Spherical design learning teaching aid and utilization and manufacturing method thereof

Abstract

The invention discloses a spherical design learning teaching aid and a utilization and manufacturing method thereof, and aims to execute difficulty mathematical concepts of regular polyhedrons and artistic creation of paving patterns together, so that mathematical learning can improve space capability and creativity at the same time.

Description

[0001] Cross-references to related applications

[0002] This application claims priority based on Korean Patent Application No. 10-2023-0019245 filed on February 14, 2023, and incorporates the entire disclosure of the Korean Patent Application into this specification as a part of this specification. Technical Field

[0003] The invention relates to a spherical surface design learning aid and a utilization and manufacturing method thereof. Background Art

[0004] Spatial ability refers to the mental process of recognizing, recalling, creating, and communicating images of objects in space. Spatial ability requires the following elements: spatial visualization, which allows one to imagine the movement of objects in space; spatial orientation, which allows one to measure direction without being distracted by changes in the visual rotation of an object; and the ability to quickly and accurately mentally rotate objects in space.

[0005] Spatial ability significantly impacts students' understanding of mathematics and science. To improve spatial ability, it's important to first understand the concepts themselves. Learning through formal or linguistic definitions can lead to misconceptions.

[0006] Regular polyhedra are regular polygons whose faces are all congruent and whose vertices have the same number of faces. There are only five types of regular polyhedra: the tetrahedron, the hexahedron, the octahedron, the dodecahedron, and the icosahedron. Geometry related to regular polyhedra utilizes three-dimensional solids, thus fostering spatial abilities. However, when learning with textbooks consisting solely of two-dimensional, flat books, such as those in Existing Document 1, problems arise with proper understanding.

[0007] Existing literature 2 proposes a learning aid based on the unfolded form of a plane to help students understand regular polyhedra in three-dimensional space. However, this learning aid is limited to regular polyhedra. Since spatial understanding varies significantly across grades, these teaching aids have limited appeal to middle and high school students.

[0008] Based on this, by using a 3D dynamic geometry program that can manipulate regular polyhedrons by itself to rotate, deform and manipulate the vertices and edges of regular polyhedrons in the mind, the visualization ability and problem-solving ability can be further improved compared to using the above-mentioned planar teaching aids.

[0009] In the present invention, a new concept teaching aid is produced, which not only helps to understand the concept of regular polyhedron, but also introduces art techniques such as paving patterns, thereby allowing the study of mathematics and art at the same time.

[0010] Paving patterns refer to the use of graphics to completely cover a plane or space without any gaps or overlaps. It is an art technique that utilizes the combined concepts of rotation, symmetry, parallel movement, etc. applicable in mathematical time.

[0011] For example, various repeating patterns can be found on bathroom tiles or floor surfaces. In the process of learning such curved details, children can naturally understand spatial division while naturally learning mathematical concepts, which can inspire an interest in mathematics.

[0012] Currently, most of the paving pattern teaching is to make polyhedrons using paper, tangram games using kits or wood, Soma cubes, and polyhedron modules, which are mainly performed on a flat surface.

[0013] The spherical paving pattern is to repeatedly form the same pattern on the sphere, so it can gain many intuitive concepts about space, and can further cultivate the sense of space, and then obtain the concept of solid geometry rather than plane geometry.

[0014] The sphere paving pattern is created by drawing vertices on the sphere using a writing instrument and then connecting or including these vertices using an angle tool to create a repeating pattern. This allows for a variety of patterns, such as the soccer ball example, to be created through the learner's creativity. Therefore, the number of vertices can be adjusted to suit the learner's level, further developing spatial cognition.

[0015] However, in the case of existing sphere paving patterns, vertices are directly drawn on the sphere to connect them into lines. Therefore, due to the characteristics of the sphere itself, it cannot be fixed during use, and it is difficult to accurately draw vertices at specific positions.

[0016] In the present invention, a new teaching aid is made, which can easily learn the sphere paving pattern.

[0017] (Patent Document 1) KR Patent Grant No. 10-11121650000 (January 27, 2012)

[0018] (Patent Document 2) KR Utility Model Authorization No. 20-04886270000 (February 25, 2019). Summary of the Invention

[0019] (Problem to be solved)

[0020] Create a teaching aid that inserts regular polyhedrons into a sphere to form repetitive patterns. This helps students understand the geometric concepts of regular polyhedrons and inspires creativity by creating various patterns.

[0021] When directly marking the vertices of a regular polyhedron on a sphere, the sphere's properties make it difficult to accurately mark the vertices. Without accurate marking of the vertices, even connecting them into straight lines and curves would make it difficult to create a repeating pattern. Furthermore, marking the vertices of a regular polyhedron on a sphere is time-consuming.

[0022] The present invention can produce a teaching aid that can accurately mark vertices on a sphere without requiring a separate fixture, thereby easily expressing various straight lines and curves. In addition, the teaching aid can be directly produced through program application to enhance learners' understanding of geometry and problem-solving ability.

[0023] (Methods of solving the problem)

[0024] The invention provides a teaching aid for designing a spherical surface game or teaching for learners.

[0025] Figure 1 This is a diagram used to illustrate teaching aids.

[0026] Reference Figure 1 The teaching aid 100 has a spherical shell 10, which is composed of a first hemisphere 11 and a second hemisphere 13. The first hemisphere 11 and the second hemisphere 13 can be separately combined with each other to form a sphere after being joined together, and a sphere accommodating space is formed inside.

[0027] The first hemisphere 11 and the second hemisphere 13 are made into hemispherical shapes to be joined together, and the end areas of the joined parts have a straight line or a curved line shape. For example, the end areas can be straight lines, waves or sawtooth shapes.

[0028] According to one embodiment, either a protruding rib or an inserting rib is formed at the end of each of the first hemisphere 11 and the second hemisphere 13, effectively coupling the first hemisphere 11 and the second hemisphere 13. Specifically, the protruding rib can be formed at the end of the first hemisphere 11 and the inserting rib at the end of the second hemisphere 13, or the inserting rib can be formed at the end of the first hemisphere 11 and the protruding rib at the end of the second hemisphere 13. The presence of these protruding and inserting ribs facilitates securing the inner sphere 20 within the spherical outer shell 10, further making it easier to mark the apex through the through-hole 15.

[0029] According to another embodiment, the first hemisphere 11 and the second hemisphere 13 form the spherical shell 10 without separate protruding ribs and inserting ribs. In this case, the ends of the first hemisphere 11 and the second hemisphere 13 have a wavy or sawtooth shape, and because of the insertion fit of the shape, the inner sphere 20 can be fixed therein.

[0030] The first hemispherical body 11 and the second hemispherical body 13 have a plurality of through holes 15 that can mark the apex of the inner sphere 20 .

[0031] The vertex is defined as the pole Pa at any point on the surface of the inner sphere 20, and the equator E is established by dividing the northern and southern hemispheres by the pole Pa. Accordingly, the center of the first hemisphere 11 or the second hemisphere 13 is the pole Pa, and the equator E is used as the basis to divide the first hemisphere 11 and the second hemisphere 13.

[0032] The through hole 15 is formed in the first hemisphere and the second hemisphere. With the equator E marking the vertex, a through hole 15a with a hemispherical shape on one side open is formed in the first hemisphere 11, and a through hole 15b with a hemispherical shape on one side open is formed in the second hemisphere 13 combined therewith. A through hole 15 is completed by combining the first hemisphere 11 and the second hemisphere 13.

[0033] The inner sphere 20 is placed in the accommodating space of the spherical outer shell 10, and the apex is marked by a writing tool.

[0034] The inner sphere 20 can be made of any material as long as it can be used to draw vertices and patterns with a writing tool, for example, it can be made of plastic, foam plastic, wood, rubber, etc.

[0035] The writing tool is a pencil, a ballpoint pen, a signature pen, etc., and the vertices can be marked on the inner sphere 20 through the through hole 15 , as long as a pattern can be drawn on the inner sphere 20 .

[0036] According to the teaching aid 100 of the present invention, the vertices of the inner sphere 20 can be accurately drawn through the through holes 15, thereby easily forming a repeating pattern of the same shape by connecting straight lines and curves. In addition, by forming a different number of through holes 15, a different number of vertices can also be formed, thereby forming a variety of shapes according to the learner's creativity.

[0037] The through holes 15 are located at the vertices of the various polyhedrons that form the inner sphere 20. Based on this, by understanding the types and properties of regular polyhedrons and applying the concept of equal division, shape deformation can be obtained by combining regular polyhedrons.

[0038] There are 5 regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron. The total number of faces, vertices and edges of these are as follows: Figure 13 As shown:

[0039] A regular tetrahedron has four vertices, and three faces are gathered at one vertex, so that the centers of adjacent faces at each vertex are connected to form an equilateral triangle.

[0040] A regular hexahedron has eight vertices, three faces gather at one vertex, and the centers of adjacent faces at each vertex are connected to form an equilateral triangle.

[0041] A regular octahedron has six vertices, four faces gather at one vertex, and the centers of adjacent faces at each vertex are connected to form a regular quadrilateral.

[0042] The regular dodecahedron has 20 vertices, with three faces gathered at one vertex, and the centers of adjacent faces at each vertex connected to form an equilateral triangle.

[0043] The icosahedron has 12 vertices, with 5 faces gathered at one vertex, and the centers of adjacent faces at each vertex are connected to form a regular pentagon.

[0044] The vertices of the various positions can be marked on the inner sphere 20 by the plurality of through holes 15 formed in the first hemisphere and the second hemisphere.

[0045] At this time, the vertices are directly connected with straight lines or curves or express predetermined shapes, thereby realizing various creative repeating patterns.

[0046] In addition, a teaching aid can also realize various shapes.

[0047] That is, regular polyhedra have different shapes of faces, the number of faces gathered at a vertex, the number of faces, the number of vertices, the number of edges, etc. Specifically, they have a characteristic of being cyclic between regular polyhedra.

[0048] The icosahedron has the same number of faces as the dodecahedron, the dodecahedron has the same number of faces as the hexahedron, the hexahedron has the same number of faces as the tetrahedron, the tetrahedron has the same number of edges as the octahedron, and the octahedron has the same number of edges as the icosahedron. Therefore, the dodecahedron can be constructed from the face centers of the icosahedron, the hexahedron can be constructed from the face diagonals of the dodecahedron, the tetrahedron can be constructed from the face diagonals of the hexahedron, the octahedron can be constructed from the edge midpoints of the tetrahedron, and the icosahedron can be constructed from the edge split points of the octahedron.

[0049] To give a specific example, the regular hexahedron and the regular octahedron, the regular dodecahedron and the regular icosahedron are dual polyhedrons. The dual polyhedron refers to a polyhedron made with the centers of each face as the vertices of the figure. Because of this characteristic, the dual polyhedron of the dual polyhedron of a polyhedron is the original polyhedron. The regular octahedron has four equilateral triangles meeting at one vertex, so it is the dual figure of the regular hexahedron {4,3}, which has three regular quadrilaterals meeting at one vertex. The regular dodecahedron has three regular pentagons meeting at one vertex, so it is the dual figure of the regular icosahedron {3,5}, which has five equilateral triangles meeting at one vertex. Therefore, even if the through hole 15 is formed to realize the regular hexahedron, the regular octahedron can also be realized.

[0050] This can also be achieved without being a dual polyhedron.

[0051] For example, connecting the golden section points of each edge of an octahedron creates an icosahedron, while connecting eight non-adjacent vertices of a dodecahedron's 20 vertices creates a hexahedron. Similarly, connecting four of the 20 vertices of a dodecahedron creates a tetrahedron.

[0052] In the above description, only the vertices of the regular tetrahedron, regular hexahedron, regular octahedron, regular dodecahedron, and regular icosahedron have been described, but it has been described that the through holes 15 constituting these exist in one spherical shell 10 .

[0053] According to an additional implementation example, all through holes 15 required for the regular polyhedron exist in a spherical shell 10, and various regular polyhedrons can be realized in an internal sphere 20 using the spherical shell 10, or the internal sphere 20 can be replaced, and regular polyhedrons can also be realized separately in multiple internal spheres 20.

[0054] According to another implementation example, through holes 15 corresponding to the vertices of the regular hexahedron and regular octahedron in the dual polyhedron are formed in a spherical shell 10, thereby making a regular hexahedron and a regular octahedron in the inner sphere 20, thereby improving the understanding of the dual polyhedron.

[0055] According to another implementation example, through holes 15 corresponding to the vertices of the regular dodecahedron and the regular icosahedron in the dual polyhedron are made in a spherical shell 10, and the regular dodecahedron and the regular icosahedron are made in the inner sphere 20 accordingly, thereby improving the understanding of the dual polyhedron.

[0056] In the above description, only the vertices of the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron are described. However, in addition to the through-holes 15 at these vertices, by forming additional through-holes 15 in the first and second hemispheres, shapes or patterns other than regular polyhedrons can be drawn. There is no limit to the number of additional through-holes 15 formed in the first and second hemispheres, and the number can be increased according to the needs of the learner. However, the additional through-holes 15 formed in the first and second hemispheres 11 and 13 are preferably formed in mutually symmetrical positions to form a repeating pattern.

[0057] The game or lesson using the teaching aid according to the present invention can be carried out in various ways.

[0058] One of the methods is as follows, the steps are:

[0059] S1), combining the first hemispherical body 11 and the second hemispherical body 13 with the through hole 15 and the inner sphere 20 as a set;

[0060] S2), using the through holes 15 to mark the vertices of the regular polyhedron on the surface of the inner sphere 20; and

[0061] S3), separating the inner sphere 20 with marked vertices, and then using the vertices to obtain a regular polyhedron or a repeated pattern of the regular polyhedron.

[0062] By simply connecting the vertices, regular polyhedra can be represented on a sphere. Additional research related to the "regular polyhedron loop" feature, which allows new regular polyhedra to be continuously created within a regular polyhedron drawn within the sphere 20, has been performed. This allows the representation of a regular hexahedron, a regular tetrahedron, a regular octahedron, a regular dodecahedron, and a regular icosahedron within a single sphere 20.

[0063] In addition to this regular polyhedron, paving patterns can also be used to perform tasks. That is, by marking lines or surfaces such as curves with vertices as the standard, a repeating pattern expressed by a paving pattern can be obtained. That is, by finding the vertices of a regular polyhedron, and by connecting the vertices and using patterns, tasks on various balls used in ball sports, such as football, volleyball, baseball, etc., can also be performed. For example, tasks on Telstar (Television Star), Teamgeist (Team Spirit), Jabulani (Celebration), Brazuca (Samba Glory), and Al Rihla (Dream Chaser) can be performed, which can improve the learners' sense of achievement.

[0064] In addition to the above courses, a course on directly manufacturing the spherical shell 10 in the teaching aid using a 3D geometry program and a 3D printer can also be conducted.

[0065] The manufacturing method of the teaching aid 100 of the present invention comprises the following steps:

[0066] P1), use 3D geometry program to find the vertices of regular polyhedron;

[0067] P2), using a 3D modeling program to model the first hemisphere and the second hemisphere so that the vertices form a through hole 15;

[0068] P3), adjusting the diameters of the first hemisphere and the second hemisphere in the 3D modeling program according to the diameter of the inner sphere 20; and

[0069] P4), using a 3D printer to produce the modeled first and second hemispheres;

[0070] P5), the first hemisphere, the second hemisphere and the inner sphere are provided as a set, and the inner sphere can be accommodated in a receiving space formed by the combination of the first hemisphere and the second hemisphere.

[0071] The teaching aid kit obtained through the steps P1) to P5) is a teaching aid kit that can be used to conduct the courses described in the steps S1) to S3).

[0072] The following describes the details related to the production of the teaching aids.

[0073] First, the course using the 3D geometry program may start by finding a vertex to form the through hole 15 ( P1 ) in the spherical housing 10 .

[0074] Figure 2 To illustrate the diagram for finding the vertices of a regular octahedron, Figure 2 As shown in (a), the length of the side on the plane is The center of the regular quadrilateral BCDE is O, and OB = OC = OD = OE = 1. At this time, a perpendicular line is formed from the center O to the regular quadrilateral BCDE, and points A and F with OA = 1 and OF = 1 are taken on opposite sides of the regular quadrilateral. In this way, the six points A, B, C, D, E, and F become the vertices of the regular octahedron. Here, if a sphere with a center of O and a radius of 1 is drawn, then Figure 2 The vertices A, B, C, D, E, and F of the regular octahedron in (b) are all located on the sphere.

[0075] Figure 3 The diagram below shows how to find the vertices of a regular hexahedron. The regular hexahedron and the regular octahedron are dual polyhedrons, so the diagram of the regular octahedron is used as a reference.

[0076] like Figure 3As shown in (a), if the centroids of the four triangles ABC, ACD, ADE, and AEB in the regular octahedron A-BCDE-F are G, H, I, and J respectively, and the centroids of the four triangles FBC, FCD, FDE, and FEB are K, L, M, and N respectively, then the eight points G, H, I, J, K, L, M, and N are the eight vertices that constitute the regular hexahedron.

[0077] Now, if Figure 3 As shown in (b), if with 8 half straight lines The points of intersection with the sphere of radius 1 are P, Q, R, S, T, U, V, and W, which are also the 8 vertices of the regular hexahedron. This is because the center of the regular octahedron is O, so the center of the dual polyhedron GHIJ-KLMN is also O. Therefore, it is equivalent to

[0078] In the regular octahedron, since ∠AGO=90°,

[0079] Therefore, if Figure 3 As shown in (c), if we take point O as the center and expand the eight points G, H, I, J, K, L, M, and N, The points are P, Q, R, S, T, U, V, and W, and these eight points form a regular hexahedron.

[0080] The lengths of all are 1. Therefore, the eight points P, Q, R, S, T, U, V, and W are located on the sphere with a radius of 1 and are the vertices of the regular hexahedron.

[0081] Figure 4 It is a graph for finding the vertices of a regular tetrahedron. In the regular hexahedron PQRS-TUVW, the four vertices P, R, U, and W form a regular tetrahedron, and the remaining four vertices Q, S, T, and V also form a regular tetrahedron.

[0082] In addition, the four points Q, S, T, and V are the centers on the spherical surface of the spherical triangles divided by the four vertices P, R, U, and W of the regular tetrahedron.

[0083] Figure 5 It is a graph used to find the vertices of a regular dodecahedron.

[0084] If we accurately select eight of the 20 vertices of a regular dodecahedron, we can exploit the property that eight vertices of a regular hexahedron can form. That is, there exists a regular dodecahedron whose vertices are the eight points P, Q, R, S, T, U, V, and W that constitute the regular hexahedron.

[0085] First, if Figure 5(a) The eight points P, Q, R, S, T, U, V, and W are eight of the 20 vertices of the regular dodecahedron.

[0086] Assume that the other 12 vertices of the regular dodecahedron are D1, D2, D3...D 12 .

[0087] Method to find point D1: If you draw a circle with center P and radius 1 on the surface of a sphere with center O and radius 1, The circle with center Q and radius The intersection of the two circles is D1.

[0088] Method to find point D2: If you draw a circle with center S and radius 1 on the surface of a sphere with center O and radius 1, The circle with center R and radius The intersection point is D2.

[0089] Continue the process as described above to obtain D3...D 12 .

[0090] That is, Figure 5 As shown in (b), the 20 vertices of the regular dodecahedron are P, Q, R, S, T, U, V, W, D1, D2, D3...D 12 All of them are located on the surface of a sphere with center O and radius 1.

[0091] This is because in the regular pentagon PD2D1SD5, In the regular pentagon QD2D1RD7 Therefore, on a sphere with center O and radius 1, the center is P and the radius is The circle with center Q and radius The intersection point of the circles is D1.

[0092] Furthermore, in the regular pentagon PD2D1SD5 In the regular pentagon QD2D1RD7 Therefore, on a sphere with center O and radius 1, the center is S and the radius is The circle with center R and radius The intersection point of the circles is D2.

[0093] Method to find point D5: If you draw a circle with center W and radius 1 on the surface of a sphere with center O and radius 1, The circle with center T and radius The intersection of the two circles is D5. This is because the regular pentagon middle Regular pentagon PD5D6TD9 Therefore, on the sphere, the center is W and the radius is The circle with center T and radius The intersection point of the circles is D5.

[0094] Figure 6 This is a diagram showing how to find the vertices of a regular icosahedron. The regular icosahedron is constructed by connecting the centers of the faces of the regular dodecahedron as a dual polyhedron.

[0095] above Figure 6 (a) Utilization Figure 5 (b) The 20 vertices P, Q, R, S, T, U, V, W, D1, D2, D3....D of the regular dodecahedron 12 .

[0096] like Figure 6 As shown in (c), if the centers of the 12 regular pentagons of the regular dodecahedron are set to I1, I2, .... I 12 , and 12 half straight lines The intersection points with the sphere with center O and radius 1 are set as X1, X2....X 12 , then the 12 points X1, X2....X 12 are the vertices of a regular icosahedron.

[0097] The three-dimensional shape connecting the centers of the faces of the regular dodecahedron as a dual shape constitutes the regular icosahedron, so the 12 centers I1, I2, .... I 12 are vertices of a regular icosahedron, and the center of the regular icosahedron is the same as the center O of the regular dodecahedron.

[0098] because Therefore, The intersection points X1, X2, ....X with the sphere with center O and radius 1 12 The figure formed by the 12 points I1, I2, ....I 12 The three-dimensional shape formed is similar. That is, the 12 points X1, X2....X 12 are the vertices of a regular dodecahedron.

[0099] Then, a 3D modeling program is used to model the first hemisphere and the second hemisphere so that the vertices form the through holes 15 ( P2 ).

[0100] Programs used for 3D modeling include Solidworks, CATIA, Rhino, Inventor, 3D MAX, Sketch UP, Z-brush, Blender, etc. Use appropriate programs considering the age of the learners.

[0101] Figure 7The image of the through holes 15 corresponding to all vertices constituting the five regular polyhedrons is shown by 3D modeling. Figure 7 As shown, a total of 38 through holes 15 are marked on the sphere, and the spherical housing 10 is manufactured using the 3D modeling.

[0102] At this time, for the spherical shell 10, the number and position of the through holes 15 are adjusted according to the type of the regular polyhedron or as shown in FIG. Figure 7 The through holes 15 may be formed including all regular polyhedrons.

[0103] Then, according to the diameter of the inner sphere 20 , the diameters ( P3 ) of the first hemisphere 11 and the second hemisphere 13 are adjusted in the 3D modeling program.

[0104] Then, the modeled first and second hemispherical bodies 11 and 13 are manufactured using a 3D printer (P4).

[0105] 3D printing (three-dimensional printing process) is based on three-dimensional digital materials obtained through scanning or modeling, and a stacking process is used to produce the desired shape by stacking the materials layer by layer.

[0106] The spherical shell 10 (first and second hemispheres) can be designed using 3D modeling techniques and printed using a 3D printer to produce teaching aids. In this case, the first hemisphere 11 and second hemisphere 13 can be designed and manufactured separately, or the spherical shell 10 can be manufactured in a combined form and then cut to form the first and second hemispheres 11, 13.

[0107] According to teaching aid of the present invention, after the course is finished, the spherical shell 10 is reused, and the used inner sphere 20 is replaced with a new one, so that the reuse of the teaching aid can be realized. Accordingly, a spherical shell 10 can be used to make spheres with various repeated patterns.

[0108] (Effects of the Invention)

[0109] The teaching aids proposed in the present invention are to implement the difficult mathematical concept of regular polyhedrons together with the artistic creativity of paving patterns, so that mathematical learning can improve spatial ability and creativity at the same time.

[0110] In addition, by using 3D geometry programs to find vertices and digitize mathematical images of regular polyhedra, and using 3D printing to output the products, we can directly create teaching aids, thereby helping students understand regular polyhedra and circularity, and create various repeating patterns that can express their own personality, which in turn has a positive effect on learners' understanding and stimulates their interest. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 1 is a perspective view showing a teaching aid according to an embodiment of the present invention.

[0112] Figure 2 This figure shows how to find the vertices of a regular octahedron in a sphere.

[0113] Figure 3 This figure shows how to find the vertices of a regular hexahedron in a sphere.

[0114] Figure 4 This figure shows how to find the vertices of a regular tetrahedron in a sphere.

[0115] Figure 5 A diagram illustrating finding the vertices of a regular dodecahedron in a sphere.

[0116] Figure 6 This is a diagram showing how to find the vertices of a regular icosahedron in a sphere.

[0117] Figure 7 This is an image showing through holes corresponding to all vertices constituting five regular polyhedrons by 3D modeling.

[0118] Figure 8 This figure shows a process of creating a soccer ball pattern similar to team spirit using the vertices of an inner sphere.

[0119] Figure 9 Shown is the use of vertices of an inner sphere to create a design similar to a volleyball.

[0120] Figure 10 Shown is the use of the vertices of the inner sphere to create a design similar to the Jakarta.

[0121] Figure 11 A design of a soccer ball is shown using the vertices of an inner sphere to create a star shape.

[0122] Figure 12 A design showing a five-winged windmill-like shape using the vertices of an inner sphere is shown.

[0123] (Explanation of Reference Numerals)

[0124] 10: Spherical shell

[0125] 11: First hemisphere

[0126] 13: Second hemisphere

[0127] 15, 15a, 15b: Through holes

[0128] 20: Inner sphere

[0129] 100: Teaching aids DETAILED DESCRIPTION

[0130] (Best Practice)

[0131] According to an implementation example of the present invention, a spherical design teaching aid can be provided as a teaching aid for spherical design games or learning for learners, comprising: a spherical shell, composed of a first hemisphere and a second hemisphere, the first hemisphere and the second hemisphere being separably combined with each other to form a sphere after being combined with each other, and forming a sphere storage space inside; an internal sphere, placed in the storage space inside the spherical shell; the first hemisphere and the second hemisphere having a plurality of through holes.

[0132] According to another embodiment of the present invention, a method for utilizing a spherical surface design teaching aid is provided, comprising the following steps: S1) combining a first hemisphere and a second hemisphere having a through hole with an inner sphere assembly;

[0133] S2), using the through holes to mark the vertices of a regular polyhedron on the surface of the inner sphere; and

[0134] S3), separating the inner sphere with the vertices marked, and then using the vertices to obtain a regular polyhedron or using the vertices to obtain a repeating pattern.

[0135] According to another embodiment of the present invention, a method for manufacturing a spherical design teaching aid may be provided, comprising the following steps: P1) finding the vertices of a regular polyhedron using a 3D geometry program;

[0136] P2), using a 3D modeling program to model the first hemisphere and the second hemisphere so that the vertices form through holes;

[0137] P3), adjusting the diameters of the first hemisphere and the second hemisphere in the 3D modeling program according to the diameter of the inner sphere;

[0138] P4) For the first and second hemispheres that have been modeled, using a 3D printer to manufacture the first hemisphere and the second hemisphere having through holes;

[0139] P5) The first hemisphere, the second hemisphere and the inner sphere are provided as a set, and the inner sphere can be accommodated in a receiving space formed by the combination of the first hemisphere and the second hemisphere.

[0140] (Implementation Method)

[0141] Manufacturing example: Manufacturing teaching aids

[0142] Use a 3D geometry program to find the vertices of the 5 regular polyhedrons, and use a 3D modeling program to obtain Figure 7 Using this pattern, the spherical shell was produced through various 3D printing processes. A translucent plastic sphere was used for the inner sphere to make it easier to identify the marked vertices.

[0143] - First group: a spherical shell formed with through holes corresponding to the vertices of each regular polyhedron;

[0144] - The second group: a spherical shell having through holes corresponding to the vertices of a regular hexahedron / octahedron, and a spherical shell having through holes corresponding to the vertices of a regular dodecahedron / icosahedron;

[0145] - The third group: formed at the same time Figure 7 Mark all vertices corresponding to the spherical shell of the through hole;

[0146] Example 1: Design using the vertices of a regular octahedron

[0147] A spherical shell (a first hemisphere and a second hemisphere) with six through holes 15 marked thereon is produced using a 3D printer, and then the vertices are marked on the inner sphere of the transparent material.

[0148] Figure 8 This figure shows a process of creating a soccer ball pattern similar to team spirit using the vertices of an inner sphere.

[0149] like Figure 8 As shown in (a), a dumbbell pattern is drawn with the six vertices of the regular octahedron as the center. When the six vertices of the regular octahedron are set as N, A, B, C, D, and S, N and S are the North Pole and the South Pole, and the four points A, B, C, and D are located on the equator, forming a regular quadrilateral in this order. Use a great circle path to connect two adjacent vertices of the regular octahedron. Take the above Points K and L. Draw an arc with point K as the center and passing through point L. This operation is also done on the arc On the side. Take point M on the top, so that point M is And smoothly connect the two arcs with point M. This operation also works on the arc As a result, a dumbbell pattern can be obtained.

[0150] This process is also carried out on the other vertices of the regular octahedron, and finally the auxiliary lines are erased to form Figure 8 (b) Design. Next, add a curve corresponding to the path of the great circle connecting the vertices of the regular octahedron to obtain Figure 8 (c).

[0151] for Figure 8 (c) Coloring can obtain Figure 8 (d) A soccer ball pattern similar to team spirit.

[0152] Example 2: Design using the vertices of a regular hexahedron and a regular octahedron

[0153] A spherical shell (a first hemisphere and a second hemisphere) with 14 through holes 15 is produced using a 3D printer, and then the vertices are marked on the inner sphere of the transparent material.

[0154] Figure 9 A design is shown in which the vertices of an inner sphere are used to create a volleyball shape.

[0155] like Figure 9 As shown in (a) and (b), let the six vertices of a regular octahedron be N, A, B, C, D, and S, and connect two adjacent points using a great circle path. Here, points N and S are the North Pole and South Pole, and the four points A, B, C, and D are located on the equator. In this order, a regular quadrilateral is formed. Furthermore, if the eight vertices of a regular hexahedron are P, Q, R, T, ..., then point P is the center of the spherical triangle NAB on the sphere. Q, R, T, ... are also the centers of the spherical triangles NBC, NCD, NDA, ..., respectively.

[0156] Now, draw a circle with center N passing through point P, then draw a circle with center A passing through point P, then draw a circle with center B passing through point P, and we get Figure 9 (a). If the same is true at points Q, R, and T, then Figure 9 As shown in (c), draw a figure connecting the four points that form one face of the regular hexahedron. Repeat this process for the points that form the other faces. Once you've completed the design connecting the eight vertices that form the regular hexahedron, the sphere will be divided into six equal parts.

[0157] Then, if Figure 9 As shown in (d), if each graph is divided into three parts, the following can be obtained: Figure 9 (e) A pattern similar to a volleyball.

[0158] Example 3: Design using the vertices of a regular tetrahedron

[0159] A spherical outer shell (a first hemisphere and a second hemisphere) having eight through holes 15 corresponding to the vertices of a regular hexahedron is produced using a 3D printer, and then the vertices are marked on the inner sphere of a transparent material.

[0160] Figure 10 It shows the use of the vertices of the inner sphere to create a design similar to the Jabulani ball, the official World Cup ball.

[0161] like Figure 10 As shown in (a) and (b), mark the eight vertices of a regular hexahedron on the sphere, select the four vertices A, B, C, and D that form a regular tetrahedron from these eight, and connect the points using a great circle path.

[0162] Select points E, F, and G that are 3 / 8 of the length of the arc from vertex A to another vertex of the tetrahedron, and use a compass to draw an arc with E as the center and passing through F and G to select the arc. Draw an arc with F as the center and passing through G and E to select the arc Draw an arc with G as the center and passing through E and F to select the arc

[0163] Next, erase the curve inside the figure surrounded by three arcs to obtain Figure 10 (c) to (e) inner sphere, color it, and you can get Figure 10 (f) is a pattern similar to the one for Universal Celebration.

[0164] Example 4: Design using the vertices of a regular dodecahedron

[0165] A spherical shell (a first hemisphere and a second hemisphere) with 20 through holes 15 formed therein was produced using a 3D printer, and then the vertices were marked on the inner sphere of the transparent material.

[0166] Figure 11 A design of a soccer ball is shown using the vertices of an inner sphere to create a star shape.

[0167] like Figure 11 As shown in (a), mark the 20 vertices (blue dots) that make up the regular dodecahedron on the sphere, and connect two adjacent points with arcs of great circles. Next, mark the midpoints of two adjacent vertices in the sphere with red dots. Each spherical pentagon has 5 such midpoints. Connect every two points with great circle paths, and then draw the following Figure 11 (b) The star shape.

[0168] If the same operation is performed on the remaining 11 spherical five-pointed stars and the inner curves of the star-shaped stars are erased, the following is formed: Figure 11 (c) The shape can be obtained by coloring Figure 11 (d) appearance.

[0169] like Figure 11 As shown in (c) and 10(d), the sphere is filled with star-shaped figures (curved-edge pentagons) and figures with six curved sides (curved-edge hexagons). There are 12 curved-edge pentagons and 20 curved-edge hexagons.

[0170] Example 5: Design using the vertices of a regular dodecahedron and a regular dodecahedron

[0171] A spherical shell (a first hemisphere and a second hemisphere) with 32 through holes 15 is produced by a 3D printer, and then the vertices are marked on the inner sphere of a transparent material.

[0172] Figure 12A design showing a five-winged windmill-like shape using the vertices of an inner sphere is shown.

[0173] like Figure 12 As shown in (a), the 12 vertices are connected to form a regular icosahedron. Furthermore, the vertices of the regular dodecahedron are the centers of the spherical triangles that divide the vertices of the regular icosahedron.

[0174] Then, if Figure 12 As shown in (b), one vertex of the icosahedron is A, and the vertices adjacent to point A are divided into B, C, D, ... and recorded. The vertices of the regular dodecahedron are recorded as F, G, H, ...

[0175] The center of the spherical triangle ABC is G. The four equal points are K, L, N, and the great arc The points that divide the circle into four equal parts are P, Q, and R. Then, connect the two points K and P with a great circle arc with M as the midpoint.

[0176] Now, we will connect the curve from point G through point M to point P, and the same way from point G to point N (rotation of curve GMP). Select the arc of the great circle. In this way, a small unit curve is drawn starting from point K, passing through N, G, and M, and ending at point P. By creating four more at vertex A, we can draw a windmill-like shape with five blades, as shown in the photo.

[0177] If this process is performed on all vertices of the regular icosahedron, the sphere is designed to be a combined 12 five-winged windmills, such as Figure 12 As shown in (c), the vertices of the icosahedron become the centers of each windmill, and the vertices of the dodecahedron become the points where the three windmills meet.

[0178] Example 6: Dual Polyhedron Design

[0179] An inner sphere made of a transparent material is placed inside a spherical outer shell having through holes corresponding to the vertices of a regular hexahedron and a regular octahedron corresponding to the dual polyhedron, and then vertices are marked on all the through holes.

[0180] If the 12 vertices of the icosahedron are connected within the sphere, the icosahedron, consisting of regular triangles, is completed. Mark the center of each regular triangle and connect the marks to create a regular dodecahedron. This explains the principle of dual polyhedra.

[0181] Example 7: Regular Polyhedron Circular Design

[0182] At the same time, there is Figure 7 Place an inner sphere of transparent material inside the spherical shell of the through-holes corresponding to all the marked vertices, and then mark the vertices of all the through-holes.

[0183] Find the vertices of a regular hexahedron within the inner sphere and connect them to create a regular hexahedron. Connect the four vertices of the regular hexahedron to create a regular tetrahedron. Create an octahedron by connecting the midpoints of each edge of the regular tetrahedron. Create an icosahedron by connecting the golden ratio internal points of each edge of the regular octahedron. Connect the centroids of the faces of the regular icosahedron to create a regular dodecahedron, and use the eight vertices of the regular dodecahedron to create a regular hexahedron.

[0184] Industrial Applicability

[0185] The present invention is applicable to a spherical surface design game or a teaching aid for learning.

Claims

1. A spherical surface design teaching aid, as a teaching aid for spherical surface design games or learning for learners, comprising: a spherical shell composed of a first hemisphere and a second hemisphere, wherein the first hemisphere and the second hemisphere can be separably combined to form a sphere after being combined, and a sphere-accommodating space is formed inside; and An inner sphere is placed in the accommodation space of the spherical outer shell; The first hemisphere and the second hemisphere have a plurality of through holes.

2. The spherical surface design teaching aid according to claim 1, characterized in that: The end areas of the first hemisphere and the second hemisphere are in a straight line, wavy or sawtooth shape.

3. The spherical surface design teaching aid according to claim 1, characterized in that: The through holes correspond to the vertices of the regular polyhedron.

4. The spherical surface design teaching aid according to claim 3, characterized in that: The regular polyhedron is any one or more of a regular tetrahedron, a regular hexahedron, a regular octahedron, a regular dodecahedron or a regular icosahedron.

5. The spherical surface design teaching aid according to claim 1, characterized in that: The through holes are formed so as to correspond to all the vertices of the regular hexahedron and the regular octahedron corresponding to the dual polyhedron.

6. The spherical surface design teaching aid according to claim 1, characterized in that: The through holes are formed so as to correspond to all vertices of the regular dodecahedron and the regular icosahedron, which are dual polyhedrons.

7. The spherical surface design teaching aid according to claim 1, characterized in that: The through holes are formed to correspond to all vertices of the regular polyhedron.

8. The spherical surface design teaching aid according to claim 3, characterized in that: Also features: The additional through holes do not correspond to the vertices of the regular polyhedron.

9. A method for utilizing a spherical design teaching aid, comprising the following steps: S1), combining the first hemisphere and the second hemisphere with the through hole with the inner sphere kit; S2), using the through holes to mark the vertices of a regular polyhedron on the surface of the inner sphere; and S3), separating the inner sphere with the vertices marked, and then using the vertices to obtain a regular polyhedron or a repeated pattern of the regular polyhedron.

10. A method for manufacturing a spherical design teaching aid, comprising the following steps: P1), use 3D geometry program to find the vertices of regular polyhedron; P2), using a 3D modeling program to model the first hemisphere and the second hemisphere so that the vertices form through holes; P3), adjusting the diameters of the first hemisphere and the second hemisphere in the 3D modeling program according to the diameter of the inner sphere; P4), using a 3D printer to produce the first and second hemispheres having through holes for the modeled first and second hemispheres; and P5), providing a kit of the first hemisphere, the second hemisphere and the inner sphere, wherein the inner sphere is accommodated in a receiving space formed by the combination of the first hemisphere and the second hemisphere.

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