JP2000247098A - Plane filling method utilizing repeated graphic pattern - Google Patents

Abstract

PROBLEM TO BE SOLVED: To merely manufacture one type of a tile having a predetermined design and to express various designs by filling a plane by using an isosceles trapezoidal shape having two other sides with a specific ratio value when a ratio of a lower bottom to an upper bottom falls within a specific range. SOLUTION: A plane is filled by using an isosceles trapezoidal shape having two other sides with a ratio of 2 when a ratio of a lower bottom to an upper bottom falls within a ratio of 1 to 3. Specifically, when nine repeating graphic pattern are constituted of a polygons 1 of repeating graphic pattern, the repeating graphic patterns 2 of a place of 9 can be set, and the same shape is repeated by combining the number of square of n (odd number of n>=3) of the patterns 1. For example, when the twelve patterns 1 are combined, a regular hexagonal shape can be formed. Tiles or sheets of the patterns 1 and 2 can be formed. As blank materials of the tile and the sheet, wood, paper, ceramics or the like can be used. The form can be used for a computer software for a game or a training material.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention can be used as decorative materials such as tiles, blocks and cloths such as walls, floors and passages, or as patterns on paper and cloth. In addition, it can be used as a puzzle toy that can be enjoyed by infants to the elderly, or as a teaching material such as computer software that can be enjoyed and learned in similar learning.

[0002]

2. Description of the Related Art When a polygon is divided into k congruent small polygons and the small polygon is similar to the original polygon, this polygon is called a k-th repetitive figure. . Polygons that fill a plane have a variety of uses as described above, but in general, it is necessary to combine two or more shapes to develop a variety of designs without using colors. Repetitive figures are suitable for expressing simple designs. Some polygons that become repetitive figures have the property of being parallelograms when combined with two other than the peculiarity of a pattern that includes the repetition of the shape by itself, which is the property of manufacturing tiles and sheets. Despite its high efficiency in construction and construction, other useful polygons and designs have been frequently used because its useful properties are not generally known.

[0003]

A repetitive figure having both a periodicity and an aperiodicity as a symbol is useful as described above, but few repetitive figures having a small value of k and having a high utility value have been known. . It is desirable to use a polygonal repetitive figure in which the value of k is as small as possible from the human visual field and the composition is highly valuable. From the relation between the similarity ratio and the area ratio, it is expected that there are k-th repetitive figures that are the square of k = n other than triangles and parallelograms, but n is an odd number of 3 or more. The k-th polygonal repetitive figure is rare,
Therefore, the uniqueness of the repetitive figure of the polygon as a pattern may be outstanding. If two repetitive figures are combined to form a parallelogram, the usefulness is further enhanced.

[0004]

SUMMARY OF THE INVENTION The present invention is a plane filling method using polygons which are highly useful polygons, each of which becomes a pair of parallelograms, and which is a repetitive figure of the 9th and 25th positions.

[0005]

DESCRIPTION OF THE PREFERRED EMBODIMENTS (1) of FIG. 1 is a polygon of a repetitive figure according to claim 1, a ninth-order repetitive figure as in (2), and (1) is a square of n (n) The same shape is repeated by combining. Combining 12 (1) results in a regular hexagon. (3) in FIG. 2 is the polygon of the repetitive figure in claim 3, which is the 25th-order repetitive figure as in (4), and combining (3) with n squares (n ≧ 5 odd numbers) Repeat the same shape with. Twelve combinations of (3) result in a regular triangle, and a combination of eight results in a regular hexagon. Also, as shown in FIGS. 3 and 4, (2) and (4)
A pattern having a three-dimensional structure can be expressed by the combination of.

[0006]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In carrying out the present invention, the following can be performed. Hereinafter, the present invention will be described with reference to FIGS. It can be used for tiles and sheets of the shapes (1) and (3). Further, the present invention can be used for sheets such as tiles and cloths having patterns as in (2) and (4). Other (2)
It can be used for a sheet such as a tile or a cloth having a combination of the patterns of (4) and (4). The material such as the tile and the sheet may be any material such as wood, paper, ceramic, glass, cloth, metal, and resin. In addition, the above-described tiles and sheets may be used with coloring. The designs of (2) and (4) can be used as computer software for games and educational materials.

[0007]

According to the present invention, for example, in the case of tiles, various patterns can be expressed simply by manufacturing one type of tile having the pattern of (1) or (3) or the pattern of (2) or (4). . Therefore, considering the ratio of the production cost to the value of the design, its value and practicality are high. Also, it can be used as cool teaching material or educational software for similar learning. We can learn while having fun from the puzzle nature.

[Brief description of the drawings]

FIG. 1 is a polygon (1) according to claim 1 of the present invention and a figure (2) indicating that it is a ninth-order repetitive figure.

FIG. 2 is a polygon (3) according to claim 2 of the present invention and a figure (4) indicating that it is a 25th-order repetitive figure.

FIG. 3 shows a pattern comprising a combination of polygons (2) according to claim 2 of the present invention.

FIG. 4 shows a pattern comprising a combination of polygons (4) according to claim 4 of the present invention.

[Description of Signs] (1) is a polygon in claim 1 (2) is a figure indicating that (1) in claim 1 is a repetitive figure (3) is a polygon in claim 3 (4) is a claim Figure showing that (3) in item 3 is a repetitive figure

Claims (6)

[Claims] 1. A plane filling method using an isosceles trapezoid in which the ratio of the upper base: lower base sides is 1: 3, and the remaining two sides are in a ratio of 2. 2. A plane filling method using a combination of figures similar to claim 1 comprising nine equal-shaped trapezoids in claim 1. 3. A plane filling method using a trapezoid in which the ratio of the upper base: lower base sides is 1: 5 and the remaining two sides are in the ratio of 8: 4√3. 4. A plane filling method using a combination of figures similar to claim 3 comprising 25 trapezoids in claim 3. 5. An isosceles trapezoid having an upper base: lower base ratio of 1: 3 and the remaining two sides having a ratio of 2 is a core, and an isosceles trapezoid congruent with the core is disposed therearound. And n squares (n
(Odd number of ≧ 3) congruent isosceles trapezoid, planar filling method using figures similar to nuclei. 6. A trapezoid having an upper base: lower base side ratio of 1: 5 and the remaining two sides having a ratio of 8: 4√3, and an isosceles contiguous with the core adjacent thereto. A plane filling method using a figure similar to a nucleus, in which trapezoids are arranged and a total of n square (n ≧ 5 odd number) congruent trapezoids are arranged.