Sunday, 28 January 2018

Knight's Tour Book Contents

I must try to post something each month at least. New Year's Resolution.
So here is the list of contents of my Knight's Tour Notes book as it now stands.
It is now back to a single book of around 800 pages.

z Theory of Moves 5 Nets, Boards, Moves, Pieces, Freedom, Mobility,
z Theory of Journeys 12 Shortest Path, Angles, 3-, 4-, 6-, 8-Moves, Touring Tests.
z Theory of Magic 24 Magic Arrays, Magic Rectangles, Magic Squares, Step Sidestep.
z Wazir Tours 36 Labyrinths, 6×6, Non-Intersecting, Around the Rocks, Snakes, Figured.
z Knight Move Geometry 53Nets, Triangles, Quadrangles, Polygons, Intersections.
z Symmetry 58 Symmetry, Coding, Generic, Central Angles, Straits and Slants.
z Shaped Boards 68 Octonary 72 Biaxial 80 Birotary 98 Rotary 120 Axial 132 Unary.
z Rectangular Boards 156 Borders, Schwenk Theorem, Symmetries, Oblongs
z Oblong Boards 159 3-rank 180 4-rank, Mediaeval 4×8 202 5-rank  6-, 7-, 8-, up to 24×37.
z Odd Square Boards 217 3×3, The 5×5 Board, 7×7,9×9, 11×11, 13×13, 15×15.
z The 6×6 Board 225 quaternary, binary, angle method, slants, open 3-slant, semimagic
z 6×6 Asymmetric 232 Closed Tours: 4-slant, 6-slant, 8-slant, 10-slant, 12-slant.
z Earliest Knight's Tours 272  Adli. Suli, Mediaeval mss, Aladdin, Nikolai, Nilakantha
z Rediscovery (1725-1825) 275 Euler, Vandermonde, Collini, Warnsdorf, Generation Rules.
z Squares and Diamonds 291 FPH, von Schinnern, Ciccolini, Franz, Wenzelides, Jaenisch
z Roget's Nets 300 Straits & Slants, 3-slant, Reentrant, S&D, Given slants, Max slants
z Pseudotours 309  Simple Linking 311 Octonary 317 Crosspatch 319 Collinian
z Double Halfboard Tours 323 Symmetric Rhombic Halfboard.
z More Squares and Diamonds, 330 Symmetric Rhombic Non-halfboard
z Compartmental 342 Tours from Crosspatches, 346 Enumeration of 8×8 Tours
z Graphic Tours: 348 Directions, Intersections, Circulation 351 Angles Max and Min
z Shapes 359 Triangles, Quadrangles 362 Stars 364 Pictorial 365 Monograms.
z 8×8 Asymmetric Tours 368 Legendre, Rothe, Bilduer, Maximum Asymmetry.
z Near Symmetry 370 Bergholtian, Octonary, Quaternary, Axial, Rotary, Diagonal
z 8×8 Symmetric Tours 382 History 391 Symmetrisation, Given Centre 396 All Centres
z Mixed Quaternary Symmetry 406 h:j:k types: h=1, k=3, h>1 k>3, h=3, j=4, k = 5
z Quaternary Pseudotours, 434 8-fold, 4-fold, 2-fold, 1-fold, Table.
z Tours from QP 489 Aladdin, Vandermond, Non-Crossing, Jaenischian, 493 Other QP.
z Lettered Tours 497 Cryptotours, Alphabetical Tours, Chess Art Here??
z Figured Tours 507 Historical development.
z Magic 8×8 Knight Tours 524 Beverley, Wenzelides, Mysore, Jaenisch, Le Siecle,
z Ligondes 1911, Lehmann 1933, Murray 1936, Marlow 1987, Roberts 2002, Completion 2003.
z Catalogue of the 8×8 Magic Knight Tours 552 Historical, Geometrical, Arithmetical.
z Theory of Magic Knight Tours 578 Existence, Braids, Quartes, Testing Procedure.
z Large Even Square Boards 588 10×10 597 12×12 612 14x14 614 16×16 622 Even Larger
z Leapers 629 Camel. Shaped, Zebra, Zebra-rider,.Giraffe, Antelope, {1,5}, {2,5}, {1,6}, {1,7}.
z King Tours 641 Knots, 2×n  3×n  4×n  5,6×n  7×n, 8×8  Alternating, Figured
z Magic King Tours 655 Magic  Biaxial Diamagic  Axial Diamagic  Larger
z Double-movers 661 2-move R, 2-Move Q, 664 Emperor, Templar, Empress
z 673 Nightrider, Lancelot, Prince, Hospitaller, Night-Commuter
z 675 Caliph?, Gnu, Bison, Fiveleaper, Root-50, Root-65, Root-85.
z Triple-movers 683 3-move R, Hyperwazir 3-Move Q, Pterodactyl,
z Triple Knights WDN, WTN, Centaur, WAN, DFN, TFN,
z Quadruple-movers 692 4-move Magic R Tours, 4-MoveQ, WDTN,
z Multi-movers 704 5-6-MRT, 5+MQT, Raven, Amazon, Wizard.
z Alternative Worlds 722 Non-Crossing Paths 730 Rider Crossovers 731 Hoppers
z New Boards 733 Bent Boards 736 Space Chess, Higher Dimensions, 745 Honeycombs,
z End Notes 751 Bibliography 787 Solutions 790 Glossary 796 Index

The z is a wingding knot symbol that hasn't come out.

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