Change demonstration teaching aid of Mobius ring

Abstract

The invention discloses a Mobius ring change demonstration teaching aid in the technical field of teaching aids, and the Mobius ring change demonstration teaching aid comprises a bottom band and a ring band which are both flexible long-strip-shaped sheet structures, the ring band can be stably pasted on the bottom band and can be conveniently twisted and deformed, the ring band is provided with a plurality of spare parts with different colors, the ring band with different colors can pass through the ring band with different colors, and the change demonstration teaching aid can be used for demonstrating the change of a Mobius ring. When the Mobius rings are split into two rings along the width center line, the ring belts deform along with the bottom belt to display the form transformation of the Mobius rings between transverse splicing and longitudinal splicing, and the two ring belts can be disassembled, so that the form change of the two Mobius rings split into the two rings along the width center line can be demonstrated and simulated, the cognition on the ring belts after the two Mobius rings are split can be obviously known to be broken after the two Mobius rings are split. Moreover, the whole process can be felt by the students, and the students can participate in the evolution process, so that the teaching is simpler and easier to understand, and the complex morphological change of the topology is visually displayed.

Description

Technical Field

[0001] The invention relates to the technical field of teaching aids, in particular to a teaching aid for demonstrating the changes of a Mobius ring. Background Art

[0002] The Möbius strip is a topological structure with only one face (surface) and one boundary. It was independently discovered by German mathematician and astronomer Johann Listing in 1858. This structure can be easily made by rotating a paper strip half a turn and then gluing the two ends together. In fact, there are two different mirror images of the Möbius strip, which are symmetrical to each other. If you rotate the paper strip clockwise and then glue it together, you will form a right-handed Möbius strip, and vice versa.

[0003] The Möbius strip itself has many interesting properties. If you cut the strip along the midline of the long closed loop of the Möbius strip and divide its width in half, you will not get two narrow strips, but a Möbius strip loop with the ends of the strip twisted twice and then combined. If you cut the loop just made with the ends of the paper strip twisted twice and then combined from the middle, it will become two loops. If you divide the width of the Möbius strip into three parts and cut it along the dividing line, you will get two loops, one is a narrower Möbius strip, and the other is a loop that is rotated twice and then combined. Another interesting property is produced by rotating the paper strip several times and then pasting the ends together. For example, a strip that is rotated three and a half turns and then cut will form a trefoil knot. Cutting the strip and then rotating it and then pasting it again will form several topological structure loops.

[0004] These structural changes are varied. Currently, this kind of topology teaching basically uses pictures or animations, which are difficult to explain and students cannot understand. The commonly used structures made of paper strips are difficult to show various morphological changes, especially when the paper strips are twisted, they cannot show parallel structures, nor can they show the morphological changes of a single paper strip in a connected state.

[0005] Based on this, the present invention designs a variation demonstration teaching aid of a Möbius ring to solve the above problems. Summary of the invention

[0006] The purpose of the present invention is to provide a teaching aid for demonstrating the changes of a Möbius ring, which can demonstrate the morphological transformation of the Möbius ring between horizontal splicing and longitudinal continuation through ring bands of different colors, and can also demonstrate the morphological change of simulating two Möbius rings being split into two rings along a width midline. It can be obviously known that the cognition of the ring band is broken after the splitting, and the whole process can be felt by students themselves, and they can also participate in the evolution process, so that the teaching is simpler and easier to understand, and the complex topological morphological changes are intuitively demonstrated.

[0007] The present invention is implemented as follows: a Möbius ring variation demonstration teaching aid, comprising:

[0008] Base band and hoop band;

[0009] The bottom belt is a flexible long strip sheet structure;

[0010] A plurality of adhesive sheets are evenly arranged on one side of the bottom belt, wherein the adhesive sheets are double-sided adhesive sheets, and the plurality of adhesive sheets can be detachably attached to the bottom belt;

[0011] End strips are provided at both ends of the bottom belt, and the two ends of the bottom belt can be detachably pasted into an annular belt structure connected end to end through the end strips;

[0012] The endless belt is a flexible sheet-like strip, and the endless belt has a plurality of spare parts of different colors. The endless belt has the same width as the spare parts, and both ends of the endless belt are provided with annular strips;

[0013] The two ends of a single ring belt can be detachably pasted by ring sticking strips to form a closed ring belt structure connected end to end;

[0014] The endless belt and the spare parts can also be detachably pasted into a closed annular belt structure through the annular pasting strip;

[0015] The endless belt and the spare parts are detachably attached to the same side of the bottom belt through an adhesive sheet, and the endless belt and the spare parts are arranged parallel to each other on the bottom belt row;

[0016] The closed annular structure formed by pasting the bottom belt, the annular belt and the spare parts is a circular ring or a Mobius ring.

[0017] Furthermore, the end stickers can also be removably attached to the two ends of the bottom belt;

[0018] The adhesive sheet, the end strips and the ring strips are all pressure-sensitive adhesive sheets or self-adhesive silicone sheets.

[0019] Furthermore, the bottom belt is a transparent and flexible PVC sheet;

[0020] The adhesive sheets are evenly distributed on the bottom belt in the same straight line;

[0021] The bottom belt has a plurality of replacement parts with different widths, the width s of the bottom belt is a multiple of the width d of the annular belt, and the bottom belt is 2, 3 or 4 times the width of the annular belt.

[0022] Furthermore, the endless belt and its spare parts are colored PVC films, and the thickness of the endless belt is smaller than the thickness of the bottom belt.

[0023] Furthermore, the edges of the endless belt and its spare parts are closely spliced ​​and pasted on the bottom belt.

[0024] The beneficial effects of the present invention are as follows: 1. The present invention adds a transparent bottom belt, which can align two or more ring belts, assemble them side by side horizontally into a complete long strip, and then carry and position them through the bottom belt, so that the two or more ring belts are spliced ​​into an overall deformed structure, and can be closely fitted with the bottom belt, so that they can be conveniently twisted or directly bent into a ring for teaching demonstration, and can conveniently display the twisted shape of a ring or a Mobius ring;

[0025] 2. Because the device adds a bottom belt, it can easily split the two spliced ​​ring belts horizontally, so that the two ring belts form separate individuals, which can easily show the difference between the state of a Mobius ring split horizontally and a circular ring split horizontally. In addition, students and teachers can manually demonstrate the whole splitting process, which is more entertaining and vivid.

[0026] 3. The ring belt and its replacement parts of the device can be connected front to back to form an overall long strip structure, and can be deformed in various forms, can overlap each other, and can be twisted into a Möbius strip after overlapping. The ring belt and its replacement parts in this state can also be unfolded again, so that the unfolding, contraction and evolution process of the Möbius strip can be easily viewed, and can also be restored through different colors, and the change process can be reversely demonstrated. The operation is simpler, the demonstration changes are diverse, and the display is more complete. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The present invention will be further described below in conjunction with embodiments with reference to the accompanying drawings.

[0028] Figure 1 It is a schematic structural diagram of the three endless belts and their replacement parts being bonded on the bottom belt of the present invention;

[0029] Figure 2 This is a schematic diagram of the structure of the present invention in which one endless belt is split into two endless belts and the two endless belts are attached to the bottom belt;

[0030] Figure 3 This is a schematic diagram of the structure of the bottom belt of the present invention in a ring-shaped bonding state;

[0031] Figure 4 It is a schematic diagram of two structures on the bottom belt of the present invention;

[0032] Figure 5 It is a schematic diagram of the structure of the present invention in which two ring belts are connected end to end and twisted into a Mobius ring;

[0033] Figure 6 It is a schematic diagram of the structure of the two ring belts of the present invention connected end to end and then overlapped to form a double-layer Möbius ring;

[0034] Figure 7It is a schematic diagram of the structure of the two overlapping Mobius rings of the present invention in a connected and unfolded state;

[0035] Figure 8 It is a schematic diagram of the structure of the unfolded state of the three overlapping Möbius rings of the present invention.

[0036] In the accompanying drawings, the components represented by the reference numerals are listed as follows:

[0037] 1-bottom tape, 11-adhesive sheet, 12-end strip, 2-ring tape, 21-ring strip. DETAILED DESCRIPTION

[0038] See also Figures 1 to 8 As shown, the present invention provides a Möbius strip variation demonstration teaching aid. In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings in the specification and specific implementation methods.

[0039] In a specific embodiment of the technical solution of the present invention:

[0040] It includes a bottom belt 1 and a ring belt 2;

[0041] The bottom belt 1 is a flexible long strip sheet structure; the bottom belt 1 is a transparent and flexible PVC sheet; it is easy to twist and deform, and can also conveniently display the ring belt 2 pasted thereon, and the transparent material does not affect the observation of the changes of the ring belt 2 on both sides.

[0042] The ring belt 2 and its spare parts are colorful PVC films. The thickness of the ring belt 2 is less than that of the bottom belt 1, so that the ring belt 2 and the bottom belt 1 can be easily deformed, avoiding the situation where the bottom belt 1 is twisted and broken due to the excessive hardness of the ring belt 2. The ring belt 2 needs to bend and deform together with the bottom belt 1. If the hardness of the ring belt 2 is too high, it will warp, and the ring belt 2 needs to be more flexible to follow the deformation.

[0043] Multiple adhesive sheets 11 are evenly arranged on one side of the bottom belt 1. The adhesive sheets 11 are double-sided adhesive sheets. The multiple adhesive sheets 11 can be detachably pasted on the bottom belt 1. The edges of the ring belt 2 and its spare parts are closely spliced ​​and pasted on the bottom belt 1, and then the edges are tightly assembled to make its structure stable, which is convenient for understanding the shape changes of the ring belts 2 and their spare parts of different colors. The adhesive sheets 11 are evenly distributed on the bottom belt 1 on the same straight line; thus, the ring belt 2 can be attached to the bottom belt 1 as a whole, avoiding the warping and separation of the middle part of the ring belt 2 and the bottom belt 1, and ensuring that it always remains attached when twisting and deforming.

[0044] End strips 12 are provided at both ends of the bottom belt 1, and the two ends of the bottom belt 1 can be detachably pasted into an annular belt structure connected end to end through the end strips 12;

[0045] The endless belt 2 is a flexible sheet-like strip. The endless belt 2 has a plurality of spare parts of different colors. The width of the endless belt 2 and the spare parts are the same, and the two ends of the endless belt 2 are provided with annular strips 21; the end strips 12 can also be removed and detached and pasted on the bottom belt 1, so that the end strips 12 can be replaced or pasted in different positions.

[0046] The adhesive sheet 11, the end strips 12 and the ring strips 21 are all pressure-sensitive adhesive sheets or self-adhesive silicone sheets.

[0047] The ring belt 2 is connected end to end with one or more spare parts in sequence, so as to facilitate the display of more different forms of Möbius ring deformation and topological structure changes.

[0048] The two ends of a single ring belt 2 can be detachably pasted by a ring sticking strip 21 to form a closed ring belt structure connected end to end;

[0049] The endless belt 2 and the spare parts can also be detachably pasted into a closed annular belt structure through the annular sticker strip 21;

[0050] The endless belt 2 and its spare parts are detachably attached to the same side of the bottom belt 1 through an adhesive sheet 11, and the endless belt 2 and the spare parts are arranged parallel to each other on the bottom belt 1;

[0051] The closed annular structure formed by pasting the bottom belt 1, the ring belt 2 and the spare parts is a circular ring or a Mobius ring.

[0052] The bottom belt 1 has multiple replacement parts with different widths. The width s of the bottom belt 1 is a multiple of the width d of the ring belt 2, and the bottom belt 1 is 2, 3 or 4 times the width of the ring belt 2. Such an integer multiple design can facilitate the bottom belt 1 to carry different numbers of ring belts 2. When two ring belts 2 are spliced ​​horizontally, a bottom belt 1 with a width of 2 is selected. When three ring belts 2 are spliced, a bottom belt 1 with a width of 3 times is selected. It can be selected according to needs.

[0053] It should be noted that:

[0054] The structure of a single Möbius strip is imaginable and easy to see in life. However, when the Möbius strip changes its shape, it will undergo unexpected changes. This change is completely different from the common circular strips. Generally, circular strips are either separated or nested, while the Möbius strip composed of a single ring belt 2 cannot be separated. Figure 4 As shown, two side-by-side rings form a ring, and then overlap the inner and outer rings to form Figure 6 When the double-layer Möbius strip is unfolded, the following Figure 7 The twisted topological structure shown in the figure, while the three-layer Möbius ring with internal and external overlap will be unfolded to obtain the following Figure 8The ring shape of the state is difficult to show with pictures. At present, some topology teaching can only be shown through simple animations, and it is impossible to show and explain each step of the whole change process, which makes the current topology teaching more difficult. Students who have not seen this change find it difficult to understand the specific changes, and those who have seen this change cannot explain it clearly. This is also the difficulty of this teaching;

[0055] 1. The current teaching method can only be animation or pictures. Students rely on pictures to memorize the results. This change process is completely unimaginable. This device can be operated directly, and various forms can be explored and studied slowly by themselves, which is more convenient.

[0056] 2. Generally, such overlapping Mobius rings and topological structures are unfolded in an instant when deformed. However, this device uses rings 2 of different colors and splices them end to end to understand the initial position, and then reversely deforms back to the initial state, so that the change process can be more deeply understood and the knowledge can be more clearly understood;

[0057] 3. The existing Möbius strips cannot be spliced ​​horizontally, and it is not known how the strips of different colors are twisted and deformed. The device sticks multiple strips 2 on the bottom strip 1, and ensures tight adhesion through the adhesive sheet 11, so that the twisting shape changes of the strips 2 spliced ​​horizontally in the left and right directions can be understood.

[0058] When the present invention is used, different numbers of ring bands 2 are selected to be pasted on the base band 1 according to the actual teaching content, and the entire ring band 2 is pasted tightly along the line through the adhesive sheet 11 to ensure that it will not curl up, and then the ring sticker strip 21 is also pasted on the base band 1. When deformation operation is required, it only needs to twist or directly bend the base band 1 to complete it. All the ring bands 2 on the base band 1 will deform together with the base band 1. Multiple ring bands 2 of different colors will be twisted in a rainbow state after deformation, and the base band 1 is made of transparent material and will not block the color of the ring band 2.

[0059] In this way, the horizontally spliced ​​ring belt 2 is also pasted on the bottom belt 1, and will not be separated even if it is twisted and held in a hovering display, which is convenient for teaching and demonstration. It is precisely because the shape of the Möbius strip is difficult to describe and its changes can only be displayed by twisting, so this device is needed for display. This device can also more intuitively and adaptively display the shape change process of the Möbius strip with different colors and different splicing methods.

[0060] When the ring belt 2 needs to be spliced ​​longitudinally, the bottom belt 1 is removed, and the ring belt 2 is directly connected end to end as required, and is firmly attached by the ring sticker strip 21, and then can be bent and deformed as required. When the end to end is connected, the ring belt 2 and its spare parts of different colors should be selected, so that the color change can be clearly seen when twisting. After the display changes, the end to end of the ring belt 2 remains firmly attached, so that it is convenient to twist in various different forms.

[0061] Although the specific implementation modes of the present invention are described above, those skilled in the art should understand that the specific implementation modes described are only illustrative and are not intended to limit the scope of the present invention. Equivalent modifications and changes made by those skilled in the art in accordance with the spirit of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A teaching aid for demonstrating the changes of a Möbius ring, characterized in that: include: A bottom belt (1) and an annular belt (2); The bottom belt (1) is a flexible long strip sheet structure; A plurality of adhesive sheets (11) are evenly arranged on one side of the base tape (1), wherein the adhesive sheets (11) are double-sided adhesive sheets, and the plurality of adhesive sheets (11) can be detachably attached to the base tape (1); End strips (12) are provided at both ends of the bottom belt (1), and the two ends of the bottom belt (1) can be detachably pasted together to form an annular belt structure connected end to end through the end strips (12); The endless belt (2) is a flexible sheet-like strip, the endless belt (2) has a plurality of spare parts of different colors, the endless belt (2) has the same width as the spare parts, and both ends of the endless belt (2) are provided with annular strips (21); The two ends of a single ring belt (2) can be detachably pasted together by a ring pasting strip (21) to form a closed ring belt structure connected end to end; The annular belt (2) and the spare parts are also detachably adhered to form a closed annular belt structure through an annular pasting strip (21); The endless belt (2) and the spare parts are detachably attached to the same side of the bottom belt (1) via an adhesive sheet (11), and the endless belt (2) and the spare parts are arranged parallel to each other on the bottom belt (1); The closed annular structure formed by pasting the base belt (1), the annular belt (2) and the spare parts is a circular ring or a Mobius ring.

2. A Möbius strip variation demonstration teaching aid according to claim 1, characterized in that: The end stickers (12) are also removably attached to the two ends of the bottom belt (1); The adhesive sheet (11), the end strip (12) and the ring strip (21) are all pressure-sensitive adhesive sheets or self-adhesive silicone sheets.

3. A teaching aid for demonstrating the changes of a Möbius ring according to claim 1, characterized in that: The bottom belt (1) is a transparent and flexible PVC sheet; The adhesive sheets (11) are evenly distributed on the bottom belt (1) on the same straight line; The bottom belt (1) has a plurality of replacement parts with different widths, the width s of the bottom belt (1) is a multiple of the width d of the ring belt (2), and the bottom belt (1) is 2, 3 or 4 times the width of the ring belt (2).

4. A teaching aid for demonstrating the changes of a Möbius ring according to claim 1, characterized in that: The endless belt (2) and its spare parts are colored PVC films, and the thickness of the endless belt (2) is smaller than the thickness of the bottom belt (1).

5. The teaching aid for demonstrating the changes of a Möbius strip according to claim 1, characterized in that: The edges of the endless belt (2) and its spare parts are tightly spliced ​​and pasted on the bottom belt (1).

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