US20050212204A1 - Method of playing board games on two-dimensional manifolds - Google Patents
Method of playing board games on two-dimensional manifolds Download PDFInfo
- Publication number
- US20050212204A1 US20050212204A1 US10/708,740 US70874004A US2005212204A1 US 20050212204 A1 US20050212204 A1 US 20050212204A1 US 70874004 A US70874004 A US 70874004A US 2005212204 A1 US2005212204 A1 US 2005212204A1
- Authority
- US
- United States
- Prior art keywords
- board
- manifold
- game
- games
- board games
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Abandoned
Links
Classifications
-
- A—HUMAN NECESSITIES
- A63—SPORTS; GAMES; AMUSEMENTS
- A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
- A63F3/00—Board games; Raffle games
- A63F3/02—Chess; Similar board games
-
- A—HUMAN NECESSITIES
- A63—SPORTS; GAMES; AMUSEMENTS
- A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
- A63F3/00—Board games; Raffle games
- A63F2003/00996—Board games available as video games
-
- A—HUMAN NECESSITIES
- A63—SPORTS; GAMES; AMUSEMENTS
- A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
- A63F3/00—Board games; Raffle games
- A63F3/00173—Characteristics of game boards, alone or in relation to supporting structures or playing piece
- A63F3/00214—Three-dimensional game boards
Definitions
- a manifold is a locally-Euclidean space; this invention is limited to two-dimensional manifolds. These manifolds can be thought of as surfaces built from flat pieces by gluing them together along their sides. See [2], [8] for definitions. Moebius tape, torus, Klein bottle are examples of such surfaces (see [1]).
- U.S. Pat. Nos. 6,595,519, 6,305,688, 6,318,726, 6,382,626, 6,491,300 deal with puzzles that use Moebius topology.
- the current invention relates to playing board games on such a surfaces as well as other possible two-dimensional surfaces.
- U.S. Pat. No. 4,026,557 relates to a group of games around Taurus game, that use the surface of torus to map its “oblique endless paths”.
- the game ‘five in line’ (add the reference) is played on a two-dimensional board consisting of a rectangular grid of square cells.
- the game is played by two players (one uses ‘crosses’ and the other using ‘zeroes’ that in turn make their moves by drawing a ‘cross’ or a ‘zero’ in a cell that was not previously occupied by a ‘cross’ or a ‘zero’.
- Board games can be played on virtual boards that are mapped to two-dimensional surfaces like cylinder, torus, Klein bottle, etc, with the necessary alteration of the rules. Such games can be played on computers or other digital devices, including game devices. In this case the edges of the board are thought of as glued according to the gluing rules; the board can be scrolled on the screen, depending on how it is glued.
- Board games such as “renju” or “five in line” can be played on such surfaces.
- the recommended minimal size of the surface for “five in line” is 6 by 8, which is very practical for cell phones or PDAs. Both torus and Klein bottle surfaces can be used to play this variant of ‘five in line’.
- a computer program, or a device can model any such game board surface and display it on the screen as if it were a flat surface with borders glued together according to the nature of the surface. If the board does not have boundaries, e.g. a torus or a Klein bottle or a projective plane, it can be panned or rotated on the screen, so that different cells move to the center of the screen. Moebius tape may be rotated on the screen only in one dimension (left-right).
Abstract
A method of playing board games on modeled compact two-dimensional manifolds. The manifold is designed to be modeled from an imaginary game board by gluing its sides in the special manner so that the result is topologically equivalent to the desired surface as defined in topology.
Description
- Copyright (c) Vladimir Patryshev, 2004
- In mathematics a manifold is a locally-Euclidean space; this invention is limited to two-dimensional manifolds. These manifolds can be thought of as surfaces built from flat pieces by gluing them together along their sides. See [2], [8] for definitions. Moebius tape, torus, Klein bottle are examples of such surfaces (see [1]).
- U.S. Pat. Nos. 6,595,519, 6,305,688, 6,318,726, 6,382,626, 6,491,300 deal with puzzles that use Moebius topology. The current invention relates to playing board games on such a surfaces as well as other possible two-dimensional surfaces.
- U.S. Pat. No. 4,026,557 relates to a group of games around Taurus game, that use the surface of torus to map its “oblique endless paths”.
- One of possible games in Renju (see [4],[5] for the game rules), another is gomoku, or ‘five in line’ (see [6], [7] for the game rules). The game ‘five in line’ (add the reference) is played on a two-dimensional board consisting of a rectangular grid of square cells. The game is played by two players (one uses ‘crosses’ and the other using ‘zeroes’ that in turn make their moves by drawing a ‘cross’ or a ‘zero’ in a cell that was not previously occupied by a ‘cross’ or a ‘zero’. The player that manages to have five adjacent ‘crosses’ or ‘zeroes’ in line, horizontal, vertical or diagonal, wins.
- Board games can be played on virtual boards that are mapped to two-dimensional surfaces like cylinder, torus, Klein bottle, etc, with the necessary alteration of the rules. Such games can be played on computers or other digital devices, including game devices. In this case the edges of the board are thought of as glued according to the gluing rules; the board can be scrolled on the screen, depending on how it is glued.
- Usually board games are played on a limited (defined as compact in mathematics) piece of flat surface. Instead, the same games could be played on other surfaces e.g. a cylinder, a Moebius tape, a torus, a Klein bottle. While some of these surfaces can be physically constructed from a piece of flat material, others can be only modeled in a computer or on a flat board, if we define which sides should be imagined as glued together.
- For instance, to produce a cylinder (a) from a chess board, one has to glue A1 to H1, A2 to H2, etc., and A8 to H8. There is no necessity to actually do it, but the rules ought to be changed to take into account this imaginary gluing. This virtual gluing can be easily visualized on a computer. To produce a Moebius tape (b), one has to glue A1 to H8, A2 to H7, etc., and A8 to H1. For torus (c), one has to take a cylinder (a), and glue together A1 and A8, B1 and B8, etc., and H1 and H8. For Klein bottle (d) one has to take a cylinder (a), and glue together A1 and H8, B1 and G8, etc., and H1 and A8. This cannot be done in actual reality, but can be easily modeled on a computer or in the game rules.
- Board games such as “renju” or “five in line” can be played on such surfaces. The recommended minimal size of the surface for “five in line” is 6 by 8, which is very practical for cell phones or PDAs. Both torus and Klein bottle surfaces can be used to play this variant of ‘five in line’.
- A computer program, or a device (“apparatus”) can model any such game board surface and display it on the screen as if it were a flat surface with borders glued together according to the nature of the surface. If the board does not have boundaries, e.g. a torus or a Klein bottle or a projective plane, it can be panned or rotated on the screen, so that different cells move to the center of the screen. Moebius tape may be rotated on the screen only in one dimension (left-right).
-
- 1. http://en2.wikipedia.org/wiki/Klein_bottle
- 2. http://en2.wikipedia.org/wiki/Manifold
- 3. Rupert Matthews, “The Game Mania”, Silver Dolphin, 2002, ISBN 1571457070
- 4. http://boardgames.about.com/cs/historiesnr/
- 5. http://www.gamerz.net/pbmserv/renju.html
- 6. http://www.gamerz.net/pbmserv/gomoku.html
- 7. http://www.gamerz.net/pbmserv/pente.html
- 8. R. Curant, H. Robbins, I. Stewart, “What Is Mathematics”, Oxford University Press, 1996, ISBN: 0195105192571457070
Claims (10)
1. A method of playing board games on models of arbitrary compact two-dimensional manifolds.
2. The method according to claim 1 wherein the manifold is a cylinder.
3. The method according to claim 1 wherein the manifold is a Moebius tape.
4. The method according to claim 1 wherein the manifold is a torus surface.
5. The method according to claim 1 wherein the manifold is a Klein bottle.
6. The method according to claim 2 , 3 , 4, or 5 wherein the game is “renju” or “five-in-line”.
7. The method of rotating the board of methods 1 to 5 that places different board cells in the visible center of the board.
8. The computer program product implementing methods declared in claims 1 to 7 wherein the player plays with a computer.
9. The computer program product implementing methods declared in claim 6 wherein the game is played on two or more portable computing, gaming or communication devices communicating via a network.
10. A special device having a display and a processor, implementing the method of 6.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10/708,740 US20050212204A1 (en) | 2004-03-23 | 2004-03-23 | Method of playing board games on two-dimensional manifolds |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10/708,740 US20050212204A1 (en) | 2004-03-23 | 2004-03-23 | Method of playing board games on two-dimensional manifolds |
Publications (1)
Publication Number | Publication Date |
---|---|
US20050212204A1 true US20050212204A1 (en) | 2005-09-29 |
Family
ID=34988856
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US10/708,740 Abandoned US20050212204A1 (en) | 2004-03-23 | 2004-03-23 | Method of playing board games on two-dimensional manifolds |
Country Status (1)
Country | Link |
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US (1) | US20050212204A1 (en) |
Citations (13)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3359003A (en) * | 1965-05-05 | 1967-12-19 | Original Toy Corp | Game board for sheckers or chess having no side borders |
US3806126A (en) * | 1973-02-14 | 1974-04-23 | B Gilbert | Space station board game apparatus |
US4026557A (en) * | 1974-10-08 | 1977-05-31 | Lebrun Paul Antony Hammet | Board game apparatus |
US4384717A (en) * | 1981-11-12 | 1983-05-24 | Morris Daniel L | Mobius strip puzzle |
US4919427A (en) * | 1989-04-03 | 1990-04-24 | Itzhak Keidar | Moebius ring puzzle |
US5324037A (en) * | 1993-06-24 | 1994-06-28 | Greeson Ewell E | Mobius strip puzzle |
US5358252A (en) * | 1993-11-23 | 1994-10-25 | Mcphaul Alfred | Three-dimensional multi-tiered chess board |
US5687970A (en) * | 1996-07-03 | 1997-11-18 | Clark; William H. | Board game device |
US5871212A (en) * | 1997-06-16 | 1999-02-16 | Lee; Ki-Suk | Sectional chessboard |
US6231441B1 (en) * | 1996-11-01 | 2001-05-15 | Adar Golad | Computer game device |
US6260847B1 (en) * | 2000-02-15 | 2001-07-17 | Lawrence A Lueder | Oblique chessboard |
US6279907B1 (en) * | 1999-01-14 | 2001-08-28 | Marvin Douglas Hullinger | Spacial game board with spacial chess and spacial checkers |
US6595519B1 (en) * | 1999-11-30 | 2003-07-22 | Mcgoveran David O. | Dimensional puzzle |
-
2004
- 2004-03-23 US US10/708,740 patent/US20050212204A1/en not_active Abandoned
Patent Citations (13)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3359003A (en) * | 1965-05-05 | 1967-12-19 | Original Toy Corp | Game board for sheckers or chess having no side borders |
US3806126A (en) * | 1973-02-14 | 1974-04-23 | B Gilbert | Space station board game apparatus |
US4026557A (en) * | 1974-10-08 | 1977-05-31 | Lebrun Paul Antony Hammet | Board game apparatus |
US4384717A (en) * | 1981-11-12 | 1983-05-24 | Morris Daniel L | Mobius strip puzzle |
US4919427A (en) * | 1989-04-03 | 1990-04-24 | Itzhak Keidar | Moebius ring puzzle |
US5324037A (en) * | 1993-06-24 | 1994-06-28 | Greeson Ewell E | Mobius strip puzzle |
US5358252A (en) * | 1993-11-23 | 1994-10-25 | Mcphaul Alfred | Three-dimensional multi-tiered chess board |
US5687970A (en) * | 1996-07-03 | 1997-11-18 | Clark; William H. | Board game device |
US6231441B1 (en) * | 1996-11-01 | 2001-05-15 | Adar Golad | Computer game device |
US5871212A (en) * | 1997-06-16 | 1999-02-16 | Lee; Ki-Suk | Sectional chessboard |
US6279907B1 (en) * | 1999-01-14 | 2001-08-28 | Marvin Douglas Hullinger | Spacial game board with spacial chess and spacial checkers |
US6595519B1 (en) * | 1999-11-30 | 2003-07-22 | Mcgoveran David O. | Dimensional puzzle |
US6260847B1 (en) * | 2000-02-15 | 2001-07-17 | Lawrence A Lueder | Oblique chessboard |
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Legal Events
Date | Code | Title | Description |
---|---|---|---|
STCB | Information on status: application discontinuation |
Free format text: ABANDONED -- FAILURE TO RESPOND TO AN OFFICE ACTION |