Circumferential angle multifunctional demonstration instrument

Abstract

A multi-functional circumferential angle demonstrator includes a demonstration panel with an annular groove. The demonstrator is characterized by: at least three circumferential sliders slidably disposed within the annular groove; a first protractor rotatably mounted on at least one of the three sliders; and each slider being plugged into and connected to the annular groove. An assembly hole is located at the center of the annular groove; a central slider rotatably disposed within the assembly hole; and a second protractor rotatably mounted on the central slider. The central slider is plugged into and connected to the assembly hole, and the diameter of the assembly hole is equal to the width of the annular groove. An elastic rope is fitted between the central slider and the circumferential sliders. This invention features a simple structure, reasonable design, convenient use, multiple uses, good dynamic demonstration effect, and low cost. It can improve teaching efficiency and quality and is beneficial for promotion and use.

Description

Technical Field

[0001] This utility model relates to the field of mathematical teaching aids, and in particular to a multifunctional demonstrator for circumferential angles. Background Technology

[0002] In junior high school mathematics teaching, when learning the concept, theorem, corollary, and properties of inscribed quadrilaterals, there are no demonstration tools. Teachers usually use blackboard drawings or courseware presentations for teaching. However, using blackboard drawings or courseware presentations has limitations. Students lack hands-on experience and cannot dynamically perceive the positional relationship between the center of the circle and the inscribed angle. The classification and discussion of the proof of the inscribed angle theorem are also difficult for students to understand.

[0003] To address this issue, Chinese patent CN202373205U discloses a demonstrator for the inscribed angle theorem. While this device solves the problem to some extent, its drawbacks are also obvious. Specifically, the first and second protractors are fixedly mounted on a circular plate, with two rubber bands forming the inscribed angle and central angle respectively. Furthermore, the curved gap, or groove, is a non-continuous circle. Under these circumstances, the device can only demonstrate the conceptual theorem of inscribed angles within a certain range, but cannot demonstrate corollaries based on this theorem or the properties of inscribed quadrilaterals. In this situation, the teaching process remains less engaging and the concepts are relatively abstract for students.

[0004] There is currently no corresponding solution to the above problems. Utility Model Content

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a multi-functional inscribed angle demonstration device that can intuitively and vividly discover the three positional relationships between the center of a circle and the inscribed angle. Through dynamic demonstration and static observation, it explores the generation process of the inscribed angle theorem and its corollaries. Students can repeat the operation experiment multiple times, making abstract mathematical knowledge intuitive, visual, and vivid. This enhances students' understanding and memory of the inscribed angle theorem and its corollaries, stimulates their desire for exploration, and develops their core competencies of spatial awareness and geometric intuition.

[0006] The device includes a demonstration panel with an annular groove. At least three circumferential sliders are slidably arranged in the annular groove. A first protractor is rotatably arranged on at least one of the three circumferential sliders, and each circumferential slider is plugged into and connected to the annular groove.

[0007] An assembly hole is provided at the center of the annular groove. A central slider is rotatably disposed in the assembly hole, and a second protractor is rotatably disposed on the central slider. The central slider is plugged into the assembly hole, and the diameter of the assembly hole is equal to the width of the annular groove.

[0008] That is, the central slider can be reassembled by plugging and unplugging, and is slidably set in the annular groove;

[0009] An elastic rope is fitted between the central slider and the circumferential slider.

[0010] The effect achieved is that, as shown in the attached diagram of the instruction manual, the device enables the learning of the concept theorem, corollary, and properties of inscribed quadrilaterals of a circle through flexible plug-and-play and elastic rope connection; during the demonstration, the circumferential slider and the central slider can rotate freely, and the elastic rope adapts to the deformation in real time, that is, the angle changes with the displacement of each slider; and the protractor can adapt to the rotation and measure angles in real time.

[0011] The beneficial effects of this utility model are: It has a simple structure, reasonable design, is easy to use, multi-functional, provides good dynamic demonstration effects, is low in cost, can improve teaching efficiency and quality, and is easy to promote and use. Its main advantages are as follows:

[0012] 1. Dynamic demonstration, intuitive and clear

[0013] The equipment facilitates intuitive and dynamic demonstrations by teachers, and also allows students to clearly see the trajectory of the inscribed angle, thus gaining an intuitive understanding of the conclusion. This helps students to deeply understand the relationship between the central angle and the inscribed angle, as well as the relationship between the inscribed angle and the diameter, thereby exploring the inscribed angle theorem and its corollaries.

[0014] 2. Materials are readily available and the cost is low.

[0015] The equipment has a simple structure, can be easily prepared using materials such as household waste, and has a simple preparation process that is easy to maintain. Its low cost also makes it easier to promote and popularize.

[0016] 3. Scientific rigor, pragmatism and innovation

[0017] This teaching aid attempts to break away from the traditional blackboard drawing or courseware presentation method. By visually demonstrating the positional relationship between the center of a circle and the inscribed angle, the inscribed angle theorem, its corollaries, and the properties of inscribed quadrilaterals, it makes abstract mathematical knowledge intuitive, vivid, and easy to perceive. The correctness of the conclusions can be proven through rigorous reasoning, thus forming good thinking habits and cultivating students' innovative thinking ability.

[0018] 4. Simple structure and easy operation

[0019] The teaching aid has a simple overall structure and is easy to demonstrate and operate. It can be repeatedly operated in a short time, or students can operate it themselves, which motivates students to engage in in-depth learning and enhances their awareness of inquiry.

[0020] 5. Multi-functional and safe

[0021] This teaching aid not only allows for an intuitive understanding of the concept of an inscribed angle, but also demonstrates the dynamic processes of the positional relationship between the center of a circle and the inscribed angle, the inscribed angle theorem, its corollaries, and the properties of cyclic quadrilaterals. It highly replicates the dynamic inscribed angle and cyclic quadrilateral models created in Geometer's Sketchpad, making abstract and complex knowledge more visual, concrete, and simple, thus enhancing students' thinking and observation skills. Furthermore, the equipment is stably assembled, easy to maintain, and can be operated with confidence by both teachers and students. Attached Figure Description

[0022] Figure 1 This is a structural schematic diagram of the basic implementation of the circumferential angle multifunctional demonstration device described in this utility model;

[0023] Figure 2 Based on Figure 1 A schematic diagram showing the positional relationship and assembly structure of the equipment in the side view.

[0024] Figure 3 Based on Figure 2 A magnified view of the local area and its assembly relationship;

[0025] Figure 4 This is a schematic diagram of Example 3;

[0026] Figure 5 This is a schematic diagram of Example 4;

[0027] Figure 6 This is a schematic diagram of Example 5;

[0028] Figure 7 This is a schematic diagram of Example 6;

[0029] Figure 8 This is a schematic diagram of Example 7;

[0030] Figure label:

[0031] 1-First protractor 2-Second protractor 3-Elastic rope 4-Annular groove 5-Suspension base plate 6-Support column foot 7-Assembly hole 8-Circular slider

[0032] 81-Elastic tailstock 82-Rotating rod 83-Positioning sleeve 84-Annular rope groove

[0033] The realization of the purpose, functional features and advantages of this utility model will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0034] Reference Figures 1-8The multi-functional circumferential angle demonstrator of this utility model includes a demonstration plate, on which an annular groove 4 is provided. At least three circumferential sliders 8 are slidably arranged in the annular groove 4. A first protractor 1 is rotatably arranged on at least one of the three circumferential sliders 8, and each circumferential slider 8 is plugged and inserted into the annular groove 4.

[0035] An assembly hole 7 is provided at the center of the annular groove 4. A central slider is rotatably disposed in the assembly hole 7, and a second protractor 2 is rotatably disposed on the central slider. The central slider is plugged into and connected to the assembly hole 7, and the diameter of the assembly hole 7 is equal to the groove width of the annular groove 4.

[0036] That is, the central slider can be reassembled by plugging and unplugging, and is slidably disposed in the annular groove 4;

[0037] An elastic rope 3 is fitted between the central slider and the circumferential slider 8.

[0038] The effect achieved is that, as shown in the attached diagram of the instruction manual, the device, through flexible plug-and-play and elastic rope 3 connection, enables the learning of the concept theorem, corollary, and properties of inscribed quadrilaterals of a circle; during the demonstration, the circumferential slider 8 and the central slider can rotate freely, and the elastic rope 3 adapts to the deformation in real time, that is, the angle changes with the displacement of each slider; and the protractor can adapt to the rotation and measure angles in real time.

[0039] Furthermore, the demonstration disk is fixedly mounted on the suspension base plate 5 by support column 6.

[0040] Preferably, the demonstration plate is made of acrylic material, and the suspension base plate 5 is a writing board.

[0041] Furthermore, the suspension base plate 5 is a rectangular plate with smooth corner transitions, and a support member is provided on the suspension base plate 5.

[0042] The demonstration disc is a circular disc, which is centrally positioned on the support member.

[0043] Preferably, the support is a hanging hook or a leg-type bracket. This facilitates the display of the equipment by hanging it with a hook or displaying it upright using a leg-type bracket.

[0044] Furthermore, the circumferential slider 8 and the central slider have the same configuration and size specifications;

[0045] Refer to the attached diagram in the instruction manual. Figure 2 and Figure 3 The circumferential slider 8 includes an elastic tailstock 81, which is set to be larger than the groove width of the annular slide groove 4 and the diameter of the mounting hole 7.

[0046] The term "greater than" here means "slightly greater than", that is, based on the elastic deformation of the elastic tailstock 81, it passes through the annular groove 4 or the assembly hole 7, and based on the above-mentioned fit, it plays the role of preventing the equipment from coming off within a certain range of external force pulling.

[0047] A rotating rod 82 is fixedly installed on the elastic tailstock 81. The outer diameter of the rotating rod 82 is smaller than the width of the annular sliding groove 4 and the assembly hole 7.

[0048] The term "less than" here means slightly less than, which ensures smooth rotation of the equipment and avoids excessive clearance.

[0049] A positioning sleeve 83 is fitted on the rotating rod 82. The positioning sleeve 83 is dampedly connected to the rotating rod 82, and the outer diameter of the positioning sleeve 83 is larger than the width of the annular groove 4 and the assembly hole 7.

[0050] Preferably, a friction plate is provided between the positioning sleeve 83 and the rotating rod 82, or the positioning sleeve 83 is made of anti-slip rubber material; the effect achieved by moving the positioning sleeve 83 to cooperate with the elastic tailstock 81 to clamp the demonstration plate, thereby playing a positioning role.

[0051] The end of the rotating rod 82 is provided with an annular rope groove 84. Between the annular rope groove 84 and the positioning sleeve 83, a protractor is rotatably mounted on the rotating rod 82. That is, the first protractor 1.

[0052] The effect achieved is that the circumferential slider 8 and the central slider can be quickly switched between the width of the annular groove 4 and the mounting hole 7. Based on the above configuration, they can rotate smoothly and position any slider at the demonstration point, thereby achieving the effect of smooth demonstration and switching between dynamic and static states.

[0053] Example 1, refer to the accompanying drawings in the instruction manual. Figure 1 As shown in the attached figure, the first protractor 1 is placed around the circumference; the second protractor 2 is placed at the center of the circle.

[0054] The elastic rope 3 is wound around the circumferential slider 8 and the central slider, and the definition of the circumferential angle can be seen, thus demonstrating the concept theorem of the circumferential angle.

[0055] Example 2, refer to the accompanying drawings in the specification. Figure 4 As shown in the attached figure, the first protractor 1 is placed on the circumference, and the second protractor 2 is placed at the center of the circle.

[0056] An elastic rope 3 is wound around the circumferential slider 8 and the central slider, showing three positional relationships between the center and the circumferential angle.

[0057] Example 3, refer to the accompanying drawings in the specification. Figure 5 As shown in the attached figure, the first protractor 1 is placed on the circumference, and the second protractor 2 is placed at the center of the circle.

[0058] The elastic rope 3 is coiled crosswise around the circumferential slider 8 and the central slider, which shows the inscribed angle theorem: the inscribed angle subtended by an arc is equal to half of the central angle subtended by it. At the same time, it is demonstrated that the inscribed angles subtended by the same arc or equal arcs are equal.

[0059] Example 4, refer to the accompanying drawings in the specification. Figure 6 As shown in the attached figure, the first protractor 1 is placed on the circumference, and the second protractor 2 is placed at the center of the circle.

[0060] With the elastic rope 3 wound around the circumferential slider 8 and the central slider, it can be seen that the corollary of the circumferential angle theorem can be derived: the circumferential angle subtended by the diameter is a right angle.

[0061] Example 5, refer to the accompanying drawings in the specification. Figure 7 Both the first protractor 1 and the second protractor 2 are placed on the circumference;

[0062] With the elastic rope 3 wound around the circumferential slider 8 and the central slider, it can be seen that the sum of two opposite angles of the inscribed quadrilateral is 180°.

[0063] Example 6, refer to the accompanying drawings in the specification. Figure 8 Both the first protractor 1 and the second protractor 2 are placed on the circumference;

[0064] The elastic rope 3 is coiled crosswise on the circumferential slider 8 and the central slider, which shows the property of the inscribed quadrilateral: the opposite angles of the inscribed quadrilateral are supplementary.

[0065] The foregoing has shown and described the basic principles, main features, and advantages of this utility model. It will be apparent to those skilled in the art that this utility model is not limited to the details of the exemplary embodiments described above, and that it can be implemented in other specific forms without departing from the spirit or basic characteristics of this utility model. Therefore, the embodiments should be considered exemplary and non-limiting in all respects. The scope of this utility model is defined by the appended claims rather than the foregoing description, and thus all variations falling within the meaning and scope of equivalents of the claims are intended to be included within this utility model. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0066] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A multi-functional circumferential angle demonstrator, comprising a demonstration plate, wherein the demonstration plate has an annular groove, characterized in that: At least three circumferential sliders are slidably arranged in the annular groove. A first protractor is rotatably arranged on at least one of the three circumferential sliders, and each circumferential slider is plugged into and connected to the annular groove. An assembly hole is provided at the center of the annular groove. A central slider is rotatably disposed in the assembly hole, and a second protractor is rotatably disposed on the central slider. The central slider is plugged into the assembly hole, and the diameter of the assembly hole is equal to the width of the annular groove. An elastic rope is fitted between the central slider and the circumferential slider.

2. The multi-functional demonstration device for circular angles according to claim 1, characterized in that, The demonstration panel is fixedly mounted on the suspended base plate by support columns.

3. The multi-functional demonstration device for circular angles according to claim 2, characterized in that, The suspension base plate is a rectangular plate with smooth corner transitions, and a support member is provided on the suspension base plate; The demonstration disc is a circular disc, which is centrally positioned on the support member.

4. The multi-functional demonstration device for circular angles according to claim 1, characterized in that, The circumferential slider and the central slider have the same configuration and size specifications; The circumferential slider includes an elastic tailstock, which is set to be larger than the width of the annular groove and the diameter of the mounting hole. A rotating rod is fixedly installed on the elastic tailstock, and the outer diameter of the rotating rod is smaller than the width of the annular sliding groove and the assembly hole. A positioning sleeve is fitted on the rotating rod, the positioning sleeve is damped and connected to the rotating rod, and the outer diameter of the positioning sleeve is larger than the width of the annular sliding groove and the assembly hole. The end of the rotating rod is provided with an annular rope groove, and a protractor is rotatably mounted on the rotating rod between the annular rope groove and the positioning sleeve.

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