A hanging valley conjecture demonstration model

Abstract

The utility model relates to the field of teaching tools, disclose a kind of hanging valley conjecture demonstration model, including shell, shell upper surface is provided with observation pointer, shell inside is provided with the pointer drive component of driving observation pointer and moving on shell upper surface, shell upper surface is also provided with the profile indicating plate of indicating the moving range of observation pointer, shell front is provided with first button, and first button is used to start and close pointer drive component, the utility model is moved on the plane formed by pointer drive component and drives observation pointer on shell upper surface, it is convenient for educatee to observe directly, by changing the moving mode of observation pointer and reducing the area swept when it turns 180 degrees, it is helpful for educatee to understand the solution train of thought of two-dimensional hanging valley conjecture.

Description

Technical Field

[0001] This utility model relates to the field of teaching tools technology, and in particular to a demonstration model of the Guagu conjecture. Background Technology

[0002] The Kakegaya conjecture was proposed in 1917. Its mathematical expression in two-dimensional space is: In Euclidean plane space, given a line segment of unit length, through continuous rigid body motion (including translation and rotation, but excluding stretching, folding, and topological deformation), the line segment eventually returns to its initial position and rotates 180°. The infimum of the area of ​​the plane swept by the line segment during this motion is the conjecture. The two-dimensional solution to this conjecture was solved in 1928, and the answer is that its area can be arbitrarily small.

[0003] Meanwhile, in the process of solving this problem, many mathematicians have proposed several methods to reduce the minimum area swept by changing the way the line segment moves. In teaching and popular science, the solution process obtained by simply calculating the two-dimensional Gugu conjecture with pen and paper is not intuitive and cannot accurately describe the continuous process of the rigid body motion of the line segment. As a result, it is often difficult for the students to quickly understand the specific way the line segment moves on the plane. Demonstrating the line segment displacement methods envisioned by many mathematicians through models helps the students understand them more quickly. Utility Model Content

[0004] The purpose of this invention is to provide a demonstration model of the Hanging Valley Conjecture, which can intuitively show how to reduce the area swept by a pointer representing a line segment when it makes rigid body motion in a planar region by changing the pointer's trajectory, thus facilitating learners' understanding of the solution to the two-dimensional Hanging Valley Conjecture.

[0005] The above-mentioned technical objective of this utility model is achieved through the following technical solution: a demonstration model of the Guagu conjecture, including a shell, an observation pointer is provided on the upper surface of the shell, a pointer driving component is provided inside the shell to drive the observation pointer to move on the upper surface of the shell, a contour indicator plate is also provided on the upper surface of the shell to indicate the range of movement of the observation pointer, and a first button is provided on the front of the shell, the first button is used to start and stop the pointer driving component.

[0006] By adopting the above technical solution, the observation pointer is installed on the upper surface of the model shell for easy observation. The observation pointer moves in close contact with the upper surface of the shell, and its movement can be regarded as the rigid movement of a line segment in two-dimensional Euclidean space. The observation pointer is driven by a pointer driving component installed inside the shell. The contour indicator plate has holes to indicate the range of movement of the observation pointer, which can intuitively show the range swept by the observation pointer. The shell also has a power supply for powering the pointer driving component and a first button for starting and stopping.

[0007] A further feature of this invention is that the pointer driving assembly includes a unidirectional rotating motor fixed inside the housing, one end of the observation pointer is coaxially connected to the output end of the unidirectional rotating motor, and a circular pointer limiting groove is provided on the contour indicator plate, the radius of which is equal to the length of the observation pointer.

[0008] By adopting the above technical solution, if the length of the observation pointer is taken as... When the pointer turns 180 degrees, it completes a semi-circular motion, and the area it sweeps is... One end of the pointer is connected to the output end of the unidirectional rotating motor by a rivet through the upper surface of the outer shell. When the unidirectional rotating motor is started, the pointer will rotate around the connection position.

[0009] A further feature of this invention is that the pointer driving assembly includes a unidirectional rotating motor fixed inside the housing, the center point of the observation pointer is coaxially connected to the output end of the unidirectional rotating motor, and a circular pointer limiting groove is provided on the contour indicator plate, the diameter of which is equal to the length of the observation pointer.

[0010] By adopting the above technical solution, the length of the pointer can be observed to be... Then the area of ​​one circular motion of the pointer is... At this point, observe that the pointer has turned 180 degrees, and observe that the midpoint of the pointer is connected to the output end of the unidirectional rotating motor by a rivet through the upper surface of the outer shell.

[0011] A further feature of this invention is that a circular hole is provided on the upper surface of the outer shell, and the pointer driving assembly includes a unidirectional rotating motor fixed inside the outer shell. The output end of the unidirectional rotating motor A is concentric with the circular hole, and a circular rotating plate that matches the size of the circular hole is connected to the output end of the unidirectional rotating motor. The center point of the pointer is rotated and connected to the edge of the circular rotating plate.

[0012] A further feature of this invention is that a pointer limiting groove is provided on the contour indicator plate, and the shape of the pointer limiting groove is a triangular cycloid with the circular rotating plate as the inscribed moving circle.

[0013] By adopting the above technical solution, the center point of the pointer is rotatably connected to the edge of a circular rotating plate via rivets. The circular rotating plate rotates via a unidirectional motor, with the pointer length as... When the circular rotating plate 211 rotates, it causes the center connection point of the observation pointer to move in a circular motion. At this time, the two edges of the observation pointer will touch the sides of the pointer limiting groove, so that the observation pointer can only move within the pointer limiting groove, and the area it sweeps is the area of ​​the pointer limiting groove. It is easy to calculate that this area is... .

[0014] A further feature of this invention is that a pointer limiting groove is provided on the contour indicator plate. The pointer limiting groove includes a "∠" shaped groove formed by two connected straight grooves. The included angle between the two straight grooves is 15-30 degrees. A fan-shaped groove for accommodating the rotation of the observation pointer is also provided at the connection of the two straight grooves and the end of the long straight groove. The pointer driving assembly includes a pointer rotation assembly for driving the observation pointer to rotate on the upper surface of the outer shell, and a pointer displacement assembly for driving the observation pointer to move along the pointer limiting groove on the upper surface of the outer shell.

[0015] The present invention is further configured such that: the pointer displacement assembly includes a bidirectional rotating motor disposed inside the housing, a motor limiting groove that mates with the pointer limiting groove is provided at the bottom of the housing, a motor limiting block that mates with the motor limiting groove is fixed at the bottom of the bidirectional rotating motor, a pointer displacement gear is connected to the output end of the pointer displacement motor, and a toothed groove is provided inside the housing to allow the pointer displacement gear to move along the direction of the pointer limiting groove, and one end of the pointer is rotatably connected to the axis of the pointer displacement gear.

[0016] A further feature of this invention is that the observation pointer is made of iron, the pointer rotation assembly includes electromagnets disposed on the two straight sides of the fan-shaped slot, and a power supply assembly is provided inside the housing to magnetize and demagnetize the two electromagnets respectively.

[0017] By adopting the above technical solution, the pointer moves within the pointer limiting groove through the pointer rotation component and the pointer displacement component. The area swept by the pointer is the area of ​​the pointer limiting groove. The pointer displacement component drives the pointer to move through the pointer displacement gear embedded in the tooth groove. The pointer rotation component attracts the iron pointer to rotate through the electromagnets on both sides.

[0018] A further feature of this invention is that: a motor rotation sensor is installed inside the housing to read the number of rotations at the output end of the bidirectional rotating motor; a display screen is installed on the front of the housing to display the area swept by the observation pointer; and the motor rotation sensor is connected to the display screen via a signal.

[0019] By adopting the above technical solution, a motor rotation sensor that can read the number of rotations at the output end is set at the unidirectional rotating motor, and the area swept by the observation pointer is displayed on the screen according to the reading of the motor rotation sensor, so that the learner can read the area swept by the observation pointer more quickly and intuitively.

[0020] A further feature of this invention is that the length of the observation pointers is the same.

[0021] By adopting the above technical solution, learners can more intuitively compare the size of the area swept by the pointer in different embodiments when the pointer length is the same.

[0022] The beneficial effects of this invention are: by using the pointer driving component to move the observation pointer on the plane formed by the upper surface of the outer shell, it is easy for the learner to directly observe that by changing the movement of the observation pointer, the area swept when it turns 180 degrees is reduced, which helps the learner understand the solution to the two-dimensional hanging valley conjecture. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this utility model, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this utility model. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A schematic diagram of the overall structure of a demonstration model of the Guagu conjecture provided in the first embodiment of this utility model;

[0025] Figure 2 This is a front sectional view of the first embodiment of the present invention;

[0026] Figure 3 This is a schematic diagram of the overall structure of the second embodiment of the present utility model;

[0027] Figure 4 This is a schematic diagram of the overall structure of the third embodiment of the present utility model;

[0028] Figure 5 This is a top view of the third embodiment of the present invention;

[0029] Figure 6 This is a schematic diagram of the overall structure of the fourth embodiment of the present utility model;

[0030] Figure 7 This is a top view of the fourth embodiment of the present invention;

[0031] Figure 8 This is an exploded view of the structure of the fourth embodiment of the present invention;

[0032] In the diagram: 1. Outer shell; 11. Observation pointer; 12. Contour indicator plate; 121. Pointer limit slot; 13. First button; 14. Circular hole; 2. Pointer drive assembly; 21A. Unidirectional rotation motor; 21B. Bidirectional rotation motor; 211. Circular rotating plate; 22. Pointer rotation assembly; 221. Electromagnet; 222. Power supply assembly; 23. Pointer displacement assembly; 232. Motor limit slot; 233. Motor limit block; 234. Pointer displacement gear; 235. Gear; 3. Motor rotation sensor; 4. Display screen. Detailed Implementation

[0033] The technical solution of this utility model will now be clearly and completely described with reference to specific embodiments. Obviously, the described embodiments are only a part of the embodiments of this utility model, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this utility model without creative effort are within the scope of protection of this utility model.

[0034] This utility model embodiment specifically provides a demonstration model of the Guagu conjecture, including a shell 1, an observation pointer 11 is provided on the upper surface of the shell 1, a pointer driving component 2 is provided inside the shell 1 to drive the observation pointer 11 to move on the upper surface of the shell 1, a contour indicator plate 12 is also provided on the upper surface of the shell 1 to indicate the range of movement of the observation pointer 11, and a first button 13 is provided on the front of the shell 1 for starting and stopping the pointer driving component 2.

[0035] To facilitate observation and understanding by learners, the observation pointer 11 is mounted on the upper surface of the model shell 1. The observation pointer 11 moves in close contact with the upper surface of the shell 1. Without considering the width of the observation pointer 11, its movement can be regarded as the rigid movement of a line segment in two-dimensional Euclidean space. The observation pointer 11 is driven by the pointer drive component 2 installed inside the shell 1. To further demonstrate the range swept by the observation pointer 11, a contour indicator plate 12 is also fixed on the upper surface of the shell 1. The contour indicator plate 12 has holes that indicate the range of movement of the observation pointer 11. Since the observation pointer 11 has thickness, it can be blocked by the edge of the hole. Inside the shell 1, a power supply for powering the pointer drive component 2 and a first button 13 for starting and stopping are also installed.

[0036] In the first embodiment of this utility model, the pointer driving component 2 includes a unidirectional rotating motor 21A fixed inside the housing 1. One end of the observation pointer 11 is coaxially connected to the output end of the unidirectional rotating motor 21A. A circular pointer limiting groove 121 is provided on the contour indicator plate 12, and the radius of the pointer limiting groove 121 is equal to the length of the observation pointer 11.

[0037] In this example, we observe pointer 11 moving in a circular motion. If we take the pointer length as... The area covered by the pointer rotating half a circle is... At this point, the observation pointer 11 turns 180 degrees. This embodiment demonstrates the most readily conceivable pointer movement method, and the area it sweeps is the largest among all embodiments provided by this utility model. One end of the observation pointer 11 passes through the upper surface of the outer shell 1 through a rivet and is connected to the output end of the unidirectional rotation motor 21A. When the unidirectional rotation motor 21A starts, the observation pointer 11 will rotate around the connection position. The area swept by the observation pointer 11 can be represented by the circular pointer limiting groove 121. The rotation speed of the rotor of the unidirectional rotation motor 21A needs to ensure that the learner can clearly observe it.

[0038] As a second embodiment of the present invention, the pointer driving assembly 2 includes a one-way rotating motor 21A fixed inside the housing 1. The center point of the observation pointer 11 is coaxially connected with the output end of the one-way rotating motor 21A. A circular pointer limiting groove 121 is provided on the contour indicator plate 12. The diameter of the pointer limiting groove 121 is equal to the length of the observation pointer 11.

[0039] In this example, the center point of the observation pointer 11 is connected to the output terminal of the one-way rotation motor 21A via a rivet. When the one-way rotation motor 21A starts, the observation pointer 11 rotates around the center point, with the pointer length being... The area it swept was Its area is smaller than the area swept by the pointer in the first embodiment, demonstrating the method of reducing the area swept by the line segment by changing the rotation point. The pointer driving component 2 in this example is the same as the pointer driving component 2 in the first embodiment.

[0040] In the third embodiment, a circular hole 14 is provided on the upper surface of the outer shell 1. The pointer driving component 2 includes a one-way rotating motor 21A fixed inside the outer shell 1. The output end of the one-way rotating motor 21A is concentric with the circular hole 14. The output end of the one-way rotating motor 21A is connected to a circular rotating plate 211 that matches the size of the circular hole 14. The center point of the pointer 11 is rotated and connected to the edge of the circular rotating plate 211.

[0041] The contour indicator plate 12 is provided with a pointer limiting groove 121, which is shaped as a triangular cycloid with the circular rotating plate 211 as the inscribed moving circle.

[0042] In this example, the center point of the observation pointer 11 is rotatably connected to the edge of the circular rotating plate 211 via a rivet. The circular rotating plate 211 is rotated by a unidirectional rotating motor 21A, with the pointer length as... Then observe the distance from the center point of pointer 11 to the rotation center of the circular rotating plate 211, that is, the radius of the circular rotating plate 211. The definition of an incycloid is: a moving circle with a smaller radius is inscribed in a fixed circle with a larger radius on a plane and rolls without slippage. The image formed by the trajectory of a fixed point on the circumference of the inscribed moving circle is the image. When the radius of the moving circle is one-third of the radius of the fixed circle, the trajectory of the fixed point is the tricuspid incycloid. The characteristic of the tricuspid incycloid is that the length of the line segment formed by the tangent at any point on its edge being cut off by the incycloid is equal to twice the diameter of the inscribed moving circle. Therefore, in this embodiment, the length of the pointer is regarded as the line segment formed by the incycloid being cut off. When the circular rotating plate 211 rotates, it drives the center connection point of the observation pointer 11 to perform a circular motion. At this time, the two edges of the observation pointer 11 will touch the side of the pointer limiting groove 121, so that the observation pointer 11 can only move within the pointer limiting groove 121, and the area it sweeps is the area of ​​the pointer limiting groove 121. It is easy to calculate that this area is The area swept by the observation pointer 11 is smaller than that in Example 2, which means that the area swept by the observation pointer 11 is reduced again by changing the position of the rotation center of the observation pointer 11.

[0043] As a fourth embodiment of the present invention, the contour indicator plate 12 is provided with a pointer limiting groove 121. The pointer limiting groove 121 includes a "∠" shaped groove formed by two connected straight grooves. The included angle between the two straight grooves is 15-30 degrees. A fan-shaped groove for accommodating the rotation of the observation pointer 11 is also provided at the connection of the two straight grooves and the end of the long straight groove. The pointer driving component 2 includes a pointer rotation component 22 for driving the observation pointer 11 to rotate on the upper surface of the outer shell 1, and a pointer displacement component 23 for driving the observation pointer 11 to move along the pointer limiting groove 121 on the upper surface of the outer shell 1.

[0044] The pointer displacement assembly 23 includes a bidirectional rotating motor 21B disposed inside the housing 1. The bottom of the housing 1 is provided with a motor limiting groove 232 that cooperates with the pointer limiting groove 121. The bottom of the bidirectional rotating motor 21B is fixed with a motor limiting block 233 that cooperates with the motor limiting groove 232. The output end of the pointer displacement motor 231 is connected to a pointer displacement gear 234. The housing 1 is provided with a toothed groove 235 that allows the pointer displacement gear 234 to move along the pointer limiting groove 121. It is observed that one end of the pointer 11 is rotatably connected to the axis of the pointer displacement gear 234.

[0045] Furthermore, the pointer 11 is made of iron, and the pointer rotation assembly 22 includes electromagnets 221 disposed on the two straight sides of the sector groove. The housing 1 is provided with a power supply assembly 222 that magnetizes and demagnetizes the two electromagnets 221 respectively.

[0046] The fourth embodiment is used to demonstrate the movement process of the Paul translation. The definition of the Paul translation is: through the combination of infinitesimal angle rotation and directional translation, the area swept by a unit line segment during the movement approaches zero infinitely. When solving the two-dimensional valley problem, the Paul translation provides proof that the minimum area swept by a line segment in the plane is zero, which is an important theoretical support for proving the valley conjecture.

[0047] In this embodiment, the observation pointer 11 simulates the specific process of a line segment performing a Bauer translation. The pointer limiting groove 121 includes a "∠" shaped groove formed by two connected straight grooves. The line connecting the ends of the two straight grooves is perpendicular to the shorter straight groove. Without considering the width of the straight grooves, the two straight grooves can be regarded as forming the adjacent right-angled side and hypotenuse of a right triangle. At the same time, a fan-shaped groove for accommodating the observation pointer 11 is also opened at the end of the straight groove representing the hypotenuse. One straight side of the fan-shaped groove coincides with the straight groove representing the hypotenuse. The radius of the fan-shaped groove is equal to the length of the observation pointer 11, and the arc is equal to the arc of the included angle between the two straight grooves. This makes the observation pointer 11 parallel to the straight groove representing the right-angled side when it is against the other straight side of the fan-shaped groove. A second fan-shaped groove that is exactly the same as the aforementioned fan-shaped groove is also provided at the connection point of the two straight grooves.

[0048] When the observation pointer 11 is against one straight edge of the sector groove and parallel to the straight groove representing the right angle, it is considered to be in the initial state. At this time, the rivet connecting the observation pointer 11 and the pointer displacement component 23 is located at the end of the straight groove representing the hypotenuse. The electromagnet 221 at the straight edge of the sector groove against which the observation pointer 11 is against is closed, and the electromagnet 221 at the other straight edge is opened. The observation pointer 11 rotates from the initial state. If the included angle of the two straight grooves is... Then observe the area swept by pointer 11 during this rotation. Subsequently, the bidirectional rotating motor 21B starts, driving the pointer displacement gear 234 to rotate. The projection of the center line of the tooth groove 235 and the pointer limiting groove 121 is the same. Therefore, the pointer displacement gear 234 moves within the tooth groove 235, thereby driving the entire pointer displacement assembly 23 and the observation pointer 11 to move along the straight groove direction. Since the limiting block 233 is rectangular and stuck in the motor limiting groove 232, it cannot rotate within the motor limiting groove 232. Therefore, it also restricts the bidirectional rotating motor 21B housing from rotating. During the displacement of the observation pointer 11, it remains parallel to the straight groove. Therefore, without considering the width of the observation pointer 11, the area it sweeps is zero. When the pointer displacement gear 234 reaches the turning angle of the pointer limiting groove 121, the bidirectional rotating motor 21B stops rotating. At this time, the observation pointer 11 is against the straight edge of the second sector groove, which is parallel to the straight groove representing the hypotenuse. The electromagnet 221 on the other side is activated, causing the observation pointer 11 to rotate again, and the swept area is... Subsequently, the bidirectional rotating motor 21B resumes rotation, and the pointer displacement gear 234 moves along the shorter straight groove until it reaches the end of the groove. At this point, the pointer 11 is observed to be in the translational completion state, remaining parallel to its initial state, and the total area swept during the movement is... Meanwhile, if it is necessary to restore the observation pointer 11 from the translation end state to the initial state, simply rotate the bidirectional rotation motor 21B in the opposite direction and perform the above operation in the reverse direction.

[0049] To facilitate observation by the learner, and considering the impact of the width of the linear grooves and the observation pointer 11 on accuracy, the included angle between the two linear grooves needs to be greater than 15 degrees. However, learners can easily relate this embodiment to the fact that when the included angle between the two linear grooves... As the pointer decreases, observe the total area swept by pointer 11. It will also decrease, and when taking the limit... That is, when the rotation angle of the line segment is arbitrarily small during the Bauer translation process, the total area swept by it is also arbitrarily small. This embodiment teaches this conclusion to the learners through an intuitive demonstration model, which helps them to understand it.

[0050] In the first, second, and third embodiments of this utility model, a motor rotation sensor 3 is provided inside the outer casing 1 to read the number of rotations of the output end of the unidirectional rotating motor 21A, and a display screen 4 is provided on the front of the outer casing 1 to display the area swept by the observation pointer 11. The motor rotation sensor 3 is connected to the display screen 4.

[0051] To enable learners to read the area swept by the observation pointer 11 more quickly and intuitively, a motor rotation sensor 3 is installed at the unidirectional rotating motor 21A, which can read the number of rotations at the output end. The area swept by the observation pointer 11 is displayed on the screen 4 based on the reading of the motor rotation sensor 3. The conversion formula is: with the length of the observation pointer 11 as... The total radian of the rotor rotation of the unidirectional rotating motor 21A obtained by the motor rotation sensor 3 is: Therefore, in the first embodiment of this utility model, the area displayed by the display screen 4 is... In the second embodiment In the third embodiment The specific structure of the motor rotation sensor and the display screen, as well as the data conversion processor, are conventional technical means well known to those skilled in the art. Their specific installation and setting methods are not within the scope of protection of this utility model. The setting of installing a button to manually clear the data of the motor rotation sensor and restore the device to its initial state is also a conventional technical solution well known to those skilled in the art, and will not be described in detail here.

[0052] In all embodiments of this utility model, the observation pointer 11 has the same length, so that the learner can more intuitively compare the size of the area swept by the observation pointer 11 in different embodiments.

[0053] The above describes the basic principles, main features, and advantages of this utility model. The standard parts used in this utility model can all be purchased from the market, and the irregular parts can be customized according to the description and drawings. The specific connection methods of each part adopt conventional methods such as bolts, rivets, and welding that are mature in the prior art. The machinery, parts, and equipment adopt conventional models in the prior art, which will not be described in detail here.

[0054] The control method of this utility model is automatic control through a controller. The control circuit of the controller can be implemented by simple programming by those skilled in the art. The power supply is also common knowledge in the field. Since this utility model is mainly used to protect mechanical devices, the control method and circuit connection will not be explained in detail.

[0055] The above description is only a preferred embodiment of the present utility model and is not intended to limit the present utility model. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present utility model should be included within the protection scope of the present utility model.

Claims

1. A demonstration model of the Guagu conjecture, comprising a shell (1), characterized in that: An observation pointer (11) is provided on the upper surface of the housing (1). Inside the housing (1) is a pointer driving component (2) that drives the observation pointer (11) to move on the upper surface of the housing (1). The upper surface of the housing (1) is also provided with a contour indicator plate (12) that indicates the range of movement of the observation pointer (11). A first button (13) is provided on the front of the housing (1). The first button (13) is used to start and stop the pointer driving component (2).

2. The demonstration model of the hanging valley conjecture according to claim 1, characterized in that: The pointer drive assembly (2) includes a unidirectional rotating motor (21A) fixed inside the housing (1). One end of the observation pointer (11) is coaxially connected to the output end of the unidirectional rotating motor (21A). A circular pointer limiting groove (121) is provided on the contour indicator plate (12). The radius of the pointer limiting groove (121) is equal to the length of the observation pointer (11).

3. The demonstration model of the hanging valley conjecture according to claim 1, characterized in that: The pointer drive assembly (2) includes a unidirectional rotating motor (21A) fixed inside the housing (1). The center point of the observation pointer (11) is coaxially connected to the output end of the unidirectional rotating motor (21A). A circular pointer limiting groove (121) is provided on the contour indicator plate (12). The diameter of the pointer limiting groove (121) is equal to the length of the observation pointer (11).

4. The demonstration model of the hanging valley conjecture according to claim 1, characterized in that: The outer shell (1) has a circular hole (14) on its upper surface. The pointer drive assembly (2) includes a one-way rotating motor (21A) fixed inside the outer shell (1). The output end of the one-way rotating motor (21A) is concentric with the circular hole (14). The output end of the one-way rotating motor (21A) is connected to a circular rotating plate (211) that matches the size of the circular hole (14). The center point of the observation pointer (11) is rotatably connected to the edge of the circular rotating plate (211).

5. A demonstration model of the hanging valley conjecture according to claim 4, characterized in that: The contour indicator plate (12) is provided with a pointer limiting groove (121), and the pointer limiting groove (121) is shaped as a triangular cycloid with the circular rotating plate (211) as the inscribed moving circle.

6. The demonstration model of the hanging valley conjecture according to claim 1, characterized in that: The contour indicator plate (12) is provided with a pointer limiting groove (121). The pointer limiting groove (121) includes a "∠" shaped groove formed by two connected straight grooves. The included angle between the two straight grooves is 15-30 degrees. A fan-shaped groove is also provided at the connection of the two straight grooves and the end of the long straight groove to accommodate the rotation of the observation pointer (11). The pointer driving component (2) includes a pointer rotation component (22) that drives the observation pointer (11) to rotate on the upper surface of the outer shell (1), and a pointer displacement component (23) that drives the observation pointer (11) to move along the pointer limiting groove (121) on the upper surface of the outer shell (1).

7. A demonstration model of the hanging valley conjecture according to claim 6, characterized in that: The pointer displacement assembly (23) includes a bidirectional rotating motor (21B) disposed inside the housing (1). The bottom of the housing (1) is provided with a motor limiting groove (232) that cooperates with the pointer limiting groove (121). The bottom of the bidirectional rotating motor (21B) is fixed with a motor limiting block (233) that cooperates with the motor limiting groove (232). The output end of the bidirectional rotating motor (21B) is connected to a pointer displacement gear (234). The housing (1) is provided with a toothed groove (235) that allows the pointer displacement gear (234) to move along the direction of the pointer limiting groove (121). One end of the observation pointer (11) is rotatably connected to the axis of the pointer displacement gear (234).

8. A demonstration model of the hanging valley conjecture according to claim 7, characterized in that: The observation pointer (11) is made of iron. The pointer rotation assembly (22) includes electromagnets (221) located on the two straight sides of the fan-shaped slot. The housing (1) is provided with a power supply assembly (222) that magnetizes and demagnetizes the two electromagnets (221) respectively.

9. A demonstration model of the Guagu conjecture according to any one of claims 2-5, characterized in that: The housing (1) is equipped with a motor rotation sensor (3) that reads the number of rotations of the output end of the unidirectional rotating motor (21A). The front of the housing (1) is equipped with a display screen (4) that displays the area swept by the observation pointer (11). The motor rotation sensor (3) is connected to the display screen (4).

10. A demonstration model of the Guagu conjecture according to any one of claims 2-8, characterized in that: The observation pointers (11) are of the same length.

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