A geometric figure deformation demonstration device based on the principle of cavaleri

Abstract

The application discloses a geometric figure deformation demonstration device based on the Cavalieri principle, which comprises a back plate, a plurality of parallel linear guides arranged on the surface of the back plate along the width direction, a plurality of strip plates with equal width and different length connected to the linear guides through linear sliders, and all the strip plates arranged in sequence to form a plane geometric figure; and a driving assembly connected to the back plate and used for driving all the strip plates to move in the same direction. The application can realize dynamic demonstration and multi-dimensional observation and exploration in the whole process, and has high expansibility.

Description

Technical Field

[0001] This invention belongs to the field of mechanical teaching toys technology, specifically relating to a geometric shape deformation demonstration device based on Cavalieri's principle. Background Technology

[0002] Existing technologies in mechanical teaching toys are mainly used for multimedia presentations and simple geometric manipulatives, but their drawbacks are: 1. The demonstration of the area of ​​geometric figures is not intuitive enough and fails to explain the underlying principles and essence; 2. Lacks interactivity and fun, and has a single perspective; 3. Lacks scalability; 4. Using simple components such as rubber bands and small balls has limitations in terms of durability and smoothness; 5. It lacks the important rule of "Cavalleria's principle" that "if the lengths of the cross sections at the same height of two figures are equal, then their areas are equal".

[0003] The utility model patent with publication number CN202838747U uses a variable triangular container filled with steel balls. By changing the triangle, the steel balls can roll freely to achieve a demonstration function with the same area. However, due to the compression and friction of the internal space, the rolling balls cannot be guaranteed to fill to the ideal position. This causes serious wear and tear on components such as plexiglass, and it cannot achieve an open interactive experience, nor does it have the function of demonstrating the "Cavalleria principle". Summary of the Invention

[0004] The purpose of this invention is to provide a geometric deformation demonstration device based on Cavalieri's principle, which enables dynamic demonstration of the entire process and multi-dimensional observation and exploration, and has high scalability.

[0005] To achieve the above objectives, the present invention provides a geometric deformation demonstration device based on Cavalieri's principle, comprising a back plate, wherein a plurality of parallel linear guide rails are provided on the surface of the back plate along the width direction, and a plurality of strip plates of equal width and unequal length are connected to the linear guide rails by linear sliders, and all strip plates are arranged in sequence to form a planar geometric figure. The back panel is connected to a drive assembly that drives all the strips to move in the same direction.

[0006] As a further embodiment of the present invention: the driving assembly includes a positioning seat, a hinge seat, an optical axis and several connecting parts. The positioning seat is fixed at one long side of the back plate, the hinge seat is fixed at the end of the strip plate away from the positioning seat, and the connecting parts are rotatably connected to the same side ends of the remaining strip plates and the positioning seat respectively. The optical axis is slidably connected to all the connecting parts and rotatably connected to the hinge seat.

[0007] As a further aspect of the present invention, a handle extends outward from the hinge seat.

[0008] As a further aspect of the present invention, the connecting element is a linear bearing.

[0009] As a further aspect of the present invention: the length of the strip plate increases sequentially along the width direction of the back plate.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: The geometric figure is cut into multiple strips along the horizontal direction. Each strip has a constant length and can be moved arbitrarily in the horizontal direction. The area of ​​the resulting geometric figure remains unchanged, making the transformation of the figure and the explanation of the principle more intuitive. The handle and optical axis allow the operator to perform a dynamic demonstration of the entire process and conduct multi-dimensional observation and exploration. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the geometric deformation demonstration device based on Cavalieri's principle of the present invention.

[0012] Figure 2 This is a schematic diagram of the deformed structure of the present invention - an acute triangle.

[0013] Figure 3 This is a schematic diagram of the deformed state structure of the present invention - a right-angled triangle.

[0014] Figure 4 This is a schematic diagram of the deformed structure of the present invention - an obtuse triangle.

[0015] In the diagram: 1. Back plate, 2. Handle, 3. Hinge seat, 4. Linear guide rail, 5. Strip plate, 6. Linear slider, 7. Flange bearing, 8. Connector, 9. Positioning seat, 10. Optical axis. Detailed Implementation

[0016] The invention will now be further described with reference to the accompanying drawings.

[0017] like Figure 1 As shown, a geometric deformation demonstration device based on Cavalieri's principle includes a back plate 1. Several parallel linear guide rails 4 are provided on the surface of the back plate 1 along the width direction. Several strip plates 5 with equal width and different lengths are connected to the linear guide rails 4 through linear sliders 6. All strip plates 5 are arranged in sequence to form a planar geometric figure. The back plate 1 is connected to a drive assembly that drives all the strip plates 5 to move in the same direction. The drive assembly drives all the strip plates 5 to move on the linear slide rail via the linear slider 6, thereby creating a deformation effect.

[0018] To achieve unidirectional movement control of all strip plates 5 and enable them to move in unison, the drive assembly further includes a positioning seat 9, a hinge seat 3, an optical shaft 10, and several connecting pieces 8. The positioning seat 9 is fixed to one long side of the back plate 1, and the hinge seat 3 is fixed to the end of the strip plate 5 away from the positioning seat 9. The connecting pieces 8 are rotatably connected to the ends of the remaining strip plates 5 on the same side and to the positioning seat 9, respectively. The connecting pieces 8 are rotatably connected to the strip plates 5 and the positioning seat 9 via flange bearings 7. The optical shaft 10 slides through all the connecting pieces 8 and is rotatably connected to the hinge seat 3. By driving the optical shaft 10 to rotate around the positioning seat 9, the optical shaft 10 slides through all the connecting pieces 8, causing them to move and adjust, thereby creating different deformation effects.

[0019] To facilitate the movement control of the drive optical axis 10, a handle 2 is further extended outward from the hinge seat 3. When the operator interacts with the device, they only need to hold the handle 2 and move it to both sides along the linear guide rail 4.

[0020] To maintain the sliding connection of the optical axis 10, the connecting piece 8 is further designed as a linear bearing, which ensures that the optical axis 10 maintains good sliding action with the connecting piece 8 during movement, thereby allowing the optical axis 10 to smoothly drive all the strip plates 5 to move and adjust.

[0021] Furthermore, the length of the strip plates 5 increases sequentially along the width direction of the back plate 1, and all the strip plates 5 are combined to form a triangular structure; by controlling the handle 2, the optical axis 10 is driven to move all the strip plates 5, thereby achieving deformation and forming a shape such as Figures 2 to 4 The acute, right, and obtuse triangles shown have the same area because the length of each strip 5 is fixed.

[0022] The core principle of this invention is Cavalieri's principle: if two planar figures are sandwiched between two parallel lines and the lengths of the line segments intercepted by any straight line parallel to these two parallel lines are equal, then the areas of the two figures are equal.

[0023] The example uses triangles with the same base and height, where the area remains unchanged, as a typical case. This visually demonstrates that two figures with equal cross-sectional lengths at the same height have equal areas. Furthermore, the interactive demonstration enhances the learning experience. This method can also be used to explain other figures such as trapezoids and parallelograms, where horizontal deformation does not change the area.

Claims

1. A geometric deformation demonstration device based on Cavalieri's principle, comprising a back plate (1), characterized in that, The back plate (1) has several parallel linear guide rails (4) arranged along the width direction. Several strip plates (5) of equal width and different lengths are connected to the linear guide rails (4) by linear sliders (6). All the strip plates (5) are arranged in sequence to form a planar geometric figure. A drive assembly is connected to the back plate (1) to drive all the strip plates (5) to move in the same direction.

2. The geometric deformation demonstration device based on Cavalieri's principle according to claim 1, characterized in that, The drive assembly includes a positioning seat (9), a hinge seat (3), an optical axis (10), and several connecting parts (8). The positioning seat (9) is fixed on one long side of the back plate (1), the hinge seat (3) is fixed on the end of the strip plate (5) away from the positioning seat (9), and the connecting parts (8) are rotatably connected to the same side end of the remaining strip plates (5) and the positioning seat (9). The optical axis (10) slides and connects all the connecting parts (8) in series, and is rotatably connected to the hinge seat (3).

3. The geometric deformation demonstration device based on Cavalieri's principle according to claim 2, characterized in that, A handle (2) extends outward from the hinge seat (3).

4. The geometric deformation demonstration device based on Cavalieri's principle according to claim 2, characterized in that, The connecting component (8) is a linear bearing.

5. A geometric deformation demonstration device based on Cavalieri's principle according to claim 2, characterized in that, The length of the strip (5) increases sequentially along the width direction of the back plate (1).

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