Regular polyhedron mathematical building block teaching aid

Abstract

The utility model relates to a regular polyhedron mathematics building block teaching aid, which comprises at least four balls and at least six connecting rods, 12 positioning holes are uniformly distributed on each ball, each connecting rod comprises an inserting concave rod and an inserting convex rod, one end of each inserting concave rod is provided with a concave part, one end of each inserting convex rod is provided with a convex part matched with the concave part, and the inserting convex rod is provided with a convex part matched with the convex part. Arc-shaped parts are arranged at the other ends of the insertion concave rod and the insertion convex rod, the length of each arc-shaped part is smaller than the distance between every two adjacent positioning holes, and convex columns used for being inserted into the positioning holes are arranged at the tail ends of the arc-shaped parts. According to the teaching aid, teaching models such as a regular tetrahedron are formed through splicing, and the mathematical space cognition of children on the regular polyhedron can be improved.

Description

Technical Field

[0001] The utility model relates to a regular polyhedron mathematical building block teaching aid. Background Art

[0002] When teaching the mathematics of regular polyhedrons, children's spatial imagination is usually weak, which makes their mathematical spatial cognition of regular polyhedrons usually poor. This is not conducive to children's enlightenment of spatial solid geometry, as well as the comparison and thinking of the spatial angles of regular polyhedrons, and is not conducive to learning the mathematical concepts of regular polyhedrons.

[0003] If a teaching aid that is easy to assemble to form a regular polyhedron can be provided, it will help children learn the mathematical concepts of regular polyhedrons during the construction process and improve children's mathematical spatial cognition of various regular polyhedrons. Utility Model Content

[0004] The utility model aims to provide a regular polyhedron mathematical building block teaching aid, which can form teaching models such as regular tetrahedrons by assembling them, thereby helping to improve children's mathematical spatial cognition of regular polyhedrons.

[0005] The technical solution of the utility model is: a regular polyhedron mathematical building block teaching aid, comprising at least four spheres and at least six connecting rods, wherein 12 positioning holes are evenly distributed on the spheres, and the connecting rods comprise plug-in concave rods and plug-in convex rods, wherein one end of the plug-in concave rod is provided with a concave portion, and one end of the plug-in convex rod is provided with a convex portion matching the concave portion, and the other ends of the plug-in concave rod and the plug-in convex rod are both provided with an arc portion, the length of the arc portion is less than the distance between two adjacent positioning holes, and the end of the arc portion is provided with a convex column for inserting into the positioning hole.

[0006] Furthermore, the angle between the axis of the convex column and the axis of the plug-in concave rod or the plug-in convex rod is 45°.

[0007] Furthermore, the sphere is provided with a first annular groove line, a second annular groove line, a third annular groove line, and a fourth annular groove line which forms an angle with the third annular groove line, which are parallel to each other, from top to bottom. Three positioning holes are evenly distributed along the first annular groove line on the sphere, three positioning holes are evenly distributed along the third annular groove line on the sphere, and five positioning holes are evenly distributed along the fourth annular groove line on the sphere.

[0008] Furthermore, each positioning hole on the third annular groove line is located on a symmetry line between two adjacent positioning holes on the first annular groove line; and one of the positioning holes on the fourth annular groove line coincides with one of the positioning holes on the third annular groove line.

[0009] Furthermore, the angle between the plane where the fourth annular groove line is located and the plane where the third annular groove line is located is 37°.

[0010] Furthermore, the radius ratio between the first annular groove line and the sphere is 1:1.7~1.8; the radius ratio between the first annular groove line and the second annular groove line is 1:1.4~1.5; the radius ratio between the first annular groove line and the third annular groove line is 1:1.6~1.7; the radius ratio between the fourth annular groove line and the first annular groove line is 1:1.45~1.55.

[0011] Compared with the prior art, the utility model has the following advantages:

[0012] 1. The building blocks composed of spheres and connecting rods can help to build regular tetrahedrons, regular hexahedrons, regular dodecahedrons, and regular icosahedrons. It is convenient to solve children's mathematical spatial cognition of various regular polyhedrons. It can not only be used for mathematics teaching, but also can be used as an enlightenment toy of spatial solid geometry, allowing users to freely play a variety of shapes.

[0013] 2. The accessories are simple. Four types of regular polyhedrons can be built using only a 12-hole ball and a rod that can be connected and selected from each other.

[0014] 3. Rich in mathematical principles, it condenses the data of all regular polyhedrons (four in total) onto a sphere, which triggers people to compare and think about the spatial angles of regular polyhedrons, and helps to learn a lot of mathematical concepts of regular polyhedrons during the construction process. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 The spherical structure of the utility model is shown in FIG. Figure 1 ;

[0016] Figure 2 The spherical structure of the utility model is shown in FIG. Figure 2 ;

[0017] Figure 3 The spherical structure of the utility model is shown in FIG. Figure 3 ;

[0018] Figure 4 It is a structural schematic diagram of the connecting rod of the utility model;

[0019] Figure 5 It is a structural schematic diagram of the plug-in concave rod of the utility model;

[0020] Figure 6 It is a structural schematic diagram of the plug-in convex rod of the utility model;

[0021] Figure 7 It is a schematic structural diagram of a regular tetrahedron assembled according to the utility model;

[0022] Figure 8It is a schematic structural diagram of a regular hexahedron assembled according to the utility model;

[0023] Fig. 9 It is a structural schematic diagram of the assembled regular dodecahedron of the utility model;

[0024] Fig.10 It is a schematic structural diagram of the assembled regular icosahedron of the utility model;

[0025] Fig.11 It is a schematic diagram of the coordination between the vertices of the regular dodecahedron and the sphere of the utility model;

[0026] Fig.12 is the height circle position of the vertex of the regular dodecahedron of the utility model on the sphere;

[0027] Fig.13 It is a schematic diagram of the vertex corners of the regular dodecahedron of the utility model;

[0028] Fig.14 The size of the height circle corresponding to the corners of the regular dodecahedron of the utility model;

[0029] Fig.15 It is a schematic diagram of the projection of the height circle of the regular dodecahedron of the utility model onto a sphere;

[0030] Fig.16 It is a schematic diagram for obtaining the height circle size of the regular tetrahedron of the utility model;

[0031] Fig.17 It is a schematic diagram for obtaining the height circle size of the regular hexahedron of the utility model;

[0032] Fig.18 It is a schematic diagram for obtaining the height circle size of the regular dodecahedron of the utility model;

[0033] Fig.19 A schematic diagram for obtaining the height circle size of a regular icosahedron of the utility model;

[0034] In the figure: 10 - sphere 11 - positioning hole 12 - first annular wire groove 13 - second annular wire groove 14 - third annular wire groove 15 - fourth annular wire groove 16 - included angle 20 - connecting rod 21 - plug-in concave rod 22 - plug-in convex rod 23 - concave part 24 - convex part 25 - arc part 26 - convex column 27 - included angle. DETAILED DESCRIPTION

[0035] In order to make the above features and advantages of the present invention more understandable, embodiments are given below with reference to the accompanying drawings for detailed description, but the present invention is not limited thereto.

[0036] refer to Figures 1 to 10

[0037] A regular polyhedron mathematical building block teaching aid comprises at least four spheres 10 and at least six connecting rods 20, wherein 12 positioning holes 11 are evenly distributed on the spheres, and the distance between any two adjacent positioning holes is equal; the connecting rod comprises a plug-in concave rod 21 and a plug-in convex rod 22, wherein one end of the plug-in concave rod is provided with a concave portion 23, and one end of the plug-in convex rod is provided with a convex portion 24 matched with the concave portion, and the other ends of the plug-in concave rod and the plug-in convex rod are both provided with an arc portion 25, the length of the arc portion is less than the distance between two adjacent positioning holes, and the end of the arc portion is provided with a convex column 26 for inserting into the positioning hole, which can rotate after being inserted into the positioning hole, and the plug-in concave rod and the plug-in convex rod are assembled to form a connecting rod so that the connecting rod can rotate around the plug-in position.

[0038] In this embodiment, the angle 27 between the axis of the protruding column and the axis of the plug-in concave rod or plug-in protruding rod is 45°, so that after the protruding column is inserted into the positioning hole, the axis of the connecting rod is perpendicular to the normal of the sphere. A reinforcing rib is provided on the arc portion.

[0039] In this embodiment, the sphere is provided with a first annular groove line 12, a second annular groove line 13, a third annular groove line 14, and a fourth annular groove line 15 which forms an angle 16 with the third annular groove line, which are parallel to each other. The sphere is provided with three positioning holes evenly distributed along the first annular groove line, three positioning holes evenly distributed along the third annular groove line, and five positioning holes evenly distributed along the fourth annular groove line. Each positioning hole on the third annular groove line is located on the symmetry line of two adjacent positioning holes on the first annular groove line; one of the positioning holes on the fourth annular groove line coincides with one of the positioning holes on the third annular groove line. One of the remaining two positioning holes is located on the bottom surface of the sphere ( Figure 1 Directly below ), another locating hole that coincides with is located above the orthographic projection of ( Figure 1 ).

[0040] The first annular groove line is used when assembling a regular tetrahedron, the second annular groove line is used when assembling a regular hexahedron, the third annular groove line is used when assembling a regular dodecahedron, and the fourth annular groove line is used when assembling a regular icosahedron.

[0041] In this embodiment, the included angle 16 between the plane where the fourth annular groove line is located and the plane where the third annular groove line is located is 37°.

[0042] In this embodiment, the sphere may be a hollow sphere, and the sphere and the connection may be made of plastic or metal.

[0043] In this embodiment, the radius ratio between the first annular groove line and the sphere is 1:1.7~1.8, specifically 1:1.76. The radius ratio between the first annular groove line and the second annular groove line is 1:1.4~1.5, specifically 1:1.44. The radius ratio between the first annular groove line and the third annular groove line is 1:1.6~1.7, specifically 1:1.65. The radius ratio between the fourth annular groove line and the first annular groove line is 1:1.45~1.55, specifically 1:1.49.

[0044] When assembling a regular tetrahedron, four spheres 10 and six connecting rods 20 are used. First, assemble the plug-in concave rod 21 and the plug-in convex rod 22 into the connecting rod 20, insert the convex column 26 at one end of the connecting rod 20 into the positioning hole 11 on the first annular groove 12, and insert the connecting rod 20 into the three positioning holes 11 on the first annular groove 12, and then rotate the connecting rod 20 so that the rod axis of the connecting rod 20 falls on the first annular groove 12; the other end of the connecting rod 20 is connected to the positioning hole 11 on the first annular groove 12 of another sphere 10, thereby forming a regular tetrahedron. When assembling, the position of the axis of the connecting rod 20 on the first annular groove 12 may have a slight deviation (slight adjustment). See Figure 7 .

[0045] When assembling a regular hexahedron, eight spheres 10 and twelve connecting rods 20 are used. Insert the boss 26 at one end of the connecting rod 20 into the positioning hole 11 on the first annular groove 12, and insert the connecting rod 20 into the three positioning holes 11 on the first annular groove 12. Then rotate the connecting rod 20 so that the axis of the connecting rod 20 falls on the second annular groove 13; the other end of the connecting rod 20 is connected to the positioning hole 11 on the first annular groove 12 of another sphere 10, and the axis of the connecting rod 20 also falls on the second annular groove 13, thereby forming a regular hexahedron. When assembling, the position of the axis of the connecting rod 20 on the second annular groove 13 may have a slight deviation (slight adjustment). See Figure 8 .

[0046] When assembling a regular dodecahedron, 20 spheres 10 and 30 connecting rods 20 are used. Insert the boss 26 at one end of the connecting rod 20 into the positioning hole 11 on the first annular groove 12, and insert the connecting rod 20 into the three positioning holes 11 on the first annular groove 12. Then rotate the connecting rod 20 so that the rod axis of the connecting rod 20 falls on the third annular groove 14; the other end of the connecting rod 20 is connected to the positioning hole 11 on the first annular groove 12 of another sphere 10, and the rod axis of the connecting rod 20 also falls on the third annular groove 14, thereby forming a regular dodecahedron. When assembling, the position of the axis of the connecting rod 20 on the third annular groove 14 may have a slight deviation (slight adjustment). See Fig. 9 .

[0047] When assembling a regular icosahedron, 12 spheres 10 and 30 connecting rods 20 are used. Insert the boss 26 at one end of the connecting rod 20 into the positioning hole 11 on the fourth annular groove 12, and insert the connecting rod 20 into the five positioning holes 11 on the fourth annular groove 15. Then rotate the connecting rod 20 so that the axis of the connecting rod 20 falls on the fourth annular groove 15; the other end of the connecting rod 20 is connected to the positioning hole 11 on the fourth annular groove 15 of another sphere 10, and the axis of the connecting rod 20 also falls on the fourth annular groove 15, thereby forming a regular icosahedron. When assembling, the position of the axis of the connecting rod 20 on the fourth annular groove 15 may have a slight deviation (slight adjustment). See Fig.10 .

[0048] Design method of sphere:

[0049] For example, the diameter of the sphere is 28 mm.

[0050] 1. Angle analysis of the dodecahedron

[0051] Each spherical block acts as a vertex when assembling a regular polyhedron. Therefore, sticks with different spatial angles should extend from the vertices of different regular polyhedra as the edges of the polygon. Fig.11 .

[0052] The three points where the three edges intersect the sphere are located on the same plane. If the number of holes is not limited, there can be an infinite number of points for the three edges to choose from in the height circle on the sphere. Figure 1 , where the black bold line is located in the figure.

[0053] Find the position of this height circle and mark it. When the rod moves to this height circle and the angle between the three edges is divided into three equal parts, a regular dodecahedron can be formed by continuous splicing.

[0054] 2. Calculate the altitude circle

[0055] Each vertex of the regular dodecahedron extends out to three pentagons. The internal angle of the pentagon is 108°, see Fig.13 . Cut off an edge from the regular dodecahedron, and each of its faces is an isosceles triangle with an angle of 108°. Its base is an equilateral triangle (the length of the side is exactly the longest side of the isosceles triangle).

[0056] The three-point circle operation in the Rhino modeling software was used to draw a circle based on the three points of an equilateral triangle. Fig.14 .

[0057] The projection operation uses the curve projection to surface operation in Rhino. The height circle (black bold line) where the 14mm radius sphere can be spliced ​​to form the angle of the regular dodecahedron is successfully obtained. Three equally divided positions are selected in the height circle, and the reverse extension line from the point to the center of the circle conforms to the angle principle of the edge of the regular dodecahedron. Fig.15 .

[0058] 3. Calculate the height circle size of the regular tetrahedron on the sphere with a diameter of 28mm: Each face of the regular tetrahedron is an equilateral triangle with an angle of 60°. Draw an equilateral triangle with a side length of 14mm and draw a circumscribed circle by drawing a circle with three points. The projection of the circumscribed circle to the surface of the sphere is the regular tetrahedron joint position circle. The diameter of the circumscribed circle is about 8.08mm. Fig.16 shown.

[0059] 4. Find the altitude circles of four polyhedrons

[0060] Calculate the height circle size of the regular hexahedron on the sphere with a diameter of 28mm: Each face of the regular hexahedron is a square with an angle of 90°. Draw an isosceles right triangle with a side length of 14mm, and draw a circumscribed circle by drawing a circle with three points. The projection of the circumscribed circle to the surface of the sphere is the regular hexahedron joint position circle, and the diameter of the circumscribed circle is about 22.86mm. Fig.17 shown.

[0061] Calculate the height circle size of the regular dodecahedron on a sphere with a diameter of 28mm: Each face of the regular dodecahedron is a pentagon with an angle of 108°. Draw an isosceles obtuse triangle with a side length of 14mm, and draw a circumscribed circle by drawing a circle with three points. The projection of the circumscribed circle to the surface of the sphere is the regular dodecahedron joint position circle. The diameter is about 26.12mm. Fig.18 shown.

[0062] Calculate the height circle size of the regular icosahedron on a sphere with a diameter of 28mm: Each face of the regular icosahedron is an equilateral triangle with an angle of 60°, but each vertex has five edges. Draw a regular pentagon with a side length of 14mm, and draw the circumscribed circle in the way of drawing a circle with three points. The projection of the circumscribed circle to the surface of the sphere is the regular icosahedron splicing position circle. The diameter is about 23.82mm. Fig.19 shown.

[0063] 5. Choose a 12-hole ball as the ball building block carrier

[0064] The 12 holes of the 12-hole ball are evenly distributed, that is, they have the characteristics of three holes on the same plane and five holes on the same plane. The arrangement of the lines on the 28mm diameter sphere: from top to bottom, the ones that need three holes are the regular tetrahedron, regular hexahedron, and regular dodecahedron, and the one that needs five holes is the regular icosahedron. Marks are engraved on each height circle, which correspond to the first annular wire groove 12, the second annular wire groove 13, the third annular wire groove 14, and the fourth annular wire groove 15 in sequence, thereby playing a role in auxiliary splicing. Participate Figures 1 to 3 .

[0065] If the words "first", "second" and the like are used in the above-mentioned text of the utility model to limit components, those skilled in the art should know that the use of "first" and "second" is only for the convenience of description to distinguish the components. Unless otherwise stated, the above-mentioned words have no special meaning.

[0066] If the present invention discloses or involves components or structures that are fixedly connected to each other, then, unless otherwise stated, the fixed connection can be understood as: a detachable fixed connection (for example, connection using bolts or screws), and can also be understood as: a non-detachable fixed connection (for example, riveting, welding). Of course, the fixed connection to each other can also be replaced by an integrated structure (for example, manufactured by one-piece molding using a casting process) (except where it is obviously impossible to use an one-piece molding process).

[0067] In addition, unless otherwise stated, the terms used to indicate positional relationships or shapes in any of the technical solutions disclosed in the above utility model include states or shapes that are approximate, similar or close thereto.

[0068] Any component provided by the utility model can be assembled from multiple separate components, or can be a separate component manufactured by an integrated molding process.

[0069] The above description is only a preferred embodiment of the present invention. All equivalent changes and modifications made according to the scope of the patent application of the present invention should fall within the scope of the present invention.

Claims

1. A regular polyhedron mathematical building block teaching aid, comprising at least four spheres and at least six connecting rods, characterized in that: There are 12 positioning holes evenly distributed on the sphere, and the connecting rod includes a plug-in concave rod and a plug-in convex rod. One end of the plug-in concave rod is provided with a concave portion, and one end of the plug-in convex rod is provided with a convex portion matching the concave portion. The other ends of the plug-in concave rod and the plug-in convex rod are both provided with an arc portion, the length of the arc portion is less than the distance between two adjacent positioning holes, and the end of the arc portion is provided with a convex column for inserting into the positioning hole.

2. The regular polyhedron mathematical building block teaching aid according to claim 1, characterized in that: The angle between the axis of the convex column and the axis of the plug-in concave rod or the plug-in convex rod is 45°.

3. The regular polyhedron mathematical building block teaching aid according to claim 1 or 2, characterized in that: The sphere is provided with a first annular groove line, a second annular groove line, a third annular groove line and a fourth annular groove line which form an angle with the third annular groove line from top to bottom, three positioning holes are evenly distributed along the first annular groove line on the sphere, three positioning holes are evenly distributed along the third annular groove line on the sphere, and five positioning holes are evenly distributed along the fourth annular groove line on the sphere.

4. The regular polyhedron mathematical building block teaching aid according to claim 3, characterized in that: Each positioning hole on the third annular groove line is located on the symmetry line of two adjacent positioning holes on the first annular groove line; one of the positioning holes on the fourth annular groove line coincides with one of the positioning holes on the third annular groove line.

5. The regular polyhedron mathematical building block teaching aid according to claim 3, characterized in that: The included angle between the plane where the fourth annular groove line is located and the plane where the third annular groove line is located is 37°.

6. The regular polyhedron mathematical building block teaching aid according to claim 3, characterized in that: The radius ratio between the first annular groove line and the sphere is 1:1.7~1.8; the radius ratio between the first annular groove line and the second annular groove line is 1:1.4~1.5; the radius ratio between the first annular groove line and the third annular groove line is 1:1.6~1.7; the radius ratio between the fourth annular groove line and the first annular groove line is 1:1.45~1.55.

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