CN110675706A - Linear transformation principle demonstration device - Google Patents
Linear transformation principle demonstration device Download PDFInfo
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- CN110675706A CN110675706A CN201911055740.4A CN201911055740A CN110675706A CN 110675706 A CN110675706 A CN 110675706A CN 201911055740 A CN201911055740 A CN 201911055740A CN 110675706 A CN110675706 A CN 110675706A
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- 230000009466 transformation Effects 0.000 title claims abstract description 34
- 235000013290 Sagittaria latifolia Nutrition 0.000 claims description 14
- 235000015246 common arrowhead Nutrition 0.000 claims description 14
- XEEYBQQBJWHFJM-UHFFFAOYSA-N Iron Chemical compound [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 claims description 6
- 230000000149 penetrating effect Effects 0.000 claims description 6
- 229910052742 iron Inorganic materials 0.000 claims description 3
- 230000001747 exhibiting effect Effects 0.000 claims 2
- 230000008859 change Effects 0.000 description 8
- 238000013507 mapping Methods 0.000 description 3
- 230000009471 action Effects 0.000 description 2
- 239000011159 matrix material Substances 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
- G09B23/04—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics for geometry, trigonometry, projection or perspective
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Abstract
The invention relates to a linear transformation principle demonstration device, which comprises a demonstration board, a rotating frame and a demonstration arrow, wherein the rotating frame is hinged on the front surface of the demonstration board, the demonstration arrow is connected on the front surface of the rotating frame, the front surface of the demonstration board is provided with a two-dimensional coordinate system line, the rotating frame is a latticed frame formed by mutually hinging a plurality of cross rods and a plurality of vertical rods, the central point of the rotating frame is hinged with the origin of the demonstration board, the hinged parts of the cross rods and the vertical rods except the central point of the rotating frame are provided with first through holes, first connecting rods are arranged in the first through holes, the hinged parts of the central point of the rotating frame and the origin of the demonstration board are respectively provided with second through holes, second connecting rods are arranged in the second through holes, the demonstration arrow consists of an initial block, an elastic belt and an arrow body, the elastic belt is connected between the initial block and the arrow body, and aims to solve the problem that the linear transformation, students cannot easily understand the problem of the linear transformation principle.
Description
Technical Field
The invention relates to the technical field of teaching aids, in particular to a linear transformation principle demonstration device.
Background
Linear mapping, which is a mapping from one vector space V to another vector space W and holds addition operations and number multiplication operations, whereas linear transformation is a linear mapping of the linear space V to itself.
The meaning of matrix multiplication is that one vector is input, and after a certain function (matrix) is passed, the output becomes another vector. Transformation means that the original vector is moved (transformed) to another place. Linear transformation, that is, on the basis of transformation, a condition is added, and linear transformation, that is, an original straight line, after transformation, should be a straight line, and the origin remains fixed.
The linear transformation concept in advanced mathematics is abstract and difficult to understand, teachers mainly use blackboard writing to explain the contents of linear transformation, the principle of linear transformation cannot be intuitively demonstrated, students are difficult to understand, and learning interest is easily lost.
Disclosure of Invention
Aiming at the problems that linear transformation in advanced mathematics is difficult to visually demonstrate and students are difficult to understand the principle of linear transformation in the prior art, the linear transformation principle demonstrating device is provided, the principle of linear transformation is intuitively demonstrated, and the students can conveniently understand the principle.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a linear transformation principle demonstration device comprises a demonstration board, a rotating frame and a demonstration arrow, wherein the rotating frame is hinged to the front surface of the demonstration board, and the demonstration arrow is connected to the front surface of the rotating frame;
the front surface of the display board is provided with a two-dimensional coordinate system line, the two-dimensional coordinate system line comprises an origin, an X-axis line and a Y-axis line, the X-axis line is a horizontal axis, the Y-axis line is a vertical axis orthogonal to the X-axis line, and the origin is a point where the X-axis line and the Y-axis line intersect;
the rotary frame is a latticed frame formed by mutually hinging a plurality of transverse rods and a plurality of vertical rods, each crossing part of the transverse rods and the vertical rods is hinged, the crossing part of the center of the transverse rods and the center of the vertical rods in the middle of the rotary frame is the center point of the rotary frame, the center point of the rotary frame is hinged with the origin of the display board, when the transverse rods are in a horizontal state and the transverse rods and the vertical rods are mutually vertical, the transverse rods and the X-axis strips in the middle of the rotary frame correspond to each other in the front-back direction, the hinging parts of the transverse rods and the vertical rods except the center point of the rotary frame are provided with first through holes corresponding in the front-back direction, first connecting rods penetrating in the transverse rods and the vertical rods are arranged in the first through holes, the outer sides of two ends of the first connecting rods are respectively provided with front cylinders and rear cylinders clamped outside the transverse rods and the vertical rods (the outer sides of the front sides, second through holes corresponding to the front and the back are respectively formed in the hinged positions of the central point of the rotating frame and the origin of the display board, second connecting rods penetrating the central point of the rotating frame and the origin of the display board are arranged in the second through holes, and a central front cylinder and a central rear cylinder clamped on the outer sides of the cross rod and the display board (the outer sides of the two ends of each second connecting rod respectively refer to the outer sides of the front of the cross rod and the outer sides of the back of the display board) are respectively arranged on the outer sides of the two ends of each second connecting rod;
the show arrow head comprises originated piece, elastic webbing and arrow head body, be provided with the first mounting hole of cover in the anterior cylinder periphery in center on the originated piece, be provided with the second mounting hole of cover in the anterior cylinder periphery of the articulated department of arbitrary one horizontal pole and montant except the central point of rotating frame on the arrow head body, connect the elastic webbing between originated piece and the arrow head body.
Further, the display board is a square plate body made of iron.
Further, a magnet is arranged on the back of a rear cylinder at the hinge joint of 4 corners of the rotating frame.
Furthermore, the back surface of the magnet is tightly attached to the front surface of the display board.
Further, the arrow head body is a triangular plate body, and the vertex direction of the triangular plate body is the same as the extending direction of the joint of the starting block and the elastic belt to the joint of the elastic belt and the arrow head body.
Further, the diameter of the first link is smaller than the diameters of the front and rear cylinders, the centers of the first link, the front and rear cylinders are in a front-rear correspondence state, the diameter of the second link is smaller than the diameters of the central front and rear cylinders, and the centers of the second link, the central front and rear cylinders are in a front-rear correspondence state.
Further, the elastic band is a cylindrical elastic body or a band-shaped elastic body made of rubber.
Further, the starting block is a sheet-shaped round or square plate body.
Further, the rotatory frame is arranged in the plane that the two-dimensional coordinate system line of show board constitutes (the upper end of rotatory frame is in the upper end below of Y axis line promptly, the lower extreme of rotatory frame is in the lower extreme top of Y axis line, the left side of rotatory frame is on the left end right side of X axis line, the right side of rotatory frame is on the right-hand member left side of X axis line), the length of horizontal pole and montant is the same, the net in the latticed frame that a plurality of horizontal poles and a plurality of montants articulated each other constitute is the equal equilateral quadrangle of size, the rotatory frame is that horizontal pole and montant articulate each other into deformable prism or square latticed frame.
Further, the rotating frame is in a static state or in a rotating state around the second connecting rod on the front surface of the display board.
Through the technical scheme, the invention has the beneficial effects that:
the display board of the invention is fixed on a blackboard or a vertical display wall in a classroom, a rotating frame is rotated by hands until a cross bar in the middle of the rotating frame corresponds to an X-axis bar in the front-back direction, a vertical bar in the middle of the rotating frame corresponds to a Y-axis bar in the front-back direction, a first mounting hole of a display arrow is sleeved on the periphery of a cylinder in the front of the center, a second mounting hole is sleeved on the periphery of a cylinder in the front of the hinged part of any cross bar and any vertical bar except the center point of the rotating frame, the display arrow represents an input vector, then the rotating frame is manually rotated or the cross bar and the vertical bar of the rotating frame are subjected to angle change (because the rotating frame is formed by mutually hinging a plurality of cross bars and a plurality of vertical bars, the cross bars and the vertical bars can be subjected to angle change under the action of an external force), the motion change represents that the input vector is multiplied by, the invention more intuitively demonstrates the linear transformation principle in advanced mathematics, facilitates understanding of students on linear transformation and improves learning interest of students.
Drawings
FIG. 1 is a front view of the present invention;
FIG. 2 is a cross-sectional view of FIG. 1A-A;
FIG. 3 is a front view of the display board of the present invention;
FIG. 4 is a front view of the present invention showing arrows;
FIG. 5 is a rear view of the rotating frame of the present invention;
fig. 6 is an enlarged schematic view of fig. 2B.
The reference numbers in the drawings are as follows: 1 is the show board, 2 is the revolving frame, 3 is the show arrow point, 10 is the two-dimensional coordinate system lines, 20 is the horizontal pole, 21 is the montant, 22 is first through-hole, 23 is the second through-hole, 30 is the starting block, 31 is the elastic webbing, 32 is the arrowhead body, 100 is the original point, 101 is the X axis lines, 102 is the Y axis lines, 200 is the rear cylinder, 201 is the front cylinder, 202 is the first connecting rod, 203 is magnet, 230 is the center rear cylinder, 231 is the center front cylinder, 232 is the second connecting rod, 300 is first mounting hole, 320 is the second mounting hole.
Detailed Description
The invention is further described with reference to the following figures and detailed description:
as shown in fig. 1 to 6, the linear transformation principle demonstration apparatus comprises a display board 1, a rotating frame 2 and a display arrow 3, wherein the rotating frame 2 is hinged on the front surface of the display board 1, and the display arrow 3 is connected on the front surface of the rotating frame 2.
The front surface of the display board 1 is provided with a two-dimensional coordinate system line 10, the two-dimensional coordinate system line 10 includes an origin 100, an X-axis line 101 and a Y-axis line 102, the X-axis line 101 is a horizontal axis, the Y-axis line 102 is a vertical axis orthogonal to the X-axis line 101, and the origin 100 is a point where the X-axis line 101 and the Y-axis line 102 intersect.
The rotating frame 2 is a latticed frame formed by mutually hinging a plurality of transverse rods 20 and a plurality of vertical rods 21, each crossing part of the transverse rods 20 and the vertical rods 21 is hinged, the crossing part of the center of the transverse rod 20 and the center of the vertical rod 21 in the middle of the rotating frame 2 is the center point of the rotating frame 2, the center point of the rotating frame 2 is hinged to the original point 100 of the display board 1, when the transverse rods 20 are in a horizontal state and the transverse rods 20 and the vertical rods 21 are mutually perpendicular, the transverse rods 20 and the X-axis strips 101 in the middle of the rotating frame 2 correspond to each other in the front and back direction, the vertical rods 21 and the Y-axis strips 102 in the middle of the rotating frame 2 correspond to each other in the front and back direction, first through holes 22 corresponding to each other in the front and back direction are arranged at the hinging parts of the transverse rods 20 and the vertical rods 21 except the center point of the rotating frame 2, first connecting rods 202 penetrating through holes 202 are arranged in the transverse rods 20 and the vertical rods 21, and the outer Rear outer side), a second through hole 23 corresponding to the front and rear is respectively arranged at the hinged position of the central point of the rotating frame 2 and the origin 100 of the display board 1, a second connecting rod 232 penetrating the central point of the rotating frame 2 and the origin 100 of the display board 1 is arranged in the second through hole 23, and a central front cylinder 231 and a central rear cylinder 230 clamped at the outer sides of the cross bar 20 and the display board 1 (the outer sides of the two ends of the second connecting rod 232 refer to the front outer side of the cross bar 20 and the rear outer side of the display board 1 respectively) are respectively arranged at the outer sides of the two ends of the second connecting rod 232.
The display board 1 is a square plate body made of iron.
The back of the rear cylinder 200 at the hinge of 4 corners of the rotating frame 2 is provided with a magnet 203.
The back surface of the magnet 203 is closely attached to the front surface of the display board 1.
The arrow head body 32 is a triangular plate body, and the vertex direction of the triangular plate body is the same as the extending direction of the joint of the starting block 30 and the elastic belt 31 to the joint of the elastic belt 31 and the arrow head body 32.
The diameter of the first link 202 is smaller than the diameters of the front and rear cylinders 201 and 200, the centers of the first link 202, the front cylinder 201 and the rear cylinder 200 are in a front-rear correspondence, the diameter of the second link 232 is smaller than the diameters of the central front cylinder 231 and the central rear cylinder 230, and the centers of the second link 232, the central front cylinder 231 and the central rear cylinder 230 are in a front-rear correspondence.
The elastic band 31 is a cylindrical elastic body or a band-shaped elastic body made of rubber.
The starting block 30 is a sheet-shaped circular or square plate.
The plane that two-dimensional coordinate system lines 10 of show board 1 constitutes is arranged in to revolving frame 2 (namely the upper end of revolving frame 2 is in the upper end below of Y axis line 102, the lower extreme of revolving frame 2 is in the lower extreme top of Y axis line 102, the left side of revolving frame 2 is on the left end right side of X axis line 101, the right side of revolving frame 2 is on the right-hand member left side of X axis line 101), horizontal pole 20 is the same with montant 21's length, the net in the latticed frame that a plurality of horizontal poles 20 and a plurality of montant 21 articulated each other constitution is the same equilateral quadrangle of size, revolving frame 2 articulates into deformable prism or square latticed frame for horizontal pole 20 and montant 21 each other.
The rotating frame 2 is in a stationary state or in a rotating state around the second connecting rod 232 on the front surface of the display board 1.
The display board 1 of the invention is fixed on a blackboard or a vertical display wall in a classroom, a rotating frame 2 is rotated by hands until a cross bar 20 at the middle part of the rotating frame 2 corresponds to an X-axis strip 101 in the front and back direction, a vertical bar 21 at the middle part of the rotating frame 2 corresponds to a Y-axis strip 102 in the front and back direction, a first mounting hole 300 for displaying an arrow 3 is sleeved on the periphery of a central front cylinder 231, a second mounting hole 320 is sleeved on the periphery of a front cylinder 201 at the hinged part of any cross bar 20 and any vertical bar 21 except the central point of the rotating frame 2, the displaying arrow 3 represents an input vector, then the rotating frame 2 is manually rotated or the cross bar 20 and the vertical bar 21 of the rotating frame 2 are subjected to angle change (because the rotating frame 2 is formed by mutually hinging a plurality of cross bars 20 and a plurality of vertical bars 21, the cross bars 20 and the vertical bars 21 can be subjected to angle change under the action of an external force), the motion change represents that the input, the other vector is output, namely when the angle of the transverse rod 20 and the vertical rod 21 changes, the length of the display arrow 3 changes, when the rotating frame 2 rotates, the display arrow 3 changes relative to the two-dimensional coordinate system line 10, the initial position of the display arrow 3 and the final position of the display arrow 3 after the rotating frame 2 rotates change, the changed display arrow 3 is still a straight line, the initial block 30 is fixed, and the change of the display arrow 3 in the two-dimensional coordinate system line 10 represents linear transformation.
The detailed description of the present invention is provided with reference to the accompanying drawings, however, the above description is not intended to limit the present invention, and various equivalent or equivalent modifications or replacements may be made within the technical scope of the present invention within the disclosure range without departing from the spirit of the present invention.
Claims (10)
1. The linear transformation principle demonstration device is characterized by comprising a demonstration board (1), a rotating frame (2) and demonstration arrows (3), wherein the rotating frame (2) is hinged to the front surface of the demonstration board (1), and the demonstration arrows (3) are connected to the front surface of the rotating frame (2);
a two-dimensional coordinate system line (10) is arranged on the front surface of the display board (1), the two-dimensional coordinate system line (10) comprises an origin (100), an X-axis line (101) and a Y-axis line (102), the X-axis line (101) is a horizontal axis, the Y-axis line (102) is a vertical axis orthogonal to the X-axis line (101), and the origin (100) is a point where the X-axis line (101) and the Y-axis line (102) intersect;
the rotary frame (2) is a latticed frame formed by mutually hinging a plurality of cross rods (20) and a plurality of vertical rods (21), each crossing part of the cross rods (20) and the vertical rods (21) is hinged, the crossing part of the center of the cross rod (20) and the center of the vertical rod (21) in the middle of the rotary frame (2) is the central point of the rotary frame (2), the central point of the rotary frame (2) is hinged with the original point (100) of the display board (1), when the cross rod (20) is in a horizontal state and the cross rod (20) is mutually vertical to the vertical rod (21), the cross rod (20) and the X-axis line (101) in the middle of the rotary frame (2) correspond to each other in the front and back directions, the vertical rod (21) and the Y-axis line (102) in the middle of the rotary frame (2) correspond to each other in the front and back directions, and corresponding first through holes (22) are arranged at the hinging parts of the cross rod (20) and, a first connecting rod (202) penetrating in the cross rod (20) and the vertical rod (21) is arranged in the first through hole (22), a front cylinder (201) and a rear cylinder (200) clamped outside the cross rod (20) and the vertical rod (21) are respectively arranged on the outer sides of two ends of the first connecting rod (202), second through holes (23) corresponding to each other in the front and back are respectively arranged at the hinged position of the central point of the rotating frame (2) and the original point (100) of the display board (1), a second connecting rod (232) penetrating in the central point of the rotating frame (2) and the original point (100) of the display board (1) is arranged in the second through hole (23), and a center front cylinder (231) and a center rear cylinder (230) clamped outside the cross rod (20) and the display board (1) are respectively arranged on the outer sides of two ends of the second connecting rod (232);
show arrow point (3) and constitute by originated piece (30), elastic webbing (31) and arrow head body (32), be provided with first mounting hole (300) of cover in center front portion cylinder (231) periphery on originated piece (30), be provided with second mounting hole (320) of the front portion cylinder (201) periphery of the articulated department of cover at arbitrary one horizontal pole (20) and montant (21) except the central point of rotatory frame (2) on arrow head body (32), connect elastic webbing (31) between originated piece (30) and arrow head body (32).
2. A linear transformation principle demonstrating device according to claim 1, wherein said exhibiting board (1) is a square plate made of iron.
3. A linear transformation principle demonstrating device according to claim 2, wherein the rear cylinder (200) at the hinge of 4 corners of the rotating frame (2) is provided with a magnet (203) on the back.
4. A linear transformation principle demonstrating device according to claim 3, wherein the back surface of the magnet (203) is closely attached to the front surface of the demonstration board (1).
5. A linear transformation principle demonstrating device according to claim 1, wherein the arrow body (32) is a triangular plate body, and the vertex direction of the triangular plate body is the same as the extending direction of the joint of the starting block (30) and the elastic band (31) to the joint of the elastic band (31) and the arrow body (32).
6. A linear transformation principle demonstration apparatus according to claim 1, wherein the diameter of the first link (202) is smaller than the diameters of the front cylinder (201) and the rear cylinder (200), the centers of the first link (202), the front cylinder (201) and the rear cylinder (200) are in a front-rear correspondence, the diameter of the second link (232) is smaller than the diameters of the central front cylinder (231) and the central rear cylinder (230), and the centers of the second link (232), the central front cylinder (231) and the central rear cylinder (230) are in a front-rear correspondence.
7. A linear transformation principle demonstrating device according to claim 1, wherein the elastic band (31) is a cylindrical elastic body or a band-shaped elastic body made of rubber.
8. The linear transformation principle demonstrating device as claimed in claim 1, wherein the starting block (30) is a plate-shaped circular or square plate.
9. The linear transformation principle demonstration device as claimed in claim 1, wherein the rotating frame (2) is placed in a plane formed by lines (10) of a two-dimensional coordinate system of the display board (1), the lengths of the cross bars (20) and the vertical bars (21) are the same, grids in a grid-shaped frame formed by mutually hinging a plurality of cross bars (20) and a plurality of vertical bars (21) are quadrangles with the same size and equal sides, and the rotating frame (2) is a grid-shaped frame formed by mutually hinging a cross bar (20) and a vertical bar (21) into a deformable prism or a square.
10. A linear transformation principle demonstrating device according to claim 1, wherein the rotating frame (2) is in a stationary state or in a rotating state around the second connecting rod (232) on the front surface of the exhibiting board (1).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911055740.4A CN110675706A (en) | 2019-10-31 | 2019-10-31 | Linear transformation principle demonstration device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911055740.4A CN110675706A (en) | 2019-10-31 | 2019-10-31 | Linear transformation principle demonstration device |
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| Publication Number | Publication Date |
|---|---|
| CN110675706A true CN110675706A (en) | 2020-01-10 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911055740.4A Withdrawn CN110675706A (en) | 2019-10-31 | 2019-10-31 | Linear transformation principle demonstration device |
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| Country | Link |
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| CN (1) | CN110675706A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111243380A (en) * | 2020-01-16 | 2020-06-05 | 遵义职业技术学院 | Teaching aid display device for mathematics education |
-
2019
- 2019-10-31 CN CN201911055740.4A patent/CN110675706A/en not_active Withdrawn
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111243380A (en) * | 2020-01-16 | 2020-06-05 | 遵义职业技术学院 | Teaching aid display device for mathematics education |
| CN111243380B (en) * | 2020-01-16 | 2021-09-28 | 遵义职业技术学院 | Teaching aid display device for mathematics education |
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Application publication date: 20200110 |
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