankara by Rudrata . Rook, Elephant and Knight tours on 4×8 board. 988: Ben Ishaq An-Nadim . Kitab al-fihrist . Bibliography lists books by al-Adli and as-Suli. ------------------------------------------------------------------------------------------------------------------------- 1069: Nami of Guzerat . Commentary on Rudrata (c. 900) Kavyalankara . 1141: al Baghdadi ms with extracts from al-Adli, as-Suli has the four as-Suli tours. 1150 ~ Manasollasa of King Somesvara III, Kalyani, India. Tour described by two-letter coordinates. 1221: Muhammad ben Hawa ben Othman . Ms with 2nd as-Suli tour. [Murray 1913, p.174-5]. 1250 Collections of chess problems ascribed to ‘Bonus Socius’ meaning Good Companion. 1257 Arabic ms in the British Museum. Problems with capture of series of pawns by knight. 1275~: The King's Library ms . Anglo-Norman. Halfboard and double halfboard tours. 1315: Manuel Moschopoulos work on magic squares using the step-sidestep method. 1325~: Nicolas de Nicolai. Latin ms. Sets halfboard tour problem with six solutions. 1330~: al Hakim ms has the tours attributed to al-Adli and Ali ibn Mani. 1350 Later collections ascribed to ‘Civis Bononiae ’ meaning ‘Citizen of Bologna’. 1350~: al Amuli (d. 1352). Persian Treasury of the Sciences . Contains a corner-to-corner tour. 1370~: — Cairo ms in Khedival Library, with three of the tours given by Baghdadi 1141. 1400~: Ala'addin Tabrizi 16th century ms asks for quarterboard tour. 1490~: Florence . Italian ms (codex XXIV) has a 4×8 tour. ------------------------------------------------------------------------------------------------------------------------- 1511: Johannes Chachi , of Terni. Ms collection of chess problems, includes a 4×8 tour. 1512: Paulo Guarini di Forli . Ms in the J. G. White collection contains the Civis Bononiae tour. 1597: Orazio Gianutio della Mantia . This has one 4×8 tour. ------------------------------------------------------------------------------------------------------------------------- 1612: Claude Gaspar Bachet Problemes Plaisans et Delectables , 1612. No tours. 1637: René Descartes (1596-1650) Discours de la méthode , (1637). Use of numerical coordinates. 1640: Bhatta Nilakant-ha Bhagavantabhaskara One tour fully symmetric 1660: Bernard Frénicle de Bessy (c.1605-1675) Catalogue of 880 diamagic squares 4×4. 1694: Jacques Ozanam (1640-1717) Recreations Mathematiques et Physiques First edition 1694. ------------------------------------------------------------------------------------------------------------------------- 1725: Pierre Rémond de Montmort (1678-1719) Open tour in Ozanam. 1725: Abraham de Moivre (1666-1754) Open tour in Ozanam (with alternative version in text). 1725: Jean-Jacques d’Ortous de Mairan (1678-1771). Open tour in Ozanam. 1736: Leonhard Euler (1707-1783). Solutio problematis ad geometriam situs pertinentis 1741. 1737: Philip Stamma (c.1705-c.1755) Essai sur le Jeu des Echecs Algebraic chess notation. ------------------------------------------------------------------------------------------------------------------------- 1751: Denis Diderot (1713-1784) Main editor of the Encyclopédie . 1751: Jean le Rond d'Alembert (1717-1783) Encyclopédie art. Echecs in Vol.5 p.244-248. 1753: William Hogarth (1696-1764) The Analysis of Beauty (1753) Serpentine ‘line of beauty’. 1757: Leonhard Euler (1707-1783) Knight's tour in letter to Christian Goldbach (1690-1764). 1759: Leonhard Euler (1707-1783) ‘Solution d’une Question ...’ Paper on Knight tours. 1766. ------------------------------------------------------------------------------------------------------------------------- 1766: Lelio dalla Volpe Corsa del Cavallo ... First to show knight's tours in diagram form. 3 . KNIGHT'S TOUR NOTES 1767: (Monsieur) B—: Letter to the editors of the Journal Encyclopédique re knight's tours. 1769: Farkas Kempelen (1734–1804) inventor of the first chess-playing ‘automaton’. 1769: Edmé Gilles Guyot Nouvelles Récréations ... Similar to Ozanam with Moivre tour. 1769: Domenico Lorenzo Ponziani (1719-1796) Il Giuoco Incomparabile... quotes Ozanam. ------------------------------------------------------------------------------------------------------------------------- 1771: Alexandre-Théophile Vandermonde (1735-1796). One 8×8 tour joining 16-move circuits. 1772: Edmé Gilles Guyot . Neue physikalische .... German edition of Guyot (1769). 1772: Cosimo Alessandro Collini (1727-1806) articles in Journal Encyclopédique with one tour. 1773: Collini Solution du Problème du Cavalier au Jeu des Echecs 20 tours. 1773: A. C. B—. in Journal Encyclopédique complaint that in Collini tour knight starts from B1. 1773: (Le Chevalier) W— ‘Capitaine au régiment de Kinski’ Journal Encyclopédique closed tour. 1774: Collini Soluzione del problema... Magazzino Toscano Italian edition of his work, 1776: (Jean Louis?) Monneron or one of his brothers sends two tours to Nouveau Dictionaire. 1778 Louis Bertrand of Geneva. Work on Mathematics, but does not mention his ideas for Euler. ------------------------------------------------------------------------------------------------------------------------- 1780: Gaspard Monge (1746-1818). Pages of symmetric tour found among his papers recently. 1780: Chapais : Essais analytiques sur les Echecs . Ten tours of Collini type, four on larger boards. 1782: Laisement (1729-1800) Essai sur les Problèmes de Situation Many tours inc 16x16. 1783: Windisch Eye-witness account of how knight's tour was exhibited by Kempelen automaton. 1787: Richard Twiss Chess (two volumes 1787 and 1789). First tour on a circular board. 1789: Giorgio Fontana , Opuscoli Matematici ... Euler. ------------------------------------------------------------------------------------------------------------------------- 1790: J. E. Montucla , revised edition of Ozanam. Adds the Chevalier W. (1773) tour. 1791: (Fr.) Wilhelm A — of Cleve, ms Der Rössel-Sprung ... in Lasa collection. One tour. 1797: Ernst von Sachsen-Gotha Reichs-Anzeiger and Auflösung ... ms Figured tours. 1798: Shir Muhammad-Khan , Sardarnama , Persian ms. Contains the Nilakant-ha tour. --------------------------------------------------------------------------------------------------------------------------------- 1800: Lalande : and Bossut Dizionario Enciclopedico delle Matematice . Euler's method. 1803: Charles Hutton Recreations in Mathematics ... , 1803, 1814. English editions of Ozanam. 1804: Maelzel Exhibited Kempelen's chessplaying automaton in England and N. America. 1804: (Rev.) Thomas Pruen , An Introduction to the History and Study of Chess . Moivre tour. 1806: Joseph Dollinger , Ein Hundert ... End-Spiele. Dann ... Arten den Springer... 24 tours. ------------------------------------------------------------------------------------------------------------------------- 1811: (Prof.) Vicenzo Brunacci Compendio del Calcolo Sublime . After Euler 1759. 1814: Charles Hutton Recreations in Mathematics ... , new edition of Hutton (1803). 1815: ‘Promenade des Springers’ Thee und caffee-Zeitvertreib , 2 Jan 1815. 1816: