A Zu Geng's Principle Demonstration Water Tank System

Abstract

The present invention discloses a Zu Geng's principle demonstration water tank system, which includes a pair of water tanks, a liftable bracket, a pair of diameter measuring mechanisms, a first cone and a second cone; a diameter measuring mechanism is horizontally placed at the upper end of each water tank, the first cone and the second cone are respectively suspended on the liftable bracket, and the liftable bracket can drive the first cone and the second cone to move up and down simultaneously. The system of the present invention can judge whether the diameters of the two sectional circles formed by the first cone and the second cone with the horizontal plane always remain the same during the movement by setting the diameter measuring mechanism; the suspension heights of the first cone and the second cone are always kept the same by setting the liftable bracket; the volumes of the first cone and the second cone can be measured through the water tanks; and finally, Zu Geng's principle is proved. In addition, through the use of teaching aids for physical demonstration and on-site teaching, it can not only better help students understand scientific principles, but also improve students' learning enthusiasm.

Description

Technical Field

[0001] The present invention relates to teaching demonstration supplies, and more particularly to a demonstration water tank system for the principle of Zu Geng. Background Art

[0002] Zu Geng (5th century - 6th century), the son of Zu Chongzhi, was a great scientist during the Southern and Northern Dynasties. Zu Geng made outstanding contributions in mathematics. Based on practice, he put forward the following volume calculation principle at the end of the 5th century: "If the powers and potentialities are the same, then the volumes cannot be different." This is the "principle of Zu Geng". "Potentiality" refers to height, and "power" refers to area. The principle of Zu Geng can be described in modern language as: "For two geometric bodies sandwiched between two parallel planes, if they are intercepted by any plane parallel to these two planes, and the areas of the two intercepted cross-sections are always equal, then the volumes of these two geometric bodies are equal."

[0003] As an item used in the classroom, teaching aids can more intuitively reflect the content being taught, enabling students to more conveniently and quickly understand the knowledge they are learning. The current high school mathematics textbooks record the "principle of Zu Geng" and provide drawings, which can help students understand. However, since such an abstract thinking dynamic process of "breaking a whole into parts and integrating parts into a whole" is taught through oral lectures without an ideal intuitive teaching aid, this not only affects students' mastery of the essence of this thinking method but also increases the difficulty of teaching and affects the classroom teaching efficiency. Therefore, we need to design a demonstration device for the principle of Zu Geng. Summary of the Invention

[0004] To overcome the defects of the prior art, the purpose of the present invention is to provide a demonstration water tank system for the principle of Zu Geng to solve the problem that there is no intuitive teaching aid to demonstrate the "principle of Zu Geng" at present, which increases the difficulty of teaching and affects the classroom teaching efficiency.

[0005] For this purpose, the present invention provides a demonstration water tank system for the principle of Zu Geng, including a pair of water tanks, a liftable support, a pair of diameter measuring mechanisms, a first cone and a second cone; a diameter measuring mechanism is horizontally placed at the upper end of each water tank, the first cone and the second cone are respectively suspended on the liftable support, and the liftable support can drive the first cone and the second cone to move up and down simultaneously.

[0006] The lower ends of the first cone and the second cone respectively correspond to a diameter measuring mechanism; a cross-sectional circle is respectively formed between the first cone, the second cone and the horizontal plane where the diameter measuring mechanism is located during the movement; the diameter measuring mechanism is used to determine whether the diameters of the two cross-sectional circles always remain the same; a first scale is provided on the side of the water tank to determine whether the volumes of the first cone and the second cone immersed in water are the same.

[0007] Furthermore, the diameter measuring mechanism includes an annular bracket and at least three sliding rods. The sliding rods extend radially on the annular bracket and are distributed in an annular array. A tension spring piece is provided between the sliding rods and the annular bracket. At the same time, a second scale is provided in the middle of the sliding rods.

[0008] Furthermore, a contact ball is provided at the front end of the sliding rod.

[0009] Furthermore, four sliding rods and four tension spring pieces are respectively provided in the diameter measuring mechanism.

[0010] Furthermore, the liftable bracket includes a cross bar, a pair of vertical rods and a pair of sliders; both ends of the cross bar are respectively connected to one of the sliders. The sliders are slidably connected to the corresponding vertical rods, and a scale is also provided at the matching section of the upper part of the vertical rods and the sliders.

[0011] Furthermore, the side surface of the slider has a mounting hole for mating with the cross bar. A threaded hole is also provided on the side surface of the slider, and a locking screw is provided in the threaded hole.

[0012] Furthermore, a bottom plate is connected to the bottom of the vertical rod.

[0013] Furthermore, a second bubble level is mounted on the cross bar.

[0014] Furthermore, a first bubble level is provided at the top of the water tank. The first bubble level is a universal level, including a horizontal bubble in the transverse direction and a horizontal bubble in the longitudinal direction.

[0015] Furthermore, the first cone and the second cone are solid cones made of metal.

[0016] The Liu Hui's principle demonstration water tank system provided by the present invention can judge whether the diameters of the two sectional circles formed by the first cone and the second cone moving in the horizontal plane where the diameter measuring mechanism is located always remain the same by setting the diameter measuring mechanism; the suspension heights of the first cone and the second cone are always kept the same by setting the liftable bracket; the volumes of the first cone and the second cone can be measured by setting the water tank with the first scale; and finally, the Liu Hui's principle is proved. In addition, through the physical demonstration and on-site teaching using teaching aids, it can not only better help students understand scientific principles, but also improve students' learning enthusiasm.

[0017] In addition to the purposes, features and advantages described above, the present application has other purposes, features and advantages. The following will refer to the drawings for a further detailed description of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments and descriptions thereof of this application are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0019] Figure 1 It is a schematic structural diagram of the Zu Geng's principle demonstration water tank system of the present invention in the initial state;

[0020] Figure 2 It is a schematic structural diagram of the Zu Geng's principle demonstration water tank system of the present invention in the middle demonstration state;

[0021] Figure 3 It is a partial enlarged view of the Zu Geng's principle demonstration water tank system of the present invention in the middle demonstration state;

[0022] Figure 4 It is a schematic structural diagram of the Zu Geng's principle demonstration water tank system of the present invention in the final demonstration state;

[0023] Explanation of reference numerals

[0024] 1. Water tank; 2. Liftable support; 3. Diameter measuring mechanism; 4. Cone one; 5. Cone two; 11. Scale one; 12. Bubble level one; 21. Vertical rod; 22. Cross bar; 23. Slide block; 24. Locking screw; 25. Bottom plate; 26. Bubble level two; 31. Ring bracket; 32. Slide rod; 33. Tensile spring piece; 34. Contact ball; 35. Scale two. Detailed implementation manners

[0025] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

[0026] As Figures 1 to 4 shown, the Zu Geng's principle demonstration water tank system of the present invention includes: a pair of water tanks 1, liftable supports 2, a pair of diameter measuring mechanisms 3, a cone one 4 and a cone two 5; a diameter measuring mechanism 3 is horizontally placed at the upper end of each water tank 1, the cone one 4 and the cone two 5 are respectively suspended on the liftable support 2, and the lower ends of both respectively correspond to a diameter measuring mechanism 3. Among them, the cone one 4 and the cone two 5 can move up and down with the liftable support 2, the diameter measuring mechanism 3 can measure the diameter of any cross-section of the cone one 4 and the cone two 5, and the water tank 1 can obtain the volume of the cone one 4 or the cone two 5 through the change of the water level height.

[0027] Specifically, the diameter measuring mechanism 3 includes an annular bracket 31 and at least three sliding rods 32. The sliding rods 32 extend radially on the annular bracket 31 and are distributed in an annular array. At the same time, the sliding rods 32 are in sliding fit with the annular bracket 31. A tension spring piece 33 is provided between the sliding rods 32 and the annular bracket 31, and the tension spring piece 33 forces the sliding rods 32 to slide towards the center point on the annular bracket 31. Among them, a contact ball 34 is provided at the front end of the sliding rod 32, and a second scale 35 is provided in the middle of the sliding rod 32.

[0028] As Figure 1 As shown, four sliding rods 32, contact balls 34 and tension spring pieces 33 are respectively provided in the diameter measuring mechanism 3. The four contact balls 34 are respectively in contact with the quadrant points of the cross-sectional circle. By measuring the four sliding rods 32 in two perpendicular directions, the diameter of the cross-sectional circle can be measured more accurately.

[0029] When the diameter measuring mechanism 3 is not under external force, the contact balls 34 at the front ends of several sliding rods 32 are in contact with each other, and the spherical shapes of multiple contact balls are located on a concentric circle. When the first cone 4 or the second cone 5 moves downward from the central position of the diameter measuring mechanism 3, the conical surfaces of the first cone 4 or the second cone 5 are simultaneously in contact with several contact balls 34, pushing several sliding rods 32 to move radially outward at the same time. The diameter of a certain horizontal section of the first cone 4 or the second cone 5 can be obtained through the second scale 35 on the sliding rod 32, and then it can be judged whether the sizes of the horizontal sections where the first cone 4 and the second cone 5 are intersected by the same horizontal plane are the same.

[0030] A first scale 11 is provided on the side of the water tank 1 for observing the change in the water level height, so as to obtain the volume of the first cone 4 or the second cone 5. A first bubble level 12 is provided at the top of the water tank 1. The first bubble level 12 is a universal level, including two horizontal bubbles in the horizontal and vertical directions, which is used to judge whether the water tank 1 is set horizontally, so as to make the measured volume more accurate.

[0031] The liftable bracket 2 includes a cross bar 22, a pair of vertical bars 21 and a pair of sliders 23. Both ends of the cross bar 22 are respectively connected with a slider 23, and the slider 23 is slidably connected with the corresponding vertical bar 21. Among them, the side of the slider 23 has a mounting hole for cooperating with the cross bar 22, and a threaded hole is also provided on the side of the slider 23. A locking screw 24 is provided in the threaded hole, and the height of the slider 23 is adjusted by screwing the locking screw 24. The lifting movement of the slider 23 can drive the cross bar 22 and the first cone 4 and the second cone 5 connected below it to move up and down.

[0032] As Figure 1As shown in the figure, the bottom of the vertical rod 21 is connected to a bottom plate 25 for support and fixation; a scale is provided on the section of the upper part of the vertical rod 21 that cooperates with the slider 23 to measure the height of the cross bar 22, and further obtain the real-time heights of the first cone 4 and the second cone 5; in addition, a bubble level two 26 is installed on the cross bar 22, and the bubble level two 26 is used to determine whether the cross bar 22 is horizontal, and further determine whether the heights of the first cone 4 and the second cone 5 are the same.

[0033] In this solution, the first cone 4 and the second cone 5 are solid cones made of high-density metal materials, and it is satisfied that the first cone 4 and the second cone 5 can rely on their own weights to push the sliding rod 32 to move outward against the elastic force of the tension spring piece 33.

[0034] It should be noted that in this case, the liftable bracket 2 can be set in addition to Figure 1 the way of the cooperation between the vertical rod and the slider described in the figure, and a linear guide rail slider module can also be directly selected, and an electric or pneumatic control module can also be added, all of which can realize the synchronous movement of the first cone 4 and the second cone 5.

[0035] Next, the working principle and process of the Zu Geng's principle demonstration water tank system of the present invention will be briefly described with reference to the accompanying drawings.

[0036] First, hang the first cone 4 and the second cone 5 on the liftable bracket 2, adjust the position of the slider by rotating the locking screw 24, and adjust the position of the slider 23 through the bubble level two 26 and the scale on the vertical rod 21 to keep the cross bar 22 horizontal, and then control the suspension heights of the first cone 4 and the second cone 5 to always be the same.

[0037] The first cone 4 and the second cone 5 move downward and respectively form a sectional circle with the plane where the central axis of the sliding rod 32 is located; the two diameter measuring mechanisms 3 measure that the diameters of the two sectional circles always remain the same; at the same time, it is observed through the first scale 11 that the water level changes in the water tank 1 are always the same; when the first cone 4 and the second cone 5 are completely immersed in water, it is measured that the volumes of the first cone 4 and the second cone 5 are equal.

[0038] Zu Geng's principle is that "for two geometric bodies sandwiched between two parallel planes, if they are intercepted by any plane parallel to these two planes, and the areas of the two intercepted sections are always equal, then the volumes of these two geometric bodies are equal".

[0039] In this embodiment, during the demonstration process of the water tank demonstration system, the diameter measuring mechanism 3 measures that the diameters of the tops of the first cone 4 and the second cone 5 are the same, and the bottoms of the first cone 4 and the second cone 5 are the vertices; at the same time, the diameter measuring mechanism 3 measures that the diameters of the two cross-sectional circles where the first cone 4 and the second cone 5 intersect with the same horizontal plane are always consistent; the above experimental characteristics correspond to the prerequisite of Zu Geng's principle, that is, "two geometric bodies sandwiched between two parallel planes, intercepted by any plane parallel to these two planes, if the areas of the two intercepted cross-sections are always equal".

[0040] During the experiment, "the first cone 4 and the second cone 5 are completely immersed in water, and the water tank with scale one measures that the volumes of the first cone 4 and the second cone 5 are equal", which corresponds to the conclusion of Zu Geng's principle, that is, "then the volumes of these two geometric bodies are equal".

[0041] Therefore, Zu Geng's principle can be proved.

[0042] The above are only the preferred embodiments of the present application and are not intended to limit the present application. For those skilled in the art, various changes and modifications can be made to the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A Zu Geng's principle demonstration water tank system, characterized in that, Comprising: A pair of water tanks (1), a liftable bracket (2), a pair of diameter measuring mechanisms (3), a first cone (4) and a second cone (5); and the first cone (4) and the second cone (5) are solid cones made of metal. At the upper end of each water tank (1), one of the diameter measuring mechanisms (3) is horizontally placed. The first cone (4) and the second cone (5) are respectively suspended on the liftable bracket (2), and the liftable bracket (2) can drive the first cone (4) and the second cone (5) to move up and down simultaneously. The lower ends of the first cone (4) and the second cone (5) respectively correspond to one of the diameter measuring mechanisms (3); when the first cone (4) and the second cone (5) move, a sectional circle is respectively formed with the horizontal plane where the diameter measuring mechanism (3) is located; the diameter measuring mechanism (3) is used to judge whether the diameters of the two sectional circles always remain the same; a first scale (11) is arranged on the side of the water tank (1) to judge whether the volumes of the first cone (4) and the second cone (5) immersed in water are the same. The diameter measuring mechanism (3) includes an annular bracket (31) and at least three sliding rods (32). The sliding rods (32) radially extend on the annular bracket (31) and are annularly and arrayedly distributed. A tension spring piece (33) is arranged between the sliding rod (32) and the annular bracket (31), and the tension spring piece (33) forces the sliding rod (32) to slide towards the center point on the annular bracket (31); at the same time, a second scale (35) is arranged in the middle of the sliding rod (32) to obtain the diameter of a certain horizontal section of the first cone (4) or the second cone (5), and then judge whether the sizes of the horizontal sections where the first cone (4) and the second cone (5) are intersected by the same horizontal plane are the same.

2. The Zu Geng's principle demonstration water tank system according to claim 1, characterized in that A contact ball (34) is arranged at the front end of the sliding rod (32).

3. The Liu Hui's principle demonstration water tank system according to claim 1, characterized in that Four sliding rods (32) and four tension spring pieces (33) are respectively arranged in the diameter measuring mechanism (3).

4. The Zu Geng's Principle demonstration water tank system according to claim 1, characterized in that, The liftable bracket (2) includes a cross bar (22), a pair of vertical bars (21) and a pair of sliders (23); both ends of the cross bar (22) are respectively connected with one of the sliders (23), the slider (23) is slidably connected with the corresponding vertical bar (21), and a scale is also arranged on the matching section of the upper part of the vertical bar (21) and the slider (23).

5. The Liu Hui's principle demonstration water tank system according to claim 4, characterized in that, The side of the slider (23) has a mounting hole matching with the cross bar (22), and a threaded hole is also arranged on the side of the slider (23), and a locking screw (24) is arranged in the threaded hole.

6. The Zu Geng's principle demonstration water tank system according to claim 4, characterized in that The bottom of the vertical bar (21) is connected with a bottom plate (25).

7. The Liu Hui's principle demonstration water tank system according to claim 4, characterized in that A second bubble level (26) is installed on the cross bar (22).

8. The Liu Hui's principle demonstration water tank system according to claim 1, characterized in that A first bubble level (12) is arranged at the top of the water tank (1), and the first bubble level (12) is a universal level, including two horizontal bubbles in the horizontal and vertical directions.

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