Triangular jointed board

Abstract

The invention relates to a triangular jointed board which is a newly created jointed board toy and has the functions of a toy, a learning tool, a teaching aid and a research tool. The theoretical support behind the triangular jointed board is the application of the ternary number, the triangular jointed board is used as a research tool, the application research of the ternary number in a number array can be carried out, and the perfect combination relation research of the number and the shape can be carried out.

Description

Technical Field

[0001] The triangular puzzle is a puzzle toy that has the functions of a toy, a learning tool, and a teaching aid. The triangular puzzle is first of all a new puzzle toy, and secondly, it can be used to deeply explore the mathematical theory contained in it - ternary numbers. Background Art

[0002] The combination of numbers and graphics creates a special mathematical beauty.

[0003] A triangle has three sides. When the ternary numbers 0, 1, and 2 are assigned to each side, a total of 27 different triangles can be designed. Then, several sets of splicing rules can be designed to study the relationship between puzzles and number arrays. Jigsaw puzzles have value in mathematical research.

[0004] A triangle has three sides. When balanced ternary numbers 0, 1, and -1 are assigned to them respectively, a total of 27 different triangles can be designed. The three sides can be matched with flat, convex, and concave shapes. The puzzle rules are simple, there are only two: flat to flat, convex to concave. Summary of the invention

[0005] 1. Let’s define some concepts first.

[0006] (1) Triangular puzzle pieces refer to movable puzzle pieces, which have a total of 27 different triangular puzzle pieces in the shape of isosceles triangles or equilateral triangles, with or without concave and convex edges.

[0007] (2) Concave-convex triangular puzzle refers to a triangular puzzle with concave-convex design on the edges of movable puzzle pieces.

[0008] (3) The puzzle plate is a designated area where movable puzzle pieces can be placed according to the puzzle rules. The puzzle plate is a triangular puzzle with edge restrictions added to increase the difficulty of the puzzle. You can design a triangular puzzle plate that can fit exactly 25 puzzle pieces, a hexagonal puzzle plate that can fit exactly 24 puzzle pieces, or a diamond puzzle plate that can fit exactly 25 puzzle pieces.

[0009] (4) The coding of the triangle sides refers to the numbers on the digits when counting in the ternary number system. There are three types: 0, 1, and 2. They are used to mark the characteristics of each side of the triangular puzzle.

[0010] (5) Triangular mosaic coding refers to the coding that is compiled using the ternary rule based on the concave and convex characteristics of the three sides, using three digits to represent the digital values ​​of the three sides in sequence.

[0011] (6) Coding type: One type is standard ternary coding, which uses the numbers 0, 1, and 2 to encode. The coding length is 3 bits, the first bit value is 9, the second bit value is 3, and the third bit value is 1. For example: The decimal value of code 102 = 9×1+3×0+1×2=11

[0012] 2. Further clarify the specific design of the triangular puzzle.

[0013] The first triangular puzzle: The puzzle triangle is designed as an equilateral triangle with three flat sides. The three sides are marked with corresponding ternary numbers 0, 1, and 2. The basic splicing rules are: the sides of every two puzzle boards are numbered, 1 and 2 can be spliced, 0 and 0 can be spliced, waists and waists can be spliced, and bottoms and bottoms can be spliced. To prevent the waist and bottom edges from being spliced ​​together, an upward sign needs to be marked on the puzzle board as a reminder.

[0014] The second type of triangular puzzle: The puzzle triangle is designed as an isosceles triangle with a length ratio of 5:5:6. The three sides are flat, and the triangle is divided into three parts by connecting the intersection of the angle bisectors to the three vertices. These three parts correspond to the ternary numbers 0, 1, and 2 in three patterns. The basic splicing rule is: the sides of every two puzzle pieces can be spliced ​​according to the patterns corresponding to the numbers 1 and 2, 0 and 0 can be spliced, waists can be spliced, and bases can be spliced.

[0015] The third triangular puzzle: The puzzle triangle is designed as an isosceles triangle with a length ratio of 5:5:6. The three sides of the triangle are designed to be flat, convex or concave. The ternary codes corresponding to the marked edges on the triangular puzzle are: 000, 001, 002, 010, 011, 012, 020, 021, 022, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222.

[0016] The fourth triangular puzzle: The puzzle triangle is designed as an isosceles triangle with a length ratio of 5:5:6. The three sides of the triangle are designed in one of three shapes: flat, convex or concave. The decimal codes corresponding to the balanced ternary codes corresponding to the marks on the triangular puzzle are: 0, 1, -1, 3, 4, 2, -3, -2, -4, 9, 10, 8, 12, 13, 11, 6, 7, 5, -9, -8, -10, -6, -5, -7, -12, -11, -13.

[0017] The fifth triangular puzzle: The puzzle triangle is designed as an isosceles triangle with a length ratio of 5:5:6. The three sides of the triangle are designed to be flat, convex or concave. There is no triangular puzzle code on the triangular puzzle.

[0018] The sixth triangular puzzle: is the online version of the triangular puzzle. The puzzle triangle is designed as an equilateral triangle, and the three sides of the triangle are designed in one of three shapes: flat, convex or concave. There is no marking code on the triangular puzzle. DETAILED DESCRIPTION 1. Make solid triangular puzzle products.

[0020] The material can be cardboard, wood, plastic board, etc. According to the design scheme of the aforementioned "Invention Content", a specific physical product can be made. Magnetic materials can also be added to make a magnetic triangular puzzle board, which is convenient for operation and makes it difficult to lose the puzzle board parts.

[0021] The first type: The puzzle board is an equilateral triangle, with a total of 27 pieces. The side of each triangle is marked with a number 0, 1, or 2. The 27 triangles have different codes, and each puzzle board is marked with a striking upward sign.

[0022] The second type: The puzzle board is an isosceles triangle with a length ratio of 5:5:6. The intersection of the angle bisectors is connected to the three vertices to divide the triangle into three parts. Three patterns are designed for these three parts. The pattern design should take into account the effect after splicing. The corresponding numbers 0 and 0 of the sides are connected, and a complete pattern can be divided into two parts, and these two parts are the same, that is, the original pattern is symmetrical. The corresponding numbers 1 and 2 of the sides are connected, and a complete pattern can be divided into two parts. When the 1 of one puzzle board and the 2 of another puzzle board are spliced ​​together, the complete pattern is presented. There are 27 triangular puzzle boards of different shapes.

[0023] The third version: The panels are isosceles triangles with a length ratio of 5:5:6. The three sides of the triangle are designed to be flat (0), convex (1) or concave (2). There are 27 triangular panels with different shapes. The ternary codes corresponding to the edges marked on the triangular panels according to the concave and convex conditions are: 000, 001, 002, 010, 011, 012, 020, 021, 022, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222.

[0024] The fourth model: The puzzle board is an isosceles triangle with a length ratio of 5:5:6. The three sides of the triangle are designed in one of three shapes: flat (0), convex (1) or concave (-1). There are 27 triangular puzzle boards of different shapes. The decimal codes corresponding to the balanced ternary codes corresponding to the concave and convex marks on the triangular puzzle boards are: 0, 1, -1, 3, 4, 2, -3, -2, -4, 9, 10, 8, 12, 13, 11, 6, 7, 5, -9, -8, -10, -6, -5, -7, -12, -11, -13.

[0025] The fifth type: the panel is an isosceles triangle with a length ratio of 5:5:6. The three sides of the triangle are designed to be flat, convex or concave. There is no triangle panel code on the triangular panel.

[0026] Design and use of platters. All of the above products can be paired with platters. The use of platters is to limit the edge effect and overall pattern after the puzzle pieces are joined. The following platters are made for use. For the design of the platter, a spare plate is designed to place the triangular puzzle pieces to be put into the platter.

[0027] (1) Triangular platter. The most natural platter for a triangular puzzle is a large triangle. The number of puzzle pieces that can be placed in a large triangle, which is closest to the total number of 27 triangular puzzle pieces, is 25.

[0028] (2) Diamond-shaped platter: The number of triangular tiles that is closest to the total number of triangular tiles, 27, is 25.

[0029] (3) Hexagonal platter: The number of triangular tiles that is closest to the total number of triangular tiles, 27, is 24.

[0030] 2. Make network triangle puzzle products.

[0031] The triangular puzzle of the online version can be designed as an equilateral triangle, and the three sides of the triangle are designed to be one of the three shapes of flat, convex or concave. There is no marking code on the triangular puzzle. There are 27 movable triangular puzzles in total, and a triangular puzzle plate that can hold 25 triangular puzzles. The operation is to move the triangular puzzles, put them into the puzzle plate, and fill the puzzle plate according to the splicing rules (no overlap and no space). The placement direction of the triangular puzzle is limited to upright and inverted placement, so the software design gives each movable puzzle a control point. Drag the operation to rotate the puzzle plate 180 degrees to become an inverted triangular puzzle. In addition, add a button to restore the initial state for quick reset, and add one or more step-by-step demonstration buttons for convenient teaching demonstration.

[0032] 3. Use triangular puzzles to conduct mathematical research.

[0033] Because there is a mathematical theory behind the triangular puzzle - the support of ternary system, the triangular puzzle can be used to do mathematical research in related fields such as ternary numbers, number arrays, numbers and shapes, etc.

Claims

1. Triangle puzzle is a kind of puzzle toy, including physical toy and online version, which has the functions of toy, learning tool and teaching aid.

2. Triangle puzzle, including 27 different movable triangle puzzles and a puzzle plate.

3. Each triangular puzzle piece has different values ​​for its three sides according to the ternary number. The normal ternary values ​​are 0, 1, and 2, and the balanced ternary values ​​are 0, 1, and -1.

4. The shapes of triangular panels include regular triangles and isosceles triangles. The structures of triangular panels include flat edges and concave-convex edges.

5. Triangular puzzle physical toys. This patent defines five styles: one is an equilateral triangle with a flat edge structure, and the other four are isosceles triangles with concave and convex edges. Among these five styles, one has no code indicating the triangle edge, two have codes indicating the triangle edge, and two have codes indicating the triangle puzzle.

6. The first coding scheme for the triangular puzzle is to assign values ​​to the three sides of the triangular puzzle in the order of bottom side, upper right side, and upper left side, and compile them into ternary codes 000, 001, 002, 010, 011, 012, 020, 021, 022, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, etc. 27 codes.

7. The second triangular puzzle coding scheme is to assign values ​​to the three sides of the triangular puzzle in the order of bottom side, upper right side, and upper left side, compile them into a balanced ternary code, and then convert them into the corresponding decimal code, which is: 0, 1, -1, 3, 4, 2, -3, -2, -4, 9, 10, 8, 12, 13, 11, 6, 7, 5, -9, -8, -10, -6, -5, -7, -12, -11, -13.

8. Platter. Based on the characteristics of the triangular puzzle pieces, this patent defines four platter shapes: an equilateral triangle platter, a regular hexagonal platter, a diamond platter, and another hexagonal platter. The equilateral triangle platter can hold 25 triangular puzzle pieces, the regular hexagonal platter can hold 24 triangular puzzle pieces, the diamond platter can hold 18 triangular puzzle pieces, and the other hexagonal platter can just hold all 27 triangular puzzle pieces.