ES2288059B1 - TABLE SET BASED ON GEOMETRIC PROPERTIES. - Google Patents

Abstract

Board game based on geometric properties formed by a plurality of tiles that are the same in shape and size but of a different color. These tokens overlap on turning axes, allowing the construction of geometric structures according to some basic rules of the game. Its use as an educational game allows to treat mathematical concepts of different levels: trigonometry, Thales' theorem, combinatorics, geometric structures, Euler's characteristic and related graphs.

Description

Property based board game geometric

Technical sector

Board game wit, strategy and educational.

State of the art

Wit board games are currently known and strategy that are formed by pieces that result from the Different combinations of elements. Such is the case of dominoes, in which the chips result from the possible combinations of two numbers from zero to six. Also the way to join two chips follow a well-known game rule that is to match one of the numbers on each tab.

There are also construction games geometric shapes in which different pieces come together or fit together to conform different structures in the plane or in space. In games known as Meccano or Multihobby there are chips different shapes and sizes that joined by screws or embedded with different possibilities allow the user the construction of models, models or various structures.

There are also games in which from certain specific tabs, the user must rebuild a certain figure, as is the case with some types of puzzles, in which the contact between the tiles is determined by the shape of its edges or by the part of the final composition represents.

Object of the invention

The present invention relates to a set of table of ingenuity, strategy and education, being formed by a plurality of tiles equal in shape and size but of different color. These tokens overlap on turning axes, allowing the construction of geometric structures according to some basic rules of game. The game can be used as a solitaire or as a game desktop for two or three players.

Its use as an educational game allows treat mathematical concepts of different levels: trigonometry, Thales theorem, combinatorial, geometric structures, Euler characteristic and related graphs.

Summary of the Invention

The game consists of eighteen equal tiles in shape and size but of different color, formed from the possible combinations of three colors, each tab being composed of three equal circles aligned and linked together by segments of the same length as the diameter. Two tokens join the superimpose a circle of one with another of the same color of the another, being able to contact in only one of its circles, that is, no being able to overlap or contact their respective segments. He game also includes some additional pieces, with which determines the overlap of two or more tiles, acting as axes of  turn.

Detailed description of the invention

The proposed game refers to the construction of a related geometric structure in the plane from tabs trying to minimize the number of visible circles. Are distinguished two types of cards, Type "A" and Type "B".

All "A" tokens (Figure 1) are the same in shape and size: they are formed by three circular elements same or polygon-shaped aligned and linked together by two segments of the same length as the diameter of the elements circular or the diameter of the circumference circumscribed in the case of using regular polygon shapes. In the center of each of said elements is a hole with diameter enough to be able to enter through the cylinder or pivot of the "B" chips.

The circular or polygonal elements of the "A" tokens are distinguished using colors, patterns or textures different (Figure 2). All the cards are different in terms of combination of these elements: they are formed from the possible combinations of different elements. In figure 7 it show as an example the eighteen cards resulting from choosing 3 colors, which are represented by white, black and striped patterns, and "A" tokens composed of 3 circular elements and two segments

The "B" tokens are formed from a circular or regular polygon shaped element (base) and a pivot, substantially cylindrical, stuck in the center of the base perpendicular to it (Figure 3).

The overlap of several tabs is done inserting the holes of the "A" pieces in the pieces "B", in the form shown in Figure 4. The "B" tabs they are supported on their base, leaving their perpendicular axis free and without being fixed to the surface, allowing total mobility of translation and rotation of the geometric structure and the chips that compose it.

The material on which the chips must have a minimum thickness so that they are not lost geometric properties by overlapping several tiles on the same axis. Simple calculations show that, for the 18-chip game, no more than twelve circles may overlap on the same axis. This fact should be considered to determine the dimensions of the axes.

Following the essence of the game and with them rules of union of the cards, can be made different Versions regarding the number of colors used:

- If two colors, patterns or textures are used and the tiles are composed of two equal aligned circles and joined by a segment of equal length to the diameter, they are obtained Three possible chips. The geometric structure with the lowest number of visible circles regardless of color consists of three visible circles, but it is not possible to get it taking into Count the color of the circles. In this case the structure Geometric with fewer visible circles has four.

- If three colors, patterns or textures are used and the tiles are composed of three equal circles aligned and joined by two segments of equal length to the diameter, they are obtained eighteen different cards, which allows the formation of Multiple geometric structures

- If four colors, patterns or textures and tokens are composed of four equal circles aligned and joined by three segments of equal length to diameter, one hundred and thirty six different chips are obtained, which It enables the formation of multiple geometric structures.

- In general it could be determined by mathematical formulas the number of tokens of each variant depending on the number of colors and the number of circles that make up the chips, as well as the smallest number of visible circles of the geometric structure regardless of color. Without however we consider that three is the most appropriate number for your manipulation and strategy approach.

The model, within its essentiality, can be carried out in other embodiments. May be built in any shape and size with the most materials adequate, as long as they do not involve an alteration of mathematical properties and the essentiality of the game.

Example: Preferred embodiment

A way in which the game can be performed proposed is as follows:

The game consists of eighteen chips "A" and "B" tokens in a maximum amount of fifty and four.

The chips are formed by three circles equal aligned and joined by two segments of equal length to the diameters In the center of each circle is a hole of appropriate size to be inserted in the tabs "B".

These files must be of identical dimensions and non-deformable, in addition to being built on a material of minimum thickness Plasticized cardboard has been used to such effect.

Each record must be different as soon as the color combination If for example three colors N, B are used and G the eighteen cards would be determined with the following Nomenclature: NNN, NNG, NNB, NGN, NGG, NGB, NBN, NBG, NBB, GNG, GNB, GGG, GGB, GBG, GBB, BNB, BGB, BBB (Figure 7).

The "B" pieces consist of a flat base on which a perpendicular axis rests on which can insert the holes of the circles of the cards. The pivot length of the "B" tab should allow about twelve "A" tokens can be inserted into it and the material must be Appropriate for handling. For example wood.

The thickness of the segments should allow the tokens are consistent, but do not interfere in the unions of the chips. As an illustrative example of embodiment, and not having to be one of the geometric structures with the least number of visible circles, we present figure 7.

The rule to join the chips is the next:

Two tokens are joined by superimposing a single circle of one with another single circle of the same color of the other. That is, the segments cannot overlap or contact with circles or with other segments. You can see some Correct union examples in Figure 5.

The spirit of the game, therefore consists of develop a strategy to arrange tokens so that the desired objective is met, that is, determine a structure flat geometric in which there is the greatest number of overlaps Between your chips.

The game as solitaire consists in forming a flat and connected geometric structure in which they are placed all the tabs and in which the number of visible circles is the as little as possible When two or more circles are inserted in the same axis, only one of them is counted as a visible circle. This allows to translate the objective of the game in using the minor number of axes for its construction, taking into account that all the circles of the geometric structure must be inserted in A shaft It is also equivalent to a greater number of overlaps between the tiles get a geometric structure with less number of visible circles.

Although the goal of the game as a loner is not is to get a specific number of visible circles, some calculations concerning related graphs and the Euler characteristic, we challenge to get a geometric structure of approximately Nineteen visible circles. This structure is the one with the lowest number of visible circles that are achieved regardless of color of the circles, which implies that when considering the color it is greater than or equal to nineteen the least number of circles visible.

Once the geometric structure is made, to check that the standards have been met, it is a requirement indispensable that the thirty are visible and without intersections and six segments that determine it.

In the board game for two or three players you distribute all the cards in equal amounts, each player not knowing the other's chips. A order of play and each player places a chip on each turn, trying to make the greatest number of overlaps with the chips that have been placed on the table. For every circle that overlaps, the corresponding player is adding a point, winning the game on That has achieved the highest score.

A variant of the board game for two or three players is to determine a score before each game different for overlaps of each color, for example: a point the black overlaps, two points for the gray ones and three points for whites. At the end of the game the player who wins has obtained the highest score.

Brief description of the illustrations

In order to complement the description that accompanied, by way of illustration and not limitation, the following figures:

Figure 1.- Shows a composite "A" tab by three equal circles aligned and joined by equal segments length to diameter In the center of each circle is a hole of appropriate size to be inserted in the axes

Figure 2.- Tab in which the circles are represented in different color, pointing to one of the eighteen combinations The segments are delimited on both sides by two dashed lines, which point the edges for a possible building.

Figure 3.- Illustratively shows the file "B", formed of a support base and a perpendicular axis.

Figure 4.- Tab overlap mode "A" and "B".

Figure 5.- Example of the same "B" tab It can be overlapped with several "A" tabs.

Figure number 6.- Shows the realization of a flat and related geometric structure constructed from the eighteen chips. In this example, the geometric structure is made with 22 visible circles (7 black, 7 white and 8 gray) In it you can see that the thirty-six segments they do not produce intersections, and that there are overlaps with Different number of circles.

Figure 7.- Shows as an example the eighteen different cards that are obtained when considering combinations of three colors; in this case black, white and striped.

Claims (11)

1. Board game comprising "A" chips composed of three or more circular elements, with a central hole, equal aligned and joined together, as observed in figure 1, by segments of the same length as the diameter of the circle, equal in shape and size, in which the circular elements are distinguished by colors, patterns or textures and the combination of colors, patterns or textures is different for each card and "B" cards (figure 3) formed by a base and a pivot of substantially cylindrical shape perpendicular to the base and whose diameter is smaller than the diameter of the holes of the circular elements of the "A" pieces, so that the "A" tabs fit the pivot, you can determine the overlap two or more "A" tiles and act as pivot axes (Figure 4). 2. Board game comprising "A" chips composed of three or more dodecagon shaped elements equal, with a central hole, aligned and joined together, as seen in figure 1, by segments of equal length that the diameter of the circumference circumscribed to the dodecagon, equal in shape and size, in which the polygonal elements are distinguished by colors, patterns or textures and the combination of colors, patterns or textures is different for each tab and chips "B" (figure 3) formed by a base and a pivot shaped substantially cylindrical, perpendicular to the base whose diameter is smaller than that of the holes in the "A" tabs, so that the "A" tabs fit the pivot, you can determine the overlapping two or more "A" pieces and acting as axes of turn (Figure 4). 3. Board game comprising "A" chips composed of three or more elements with a regular polygon shape, with a central hole, aligned and joined together, as observed in figure 1, by segments of the same length as the circumscribed circumference diameter, equal in shape and size, in which the polygonal elements are distinguished by colors, patterns or textures and the combination of colors, patterns or textures are different for each card and "B" cards (figure 3) formed by a base and a pivot of substantially cylindrical shape, perpendicular to the base whose diameter is smaller than that of the holes of the "A" tabs, so that the "A" tabs fit the pivot, the overlap of two or more chips "A" and act as axes of rotation (Figure 4). 4. Set according to the preceding claims, characterized in that the pieces "B" can be supported on their base, leaving their perpendicular axis free and without being fixed to the surface in such a way as to allow a total mobility of translation and rotation of the structures that leave forming by combination of cards "A" and "B" and the cards that compose it. 5. Board game according to previous claims, characterized in that the thickness of the "A" pieces allows to superimpose pieces in a non-parallel way. 6. Board game according to claims 1 to 4, characterized in that the thickness of the chips "A" is between 0.01 mm and 1 mm, allowing non-parallel pieces to be superimposed. 7. Board game according to claims 1 to 4, characterized in that the thickness of the "A" pieces allows pieces to be superimposed so that they remain parallel to the plane. 8. Board game according to claims 1 to 4, characterized in that the thickness of the chips "A" is between 0.1 mm and 3 mm, allowing pieces to be superimposed so that they remain parallel to the plane. 9. Board game according to previous claims characterized in that the cylinder or pivot the "B" tab has a height sufficient to be able to overlap 12 "A" tiles. 10. Board game, according to previous claims, characterized in that it consists of eighteen "A" tiles composed of 3 elements with a circular or polygonal shape, 2 segments and which are distinguished by applying all possible combinations of 3 color patterns or textures, and between 18 and 54 "B" tokens. 11. Board game, according to claims 1 to 9, characterized in that it consists of 136 "A" pieces composed of 4 elements with a circular or polygonal shape, 3 segments and which are distinguished by applying all possible combinations of 4 colors, patterns or textures, and between 136 and 544 "B" pieces.