A mechanical device for teaching linear algebra

Abstract

The invention relates to the field of teaching tools and discloses a mechanical device for teaching linear algebra, comprising a demonstration frame composed of three groups of horizontal plates and a deformable soft ellipsoid, the three groups of horizontal plates being fixedly installed vertically to each other so as to form a three-dimensional coordinate system for the demonstration frame, a suspended soft ellipsoid being provided at the center of the demonstration frame through mounting members on three inner walls, multiple groups of horizontal groove tubes being installed at the centers of the three inner walls of the demonstration frame, driven push rods extending on both sides of the horizontal plates being slidably sleeved in the multiple groups of horizontal groove tubes, end face outer walls of the multiple groups of driven push rods on the three groups of horizontal plates being fitted with the outer wall of the soft ellipsoid, active push rods being fixedly installed on the end face outer wall of the multiple groups of driven push rods extending outside the demonstration frame, the multiple groups of active push rods being connected to each other through different connecting mechanisms, the device can intuitively demonstrate the concept of matrix in linear algebra, and is conducive to better learning for students.

Description

Technical Field

[0001] The present invention relates to the field of teaching tools, in particular to a mechanical device for teaching linear algebra. Background Art

[0002] Linear algebra is a branch of mathematics concerned with vector spaces and linear mappings. It includes the study of lines, surfaces, and subspaces, and also touches on the general properties of all vector spaces. Linear algebra is at the core of both pure and applied mathematics. Its meaning has continuously expanded with the development of mathematics, and its theories and methods have permeated many branches of mathematics. It has also become an indispensable algebraic foundation for theoretical physics and theoretical chemistry. Linear algebra is a branch of algebra that primarily deals with linear relationships. A linear relationship refers to the relationship between mathematical objects expressed in a linear form. For example, in analytic geometry, the equation of a line on a plane is a linear equation in two variables, while the equation of a plane in space is a linear equation in three variables. However, existing advanced mathematics teaching aids lack effective tools that allow students to intuitively understand the concepts of space vectors and matrices in linear algebra, as well as the transformations between space vectors and matrices. This hinders students' learning of linear algebra. To address this issue, we propose a mechanical device for teaching linear algebra. Summary of the Invention

[0003] (1) Technical problems solved

[0004] In view of the deficiencies in the prior art, the present invention provides a mechanical device for teaching linear algebra, which solves the above-mentioned problems.

[0005] (2) Technical solution

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solutions: a mechanical device for teaching linear algebra, comprising a demonstration frame composed of three groups of horizontal plates and a deformable soft ellipsoid, the three groups of horizontal plates being fixedly installed vertically to each other so that the demonstration frame forms a three-dimensional coordinate system, a suspended soft ellipsoid is provided at the inner center of the demonstration frame through mounting parts on three inner walls, multiple groups of horizontal groove tubes are installed at the centers of the three inner walls of the demonstration frame, multiple groups of horizontal groove tubes are slidably sleeved with driven push rods extending on both sides of the horizontal plates, the end face outer walls of the multiple groups of driven push rods on the three groups of horizontal plates are all in contact with the outer wall of the soft ellipsoid, the multiple groups of driven push rods are fixedly installed with active push rods on the end face outer wall extending outside the demonstration frame, and the multiple groups of active push rods are connected to each other by a connecting mechanism.

[0007] Preferably, the driven push rods arranged on the three inner walls of the demonstration frame are perpendicular to each corresponding set of horizontal plates, and an umbrella-shaped soft head is fixedly installed on the outer wall of the end face of the driven push rod corresponding to the soft ellipsoid, and the length of the driven push rod is greater than that of the active push rod.

[0008] Preferably, the multiple groups of transverse groove through-tubes provided on the inner wall of each group of the transverse plates are arranged in a matrix, with the number of rows being at least eight and the number of columns also being at least eight.

[0009] Preferably, the connecting mechanism includes an annular connecting groove and a connecting piece. At least four groups of equidistantly arranged annular connecting grooves are provided on the outer wall of the active push rod, and the annular connecting grooves are inwardly concave. Each adjacent group of active push rods is connected to the active push rods by a connecting piece that is sleeved on the annular connecting groove. The active push rod can be connected to the four adjacent groups of active push rods on all sides through the connecting mechanism to form a cross shape, or connected to the three adjacent groups of active push rods to form a square shape.

[0010] Preferably, the active push rod and the adjacent active push rod are connected via a connecting mechanism to form an annular connecting groove opened at the same position, or to form an annular connecting groove opened at different positions.

[0011] Preferably, the connecting member is an elastic rope, and the elastic rope end is provided with an annular sleeve for being sleeved in the annular connecting groove.

[0012] Preferably, the connecting member is a chain composed of multiple groups of arc-shaped fasteners, and at least four groups of connecting rings are fixedly installed on the inner wall of the annular connecting groove. Each adjacent group of active push rods is connected to the active push rods by chain buckling on the connecting ring. The two groups of arc-shaped fasteners are provided with the same annular buckle groove, and the corresponding two ends of the arc-shaped fasteners are provided with symmetrical arc-shaped buckle heads through elastic members. The elastic member includes a sleeve rod 1 and a sleeve rod 2 that are slidably sleeved together, and the outer wall of the end face of the sleeve rod 1 facing away from the sleeve rod 2 is fixedly installed on the inner wall of the buckle head, and the outer wall of the end face of the sleeve rod 2 facing away from the sleeve rod 1 is fixedly installed on the inner wall of the annular buckle groove, and a spring is fixedly connected to the inner walls of the end faces of the sleeve rod 1 and the sleeve rod 2 that are close to each other, and the elastic member is arranged on the horizontal center line of the annular buckle groove.

[0013] Preferably, the active push rod is connected to the separated active push rods through an arc-shaped fastener.

[0014] (3) Beneficial effects

[0015] Compared with the prior art, the present invention provides a mechanical device for teaching linear algebra, which has the following beneficial effects:

[0016] 1. In this mechanical device for teaching linear algebra, the driven push rods arranged on the three inner walls of the demonstration frame are perpendicular to each corresponding set of horizontal plates, and an umbrella-shaped soft head is fixedly installed on the outer wall of the driven push rod corresponding to the end surface that fits the soft ellipsoid. This ensures that the surface of the soft ellipsoid is not damaged when it is squeezed and deformed. At the same time, the convex point of the soft ellipsoid's deformation is not a sharp point, but a rounded arc, which improves the aesthetics of the device during demonstration.

[0017] 2. The length of the driven push rod of the mechanical device for linear algebra teaching is greater than that of the active push rod; when the active push rod is pushed to extrude the soft ellipsoid, only the driven push rod always moves on the wall of the horizontal plate, and the active push rod always remains on the outside of the demonstration frame and does not enter the horizontal groove pipe, thereby improving the practicality of the device.

[0018] 3. This mechanical device for teaching linear algebra uses active push rods arranged in a matrix to push and squeeze the soft ellipsoid to deform, which can intuitively demonstrate the concept of space vectors in linear algebra.

[0019] 4. This mechanical device for teaching linear algebra increases the randomness of demonstration results by making different changes to the connection mechanism between the active push rods, allowing students to intuitively and better grasp the concept of matrices in linear algebra.

[0020] 5. This mechanical device for teaching linear algebra allows teachers to push the active push rods on the horizontal plate in different directions, causing the driven push rods to squeeze the surface of the soft ellipsoid, causing the soft ellipsoid to deform irregularly. The propulsion of multiple groups of driven push rods and active push rods can replace the space vector group in the three-dimensional coordinate system, allowing students to intuitively feel the results brought about by the changes in the space vector group in linear algebra, and have a deeper understanding of the concept of matrix in linear algebra.

[0021] 6. The mechanical device used for teaching linear algebra only needs to pull the buckle head to both sides to drive the sleeve rod to slide along the sleeve rod, and at the same time cause the spring to deform, so that the buckle head and the arc-shaped fastener are separated, and the two sets of chains can be separated or interlocked, which is convenient for increasing or decreasing the length of the chain connecting the active push rod and other active push rods, improving the demonstration performance of the device, and facilitating teachers to demonstrate the device for different matrices. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a schematic diagram of the structure of the present invention;

[0023] Figure 2 This is a schematic diagram of the structure of the demonstration frame of the present invention;

[0024] Figure 3 This is a schematic structural diagram of the connecting mechanism of the present invention;

[0025] Figure 4 This is a schematic structural diagram of the connecting mechanism of the present invention;

[0026] Figure 5 This is a schematic structural diagram of the connecting mechanism of the present invention;

[0027] Figure 6 This is a schematic diagram of the active push rod of the present invention;

[0028] Figure 7 Schematic diagram of the chain structure of the present invention;

[0029] Figure 8 This is a schematic diagram of the arc-shaped fastener structure of the present invention;

[0030] Figure 9 It is a cross-sectional schematic diagram of the sleeve rod of the present invention.

[0031] In the figure: 1. Demonstration stand; 2. Horizontal board; 3. Horizontal groove pipe; 4. Soft ellipsoid; 5. Driven push rod; 6. Active push rod; 7. Soft head; 8. Connecting mechanism; 9. Annular connecting groove; 10. Connecting piece; 11. Connecting ring; 12. Chain; 13. Arc-shaped fastener; 14. Annular buckle groove; 15. Buckle head; 16. Sleeve rod 1; 17. Sleeve rod 2; 18. Spring. DETAILED DESCRIPTION

[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0033] See also Figure 1-9 A mechanical device for teaching linear algebra includes a demonstration frame 1 composed of three groups of horizontal plates 2 and a deformable soft ellipsoid 4. The three groups of horizontal plates 2 are fixedly installed vertically to each other so that the demonstration frame 1 forms a three-dimensional coordinate system. A suspended soft ellipsoid 4 is provided at the center of the inner center of the demonstration frame 1 through mounting parts on the three inner walls. Multiple groups of horizontal groove tubes 3 are installed at the centers of the three inner walls of the demonstration frame 1. The multiple groups of horizontal groove tubes 3 are slidably sleeved with driven push rods 5 extending on both sides of the horizontal plates 2. The end outer walls of the multiple groups of driven push rods 5 on the three groups of horizontal plates 2 are all in contact with the outer wall of the soft ellipsoid 4. Active push rods 6 are fixedly installed on the end outer wall of the outer side of the multiple groups of driven push rods 5, and the multiple groups of active push rods 6 are connected to each other through a connecting mechanism 8.

[0034] Furthermore, the driven push rods 5 arranged on the three inner walls of the demonstration frame 1 are perpendicular to each corresponding group of horizontal plates 2, and the driven push rods 5 are fixedly installed with an umbrella-shaped soft head 7 on the outer wall of the end surface corresponding to the soft ellipsoid 4, ensuring that the surface of the soft ellipsoid 4 will not be damaged when the soft ellipsoid 4 is squeezed and deformed, and at the same time, the convex point of the soft ellipsoid 4 deformation is not a tip, but a rounded arc, which improves the aesthetics of the device during demonstration. The length of the driven push rod 5 is greater than that of the active push rod 6; when the active push rod 6 is pushed to squeeze the soft ellipsoid 4 to deform, only the driven push rod 5 moves on the wall of the horizontal plate 2, and the active push rod 6 always remains on the outside of the demonstration frame 1 and does not enter the horizontal groove through pipe 3.

[0035] Furthermore, the multiple groups of transverse groove through-tubes 3 provided on the inner wall of each group of transverse plates 2 are arranged in a matrix, with the number of rows being at least eight and the number of columns also being at least eight.

[0036] Furthermore, the connecting mechanism 8 includes an annular connecting groove 9 and a connecting piece 10. At least four groups of equidistantly arranged annular connecting grooves 9 are provided on the outer wall of the active push rod 6, and the annular connecting grooves 9 are concave inward. Each adjacent group of active push rods 6 is connected to the active push rods 6 by a connecting piece 10 that is sleeved on the annular connecting groove 9. The active push rod 6 can be connected to the four adjacent groups of active push rods 6 on all sides through the connecting mechanism 8 to form a cross shape, or connected to the three adjacent groups of active push rods 6 to form a square.

[0037] Furthermore, the active push rod 6 and the adjacent active push rod 6 are connected by a connecting mechanism 8 to form an annular connecting groove 9 opened at the same position, or to form an annular connecting groove 9 opened at different positions.

[0038] Furthermore, the connecting member 10 is an elastic rope, and the elastic rope end is provided with an annular sleeve for being sleeved in the annular connecting groove 9 .

[0039] Furthermore, the connecting member 10 is a chain 12 composed of multiple groups of arc-shaped fasteners 13, and at least four groups of connecting rings 11 are fixedly installed on the inner wall of the annular connecting groove 9. Each adjacent group of active push rods 6 is connected to the active push rods 6 by the chain 12. The two groups of arc-shaped fasteners 13 are provided with the same annular buckle groove 14. The arc-shaped fasteners 13 are provided with symmetrical arc-shaped buckle heads 15 at the corresponding two ends through elastic members. The elastic member includes a sleeve rod 16 and a sleeve rod 2 17 that are slidably sleeved together. The outer wall of the end face of the sleeve rod 16 away from the sleeve rod 2 17 is fixed on the inner wall of the buckle head 15, and the outer wall of the end face of the sleeve rod 2 17 away from the sleeve rod 1 16 is fixed. Installed on the inner wall of the annular buckle groove 14, the sleeve rod 16 and the sleeve rod 2 17 are both closed at one end and open at the other end, and the ends facing away from each other are closed ends, and a spring 18 is fixedly connected to the inner wall of the end surface of the sleeve rod 16 and the sleeve rod 2 17 that are close to each other, and the elastic member is arranged on the horizontal center line of the annular buckle groove 14; when the chain 12 is separated or interlocked with the chain 12, it is only necessary to pull the buckle head 15 to both sides to drive the sleeve rod 16 to slide along the sleeve rod 2 17, and at the same time cause the deformation of the spring 18, so that the buckle head 15 is separated from the arc-shaped fastener 13, and the separation or interlocking of the two groups of chains 12 can be completed; the active push rod 6 can be connected to the separated active push rod 6 through the arc-shaped fastener 13.

[0040] Working principle: When demonstrating linear concepts in class, the teacher can push the active push rods 6 on the horizontal board 2 in different directions to make the driven push rods 5 squeeze the surface of the soft ellipsoid 4, causing the soft ellipsoid 4 to undergo irregular deformation. The propulsion of multiple groups of driven push rods 5 and active push rods 6 can replace the space vector group in the three-dimensional coordinate system, so that students can intuitively feel the results of the changes in the space vector group in linear algebra, and have a deeper understanding of the concept of matrix in linear algebra. At the same time, each group of active push rods 6 is connected to the active push rods 6 by a connecting piece 10. When one group of active push rods 6 is pushed, multiple groups of active push rods 6 can be driven to move at the same time, and the connecting piece 10 connecting the active push rods 6 and the active push rods 6 can be used as the connecting piece. When the elastic rope is used or the connecting member 10 is an arc-shaped fastener 13, it is clearly observed that the different degrees of linkage of multiple groups of active push rods 6 cause different deformations of the soft ellipsoid 4, which intuitively reflects the changes in the vector group in linear algebra. The results can also be changed by the annular connection groove 9 at the connection between the active push rods 6 and the active push rods 6 being in the same position or different positions. The device can intuitively demonstrate the concept of space vectors in linear algebra by pushing and squeezing the soft ellipsoid 4 through multiple active push rods 6 arranged in a matrix, and at the same time, the randomness of the demonstration results is increased by different changes in the connection mechanism 8 between the active push rods 6, so that students can intuitively and better understand the concept of matrices in linear algebra. When the chain 12 is separated or interlocked with the chain 12, it is only necessary to pull the buckle 15 to the sides to drive the sleeve rod 16 to slide along the sleeve rod 2 17, while causing the deformation of the spring 18, so that the buckle 15 and the arc-shaped fastener 13 are separated, and the separation or interlocking of the two groups of chains 12 can be completed.

[0041] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A mechanical device for teaching linear algebra, comprising a demonstration stand (1) consisting of three sets of horizontal plates (2) and a deformable soft ellipsoid (4), characterized in that: The three groups of transverse plates (2) are fixedly installed vertically to each other and form a three-dimensional coordinate system for the demonstration frame (1). A suspended soft ellipsoid (4) is provided at the center of the interior of the demonstration frame (1) through mounting members on three inner walls. Multiple groups of transverse groove tubes (3) are installed at the centers of the three inner walls of the demonstration frame (1). The multiple groups of transverse groove tubes (3) are slidably sleeved with driven push rods (5) extending on both sides of the transverse plates (2). The end surface outer walls of the multiple groups of driven push rods (5) on the three groups of transverse plates (2) are all fitted with the outer wall of the soft ellipsoid (4). Active push rods (6) are fixedly installed on the end surface outer wall of the multiple groups of driven push rods (5) extending outside the demonstration frame (1). The multiple groups of active push rods (6) are connected to each other through a connecting mechanism (8). The connecting mechanism (8) includes an annular connecting groove (9) and a connecting piece (10). At least four groups of annular connecting grooves (9) arranged at equal intervals are provided on the outer wall of the active push rod (6), and the annular connecting grooves (9) are inwardly concave. Each adjacent group of active push rods (6) is connected to the active push rods (6) by the connecting piece (10) sleeved on the annular connecting groove (9). The active push rod (6) can be connected to the four adjacent groups of active push rods (6) in a cross shape or connected to the three adjacent groups of active push rods (6) in a square shape through the connecting mechanism (8). The active push rod (6) and the adjacent active push rod (6) are connected via a connecting mechanism (8) to form an annular connecting groove (9) opened at the same position, or to form an annular connecting groove (9) opened at different positions.

2. A mechanical device for teaching linear algebra according to claim 1, characterized in that: The driven push rods (5) arranged on the three inner walls of the demonstration frame (1) are perpendicular to each corresponding set of horizontal plates (2), and an umbrella-shaped soft head (7) is fixedly installed on the outer wall of the end surface of the driven push rod (5) corresponding to the soft ellipsoid (4), and the length of the driven push rod (5) is greater than the length of the active push rod (6).

3. The mechanical device for teaching linear algebra according to claim 1, characterized in that: The multiple groups of transverse groove through pipes (3) provided on the inner wall of each group of transverse plates (2) are arranged in a matrix, with the number of rows being at least eight and the number of columns also being at least eight.

4. The mechanical device for teaching linear algebra according to claim 1, characterized in that: The connecting piece (10) is an elastic rope, and the elastic rope end is provided with an annular sleeve for being sleeved in the annular connecting groove (9).

5. The mechanical device for teaching linear algebra according to claim 1, characterized in that: The connecting member (10) is a chain (12) composed of multiple groups of arc-shaped fasteners (13) interlocked with each other, at least four groups of connecting rings (11) are fixedly installed on the inner wall of the annular connecting groove (9), and each adjacent group of active push rods (6) are connected to the connecting ring (11) by the chain (12), and the two groups of the arc-shaped fasteners (13) are provided with the same annular buckle groove (14), and the corresponding two ends of the arc-shaped fasteners (13) are provided with symmetrical arc-shaped buckle heads (11) through elastic members. 5), the elastic member comprises a sleeve rod 1 (16) and a sleeve rod 2 (17) which are slidably sleeved together, the outer wall of the end face of the sleeve rod 1 (16) away from the sleeve rod 2 (17) is fixedly mounted on the inner wall of the buckle head (15), the outer wall of the end face of the sleeve rod 2 (17) away from the sleeve rod 1 (16) is fixedly mounted on the inner wall of the annular buckle groove (14), and a spring (18) is fixedly connected to the inner walls of the end faces of the sleeve rod 1 (16) and the sleeve rod 2 (17) which are close to each other, and the elastic member is arranged on the horizontal center line of the annular buckle groove (14).

6. The mechanical device for teaching linear algebra according to claim 5, characterized in that: The active push rod (6) is connected to the spaced active push rod (6) via an arc-shaped fastener (13).

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