CN213716278U

CN213716278U - Spatial geometry teaching mould related to cube

Info

Publication number: CN213716278U
Application number: CN202022639133.7U
Authority: CN
Inventors: 侯毅男
Original assignee: Individual
Current assignee: Individual
Priority date: 2020-11-13
Filing date: 2020-11-13
Publication date: 2021-07-16
Anticipated expiration: 2030-11-13

Abstract

The utility model relates to a teaching auxiliary tool technical field, a space geometry body teaching mould relevant with the square. The teaching mould for the spatial geometry related to the cube comprises: a sphere and a geometric body; the sphere is a hollow transparent sphere, and the geometric body is arranged in the sphere and detachably connected with the sphere; each vertex of the geometric body is connected with the sphere. Through this teaching mode, the student of being convenient for can assist the teacher to impart knowledge to students to spatial solid geometry's study simultaneously.

Description

Spatial geometry teaching mould related to cube

Technical Field

The utility model relates to a teaching auxiliary tool technical field, more specifically say, a space geometry teaching aid utensil relevant with square.

Background

The solid geometry is the key point and difficulty in teaching in the middle school stage, and the external ball-connecting problem of the space geometry is the hot point of college entrance examination. For students who initially contact the solid geometry, it is difficult to establish correct spatial imagination, so that the spatial imagination is difficult to accept, and the challenge is also for teachers to give lessons, no good teaching assistance mold is available in the prior art to help teachers to teach, help students to intuitively feel the position relation of some space geometry body points and lines and the spatial structure of some assemblies, and generally, the spatial imagination and the spatial structure of some assemblies are demonstrated through plane demonstration or video animation, so the following problems can be caused:

first, it is difficult to show students the inscribed relationship of a sphere and a geometric body if only through plane demonstration.

Secondly, if the relation of the cube and the geometry is difficult to show to students only through the demonstration of the plane, for example, what geometry can be spliced into the cube.

Thirdly, the solution of the radius of the circumscribed sphere usually uses a shape complementing method, but how to complement the shape, students can hardly understand the method.

Fourthly, if the students lack visual perception only through animation demonstration, the spatial imagination ability is difficult to cultivate for part of the students.

SUMMERY OF THE UTILITY MODEL

Not enough to prior art exists, the utility model aims to provide a teaching mould with the relevant space geometry of square, through this teaching mould, the student of being convenient for can assist the teacher to impart knowledge to students to the study of space solid geometry simultaneously.

The above technical purpose of the present invention can be achieved by the following technical solutions:

a cube-related teaching model of spatial geometry comprises a sphere and a geometry;

the sphere is a hollow transparent sphere, and the geometric body is arranged in the sphere and detachably connected with the sphere; each vertex of the geometric body is connected with the sphere.

In one embodiment, the geometry comprises: a first triangular pyramid, a second triangular pyramid, a third triangular pyramid, a regular tetrahedron, a rectangular pyramid, a right triangular prism and a cube.

In one embodiment, the transparent sphere comprises a first plastic hemisphere and a second plastic hemisphere, and the first plastic hemisphere and the second plastic hemisphere are detachably connected, so that the transparent sphere is combined. When a teacher wants to show the external ball of the cube for students, the teacher only needs to put the cube into the first plastic hemisphere and then combine the second plastic hemisphere, so that the external ball of the cube is obtained, the students can observe the position relation between the cube and the external ball, and the vertex, the edge, the surface and the spherical surface of the student can be in position relation through visual perception. Meanwhile, if the teacher wants to show the student with the external ball of other geometric bodies, the teacher only needs to put the displayed geometric bodies into the transparent ball.

In one embodiment, several geometric bodies are selected from the first triangular pyramid, the second triangular pyramid, the third triangular pyramid, the regular tetrahedron, the rectangular pyramid and the right triangular prism and are spliced to form a cube with the same edge length. Can let the student splice out the cube with this teaching mould, be favorable to the student to experience the relation of these geometry and cube at the in-process of concatenation cube to think the possibility of what kind of concatenation cubes have.

In one embodiment, the cube is a hollow box body, and a box cover is arranged at the top of the cube and detachably connected with the cube.

In one embodiment, the first triangular pyramid, the second triangular pyramid, the third triangular pyramid, the regular tetrahedron, the quadrangular pyramid, and the right triangular prism are disposed inside a cube, and respective vertexes of the first triangular pyramid, the second triangular pyramid, the third triangular pyramid, the regular tetrahedron, the quadrangular pyramid, and the right triangular prism coincide with vertexes of the cube. After the student has learned the concatenation cube, the student can know that these little geometry are all a part of cube to can let the student try on putting into the inside of mould cube a geometry, at the in-process of putting, have a lot of possibilities, thereby further the multi-angle can experience the structural relation of other geometries and cubes. Since these other geometric bodies are part of the cube and have the same sphere as the cube, students can be guided to determine the sphere radius of the geometric body by using a complementary method. And if the visual images of the first triangular pyramid, the second triangular pyramid, the third triangular pyramid, the regular tetrahedron and the rectangular pyramid are required to be drawn, the geometric body is spliced into the cube, the visual image of the cube is drawn at the same time, and the positions of all vertexes of the geometric body in the cube are utilized to determine the positions of all vertexes corresponding to the visual image of the geometric body in the visual image of the cube, so that students can draw the visual image.

To sum up, the utility model discloses following beneficial effect has: through this teaching mode, be convenient for the student to the study of space solid geometry, train student's space imagination ability, can assist the teacher to impart knowledge to students simultaneously.

One of them can show the external ball of geometry to the student through this teaching mould, includes two transparent spheroid and geometry in the teaching aid, puts into transparent spheroid with the geometry, can let the student observe the position relation of square and its external ball, through directly perceived impression, lets the student obtain the position relation of the summit, arris, surface and sphere of square.

Secondly, the student utilizes this teaching mould, can splice into the cube with a plurality of geometry, and the process of concatenation is convenient for the student and thinks.

Thirdly, after splicing, the geometric solid can be determined to be a part of the cube and has the same external sphere with the cube, so that students are guided to solve the external sphere radius of the geometric solid by a complementary method.

Fourthly, through this teaching mould, can help the student to draw the map directly perceived.

Drawings

FIG. 1 is an assembly view of the sphere and geometry of the present invention;

figure 2 is a schematic view of a first triangular prism in the geometry of the present invention;

figure 3 is a schematic view of a second triangular prism in the geometry of the present invention;

figure 4 is a schematic view of a third triangular prism in the geometry of the present invention;

fig. 5 is a schematic diagram of a regular tetrahedron in the geometry of the present invention;

figure 6 is a schematic view of a rectangular pyramid in the geometry of the present invention;

figure 7 is a schematic view of a right triangular prism in the geometry of the present invention;

FIG. 8 is a schematic diagram of a cube in the geometry of the present invention;

FIG. 9 is a first embodiment of an assembly view of the cube of the present invention;

FIG. 10 is an exploded view of a first embodiment of an assembly view of the cube of the present invention;

FIG. 11 is a second embodiment of an assembly view of the cube of the present invention;

FIG. 12 is an exploded view of a second embodiment of an assembly view of the cube of the present invention;

FIG. 13 is a third embodiment of an assembly view of the cube of the present invention;

FIG. 14 is an exploded view of a third embodiment of an assembly view of the cube of the present invention;

Detailed Description

The present invention will be described in detail with reference to the accompanying drawings and examples.

It should be noted that all the directional terms such as "upper" and "lower" referred to herein are used with respect to the view of the drawings, and are only for convenience of description, and should not be construed as limiting the technical solution.

Example 1

A cube-related teaching model of spatial geometry comprises a sphere 1 and a geometry 2;

the sphere 1 is a hollow transparent sphere, and the geometric body 2 is arranged inside the sphere 1 and is detachably connected with the sphere 1; the respective vertices of the geometric body 2 meet the sphere 1.

As shown in fig. 2-8, the geometry includes: a first triangular pyramid 23, a second triangular pyramid 24, a third triangular pyramid 25, a regular tetrahedron 26, a quadrangular pyramid 27, a right triangular prism 28, and a cube 29.

The transparent sphere 1 comprises a first plastic hemisphere and a second plastic hemisphere, and the first plastic hemisphere and the second plastic hemisphere are detachably connected to form the transparent sphere. When the teaching aid is specifically implemented, when a teacher wants to show the external ball of the cube to students, the cube 29 is placed into the first plastic hemisphere, and then the second plastic hemisphere is combined, so that the external ball of the cube is obtained, the students can observe the position relation of the cube and the external ball, and the students can obtain the position relation of the vertex, the edge, the surface and the spherical surface of the cube through visual perception. Meanwhile, if the teacher wants to show the student with the external ball of other geometric bodies, the teacher only needs to put the displayed geometric bodies into the transparent ball.

And a plurality of geometric bodies are selected from the first triangular pyramid 23, the second triangular pyramid 24, the third triangular pyramid 25, the regular tetrahedron 26, the rectangular pyramid 27 and the straight triangular prism 28 to be spliced to form a cube with the same edge length. Can let the student splice out the cube with this teaching mould, be favorable to the student to experience the relation of these geometry and cube at the in-process of concatenation cube to think the possibility of what kind of concatenation cubes have.

The square 29 is a hollow box body, a box cover is arranged at the top of the square 29, and the box cover is detachably connected with the square.

The first triangular pyramid 23, the second triangular pyramid 24, the third triangular pyramid 25, the regular tetrahedron 26, the rectangular pyramid 27 and the right triangular prism 28 are arranged inside the cube, and the vertexes of the first triangular pyramid 23, the second triangular pyramid 24, the third triangular pyramid 25, the regular tetrahedron 26, the rectangular pyramid 27 and the right triangular prism 28 coincide with the vertex of the cube 29. After the student has learned the concatenation cube, the student can know that these little geometry are all a part of cube to can let the student try on putting into the inside of cube in the mould a geometry, in the in-process of putting, have a lot of possibilities, thereby further multi-angle realises the structural relation of this geometry and cube. Since the geometric bodies are part of the cube and have the same external sphere as the cube, students can be guided to use a complementary method to determine the external sphere radius of the geometric bodies. The method comprises the steps of splicing a geometric body into a cube when drawing intuitive graphs of a first triangular pyramid, a second triangular pyramid, a third triangular pyramid, a regular tetrahedron and a rectangular pyramid, drawing the intuitive graph of the cube at the same time, determining the positions of all vertexes corresponding to the intuitive graph of the geometric body in the intuitive graph of the cube by using the positions of all vertexes of the geometric body in the cube, and thus helping students draw the intuitive graph.

As shown in fig. 9, a method for splicing a cube by geometry is given, and the cube 3 is spliced by a first triangular pyramid 33, a second triangular pyramid 34, a third triangular pyramid 35 and a triangular prism 38. As shown in fig. 10, an exploded view of the cube 3 is given.

For example, the following steps are carried out: in specific implementation, the utility model people has the following experiment to determine that the diameter of the transparent ball is set to be 20 cm, so that the required geometrical body has the following edge length by calculation:

the edge length of the cube is

The face of the cube is diagonal to

The body diagonal of the cube is

The first triangular pyramid 23, the second triangular pyramid 24, the third triangular pyramid 25, the regular tetrahedron 26, the quadrangular pyramid 27 and the right triangular prism 28 shown in fig. 2 to 8 are actually part of a cube, so the edge lengths thereof can be respectively denoted by a, b and c in the figures.

And drawing the bottom surface and the side surface of the needed geometric body on the color card paper according to the edge length, cutting the bottom surface and the side surface, and bonding the bottom surface and the side surface by using glue or adhesive tapes.

In practical teaching, there are uses as follows:

example 1: guiding students to search the external sphere center of the cube and calculating the radius of the external sphere of the cube. Eight vertexes of a cube in the displayed model ball are all arranged on the spherical surface, and the ball is the external sphere of the cube. Since the eight vertices of the cube are on the sphere, the distances from the eight vertices to the center of the sphere should be equal and equal to the radius. At which point is the center of the ball? The diagonal surface of the cube is a rectangle, and the diagonals of the rectangle are bisected by each other, so that the intersection point of the two diagonals has equal distance to the four vertexes. Other body diagonal surfaces have the same properties, as well. Thus, this intersection point is the center of the cube circumscribing the ball.

Students can understand what the external ball of the geometric body is through the visual perception, which is helpful to develop the space imagination of the students. The students further deepen understanding through actual operations.

At the moment, the external sphere center and the radius of the cube with the edge length of 2 cm are solved, the intersection point of the diagonal lines of the cube is the sphere center, and the radius is

Centimeters.

Example 2, problem: please ask students to splice a cube with the geometry given by the teacher and think how many different possibilities are in the process of splicing the cube? We find out what relationship between these geometric bodies and cubes after we splice these geometric bodies into cubes?

In fact, these geometries are all part of a cube.

Continuing to show the teaching model, the teacher puts the used small geometry into the transparent model to find that they all have the same external ball. And is also in the same circumscribed sphere with the cube. When the external sphere radius is obtained, the external sphere radius can be obtained by firstly supplementing the external sphere radius to a cube having the same external sphere as the external sphere radius.

Students can feel more intuitively through actual manual operation, and the relation between the related geometry of the cube and the cube is more obvious. It is known which part of the cube these geometries are. The learning condition of the student is checked through practice. The students can disperse the thinking to the cuboid through practice.

The utility model discloses the people realizes in daily teaching, and the external ball problem of space geometry is the focus of the examination of college entrance in recent years, and this type of theme is more abstract to the student, and the difficult cut-in point and the breach of finding the solution problem for this reason, this part content will utilize teaching mould key explanation square and the external ball's of the relevant geometry of square relation and radial method of seeking. Therefore, the volume and surface area formula of the sphere can be clearly remembered, the relation between the radius of the sphere and the cube connected in the sphere can be mastered, and the related geometry of the cube can be reduced into a cube. It is known what the relevant geometry of the cube is. The method for obtaining the external ball-catching of the cube related geometry can be mastered, and the generation process that the cube related geometry and the cube have the same external ball-catching process can be understood. The spatial imagination ability of students is fully exerted, the learned knowledge is correctly expanded through the exploration process of the external sphere radius, and the model is built in time to summarize the learned content, so that the knowledge module system is perfectly built. The capability of training the mathematical modeling and visual imagination of students.

Example 2

Example 2 contains all the technical features of example 1, except that a second scheme of splicing into a cube by geometric bodies is given, for example, fig. 11, and the cube 3 is spliced by a second triangular pyramid 34, a quadrangular pyramid 37 and a right triangular prism 38, for example, fig. 12 shows an explosion diagram of the cube 3.

Example 3

Example 3 contains all the technical features of example 1, except that a third solution is given for the splicing of cubes by means of geometric bodies, as in fig. 13, the cube 3 being spliced by means of four identical first

triangular pyramids

331, 332, 333, 334 and a regular tetrahedron 36, as in fig. 14, the exploded view of the cube 3 being given.

It is above only the utility model discloses a preferred embodiment, the utility model discloses a scope of protection does not only confine above-mentioned embodiment, the all belongs to the utility model discloses a technical scheme under the thinking all belongs to the utility model discloses a scope of protection. It should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims

1. A cube-related teaching model of spatial geometry is characterized by comprising a sphere and a geometry;

2. A cube-related teaching aid as claimed in claim 1 wherein said geometry comprises: a first triangular pyramid, a second triangular pyramid, a third triangular pyramid, a regular tetrahedron, a rectangular pyramid, a right triangular prism and a cube.

3. A cube-related teaching aid as claimed in claim 2 wherein said transparent sphere comprises a first plastic hemisphere and a second plastic hemisphere, said first plastic hemisphere and said second plastic hemisphere being removably connected to form said transparent sphere.

4. A teaching aid as claimed in claim 3 wherein said cubes are of the same length by selecting a plurality of geometric shapes from said first triangular pyramid, said second triangular pyramid, said third triangular pyramid, said regular tetrahedron, said rectangular pyramid, and said right triangular prism.

5. A cube-related spatial geometry teaching aid according to claim 4 wherein the cube is a hollow box with a lid at the top of the cube, the lid being removably attachable to the cube.

6. A teaching aid for a spatial geometry associated with a cube as claimed in claim 5 wherein the first triangular pyramid, the second triangular pyramid, the third triangular pyramid, the regular tetrahedron, the quadrangular pyramid, the right triangular prism are disposed within the cube and the respective vertices of the first triangular pyramid, the second triangular pyramid, the third triangular pyramid, the regular tetrahedron, the quadrangular pyramid, the right triangular prism coincide with the vertices of the cube.