Change demonstration teaching aid of Mobius ring

Abstract

The utility model discloses a Mobius ring change demonstration teaching aid, which belongs to the technical field of teaching aids, and comprises a bottom band and a ring band, the bottom band and the ring band are both flexible strip-shaped sheet structures, the ring band can be stably adhered to 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 of the Mobius ring can be demonstrated. 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 utility model relates to teaching aid technical field, especially a change demonstration teaching aid of mobius ring. BACKGROUND

[0002] Mobius band is a topological structure, which has only one face (surface) and one boundary. It was independently discovered by the German mathematician and astronomer, August Ferdinand Mobius, and Johann Benedict Listing in 1858. This structure can be easily made by rotating a paper band half a turn and then sticking the ends together. In fact, there are two different mirror images of the Mobius band, which are symmetrical to each other. If the paper band is rotated clockwise and then stuck together, a right-handed Mobius band is formed, and vice versa.

[0003] The Mobius band itself has many wonderful properties. If you cut along the long closed loop of the Mobius band, dividing its width in half, you will not get two narrow strips, but a Mobius band ring that twists the ends of the Mobius band twice and then rejoins them. If you cut the ring in half, you will get two rings. If you divide the width of the Mobius band into three parts and cut along the dividing lines, you will get two rings, one of which is a narrower Mobius band, and the other is a ring that has been twisted twice and then rejoined. Another interesting property is the result of rotating the paper band several times and then sticking the ends together. For example, a three-leafed knot can be formed by rotating the band three and a half turns and then cutting it. If you rotate the cut band and then stick it back together, you will get several topological structure rings.

[0004] These structural changes are diverse, and currently, topological teaching is basically explained using pictures or animations, which is difficult to explain, and students cannot understand. The structures made of paper strips are difficult to demonstrate various morphological changes, especially when the paper strip is twisted, it is difficult to demonstrate the side-by-side structure and the single paper strip morphological change in the continuation state.

[0005] Therefore, the utility model designs a change demonstration teaching aid of mobius ring to solve the above problems. UTILITY MODEL CONTENTS

[0006] The utility model aims at providing a change demonstration teaching aid of mobius ring, which can demonstrate the morphological transformation of the mobius ring between horizontal splicing and vertical continuation through the ring bands of different colors, and can also demonstrate the form change of two mobius rings being split into two rings along the width center line. The split breaks the recognition of the ring-shaped band, and the whole process can be experienced by students themselves, and they can also participate in the evolution process, making the teaching more simple and easy to understand, and the complex topological form change is intuitively displayed.

[0007] The utility model discloses a change demonstration teaching aid of mobius ring, including:

[0008] Bottom tape and ring tape;

[0009] The bottom tape is long strip sheet structure of pliable;

[0010] Uniformly set up a plurality of viscose sheet on the side of bottom tape, viscose sheet is the patch of double -sided viscose, a plurality of viscose sheet can separate and stick on bottom tape;

[0011] The end of bottom tape is set up end strip, and the end of bottom tape can be split and stick as annular belt structure of head -to -tail through end strip;

[0012] The ring tape is long strip sheet of pliable, and the ring tape has a plurality of different color spare parts, and the ring tape and spare part width are same, and the both ends of ring tape are provided with ring strip;

[0013] The both ends of single ring tape can be split and stick as closed annular belt structure of head -to -tail through ring strip;

[0014] The ring tape and spare part can also be split and stick as closed annular belt structure through ring strip;

[0015] The ring tape and spare part can be separated and attached on the same side of bottom tape through viscose sheet, and the ring tape and spare part are arranged in parallel on bottom tape;

[0016] The closed annular structure of bottom tape, ring tape and spare part pasting is circular ring or mobius ring.

[0017] Further, the end strip can also be removed and pasted on the both ends of bottom tape;

[0018] The viscose sheet, end strip and ring strip are pressure-sensitive adhesive sheet or self-adhesive silicone sheet.

[0019] Further, the bottom tape is transparent pliable PVC sheet;

[0020] The viscose sheet is evenly distributed on the bottom tape on the same straight line;

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

[0022] Further, the ring tape and spare part are colored PVC film, and the thickness of ring tape is less than the thickness of bottom tape.

[0023] Further, the edges of ring tape and spare part are closely spliced and pasted on the bottom tape.

[0024] The utility model discloses a beneficial effect is: 1, the utility model increases the transparent bottom tape, can two or more than one ring band alignment, and horizontally side by side spliced into a complete strip, then carries out positioning through the bottom tape, and two or more than one ring band splicing is the structure of integral deformation, and can closely with bottom tape and adhere, to twist or directly bend into ring and show teaching conveniently, can conveniently show the twist mode of torus or mobius ring,

[0025] 2, just because the device increases the bottom tape, can conveniently two spliced into one's body ring band again horizontal split, is two ring bands form separate individual, can conveniently show the state difference of one mobius ring horizontal split and one torus horizontal split, and whole split process, student and teacher can all manually demonstrate operation, more inculcate morality in recreation, also more vividly easy to understand,

[0026] 3, the ring band of the device and its replacement spare can be connected as a whole strip structure in front and back, and can be deformed in multiple modes, can be mutually coincident and looped, also can be overlapped and twisted into a mobius ring, and the ring band and its replacement spare in this state can also be unfolded, conveniently view the unfolding and folding and evolution process of the mobius ring, and also can be restored through the difference of color, demonstrate the change process reversely, operation is simpler, and demonstration changes variously, and show is more complete. BRIEF DESCRIPTION OF DRAWINGS

[0027] The utility model will be further described in connection with the embodiments with reference to the drawings.

[0028] Figure 1 It is the structure schematic diagram of the utility model three ring bands and its replacement spare on the bottom tape adhesive state structure;

[0029] Figure 2 It is the structure schematic diagram of the utility model one ring band split two ring bands on the bottom tape adhesive state structure;

[0030] Figure 3 It is the structure schematic diagram of the utility model bottom tape into ring shape adhesive state structure;

[0031] Figure 4 It is the structure schematic diagram of the utility model two structures on the bottom tape;

[0032] Figure 5 It is the structure schematic diagram of the utility model two ring bands before and after head to tail connection twist into mobius ring state structure;

[0033] Figure 6 It is the structure schematic diagram of the utility model two ring bands before and after head to tail connection and superimposed as double layer mobius ring structure;

[0034] Figure 7 The structure schematic diagram of the Mobius ring with three ring bands in the unfolded state is shown in Figure 3.

[0035] Figure 8 The structure schematic diagram of the Mobius ring with three ring bands in the unfolded state is shown in Figure 3.

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

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

[0038] Referring to Figures 1 to 8 The utility model provides a Mobius ring's change demonstration teaching aid, in order to better understand the above technical scheme, the following will combine with the description drawing and specific implementation mode to the above technical scheme carries out the detailed explanation.

[0039] In one specific embodiment of the technical scheme of the utility model:

[0040] The bottom band 1 and the ring band 2 are included;

[0041] The bottom band 1 is a flexible long strip-shaped sheet structure; the bottom band 1 is a transparent flexible PVC sheet; it is convenient to twist and deform, and also can conveniently show the ring band 2 pasted thereon, and the transparent material does not affect the observation of the changes of the ring band 2 on the front and back surfaces.

[0042] The ring band 2 and the spare part thereof are colored PVC films, the thickness of the ring band 2 is less than the thickness of the bottom band 1, so that the ring band 2 and the bottom band 1 can be conveniently deformed, and the condition that the bottom band 1 is twisted and broken due to the excessive hardness of the ring band 2 is avoided; the ring band 2 needs to be bent and deformed together with the bottom band 1, and the ring band 2 needs to be more flexible to follow the deformation.

[0043] A plurality of adhesive sheets 11 are uniformly arranged on one side of the bottom band 1; the adhesive sheet 11 is a patch with adhesive on both sides, and the plurality of adhesive sheets 11 can be detachably pasted on the bottom band 1; the edges of the ring band 2 and the spare part thereof are closely spliced and pasted on the bottom band 1, and then the edges are closely spliced, so that the structure is stable, and the morphological changes of the ring band 2 and the spare part thereof of different colors can be conveniently understood. The adhesive sheets 11 are uniformly distributed on the bottom band 1 on the same straight line; so that the ring band 2 can be integrally pasted on the bottom band 1, the middle part of the ring band 2 and the bottom band 1 is prevented from being raised and separated, and it is ensured that the pasting is maintained during the twisting and deformation.

[0044] End strips 12 are arranged at both ends of the bottom band 1, and the bottom band 1 can be detachably pasted into a ring-shaped band structure with the ends connected through the end strips 12;

[0045] The ring belt 2 is a flexible sheet-shaped long strip, the ring belt 2 has a plurality of different color spare parts, the ring belt 2 has the same width as the spare part, and both ends of the ring belt 2 are provided with ring stickers 21; the end stickers 12 can also be removed and adhered to the bottom tape 1, facilitating replacement or adhesion to different positions of the end stickers 12.

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

[0047] The ring belt 2 and one or more spare parts are connected end to end in sequence, facilitating the display of more different morphological Mobius ring deformation and topological structure morphological change.

[0048] The two ends of a single ring belt 2 are adhered by the ring stickers 21 to form a closed ring-shaped belt structure connected end to end;

[0049] The ring belt 2 and the spare part are adhered by the ring stickers 21 to form a closed ring-shaped belt structure;

[0050] The ring belt 2 and the spare part are adhered by the ring stickers 21 to form a closed ring-shaped belt structure;

[0051] The bottom tape 1, the ring belt 2 and the spare part are adhered to form a closed ring structure, which is a circular ring or a Mobius ring.

[0052] The bottom tape 1 has a plurality of different width replacement parts, the width s of the bottom tape 1 is a multiple of the width d of the ring belt 2, and the width of the bottom tape 1 is 2, 3 or 4 times the width of the ring belt 2. Such integral multiple design can facilitate the bottom tape 1 to carry different number of ring belts 2, when two ring belts 2 are transversely spliced, a bottom tape 1 with a width of 2 times is selected, when three ring belts 2 are spliced, a bottom tape 1 with a width of 3 times is selected.

[0053] It should be noted that:

[0054] The structure of a single Mobius ring can be imagined and easily seen in life. When the Mobius ring changes its shape, unexpected changes will occur, which are completely different from the general circular ring. Generally, the circular ring is either separated or nested, while the Mobius ring composed of a single ring belt 2 cannot be separated, and when Figure 4 two ring belts are arranged side by side to form a circular ring, and then the inner and outer layers are overlapped to form a double-layer Mobius ring in Figure 6 state, when it is unfolded, a twisted topological structure as shown in Figure 7 is obtained, and a three-layer inner and outer overlapping state Mobius ring is unfolded to obtain a twisted topological structure as shown in Figure 8The ring-shaped state is a change that is difficult to show with pictures. Currently, some topology teaching can only show it through simple animations, and cannot show and explain every step of the entire change process. This greatly increases the difficulty of current topology teaching. Students who have never seen this change find it difficult to understand the specific changes, while those who have seen this change cannot explain it clearly. This is also the difficulty of this teaching.

[0055] 1. Current teaching methods can only use animation or pictures, and students rely on pictures to memorize the results. They cannot imagine the process of change. This device can be operated directly by hand, and its various forms can be explored and studied on their own, which is more convenient.

[0056] 2. In general, when such overlapping Möbius strips and topological structures deform, they are unfolded in an instant. However, this device, through different colored rings 2 and splicing them end to end, can determine the initial position and then deform them back to the initial state. This allows for a deeper understanding of the change process and a clearer understanding of the knowledge.

[0057] 3. Existing Möbius strips cannot be spliced ​​horizontally, and it is unclear how different colored rings twist and deform. This device attaches multiple rings 2 to the base strip 1 and ensures tight adhesion through adhesive sheet 11, thus enabling the understanding of the twisting shape changes of the rings 2 spliced ​​horizontally in the left and right directions.

[0058] In use, according to the actual teaching content, different numbers of rings 2 are selected and pasted onto the base belt 1. The entire ring 2 is tightly pasted along the line using adhesive sheet 11 to ensure that it will not lift up. Then, the ring strip 21 is also pasted onto the base belt 1. When deformation is required, simply twist or bend the base belt 1. All the rings 2 on the base belt 1 will deform along with the base belt 1. Multiple rings 2 of different colors will be twisted in a rainbow state after deformation. The base belt 1 is made of transparent material and will not obscure the color of the rings 2.

[0059] The horizontally spliced ​​ring 2 is also pasted on the base 1. Even when twisted and held in a suspended position for display, it will not separate, which is convenient for teaching demonstrations. It is precisely because the shape of the Möbius strip is difficult to describe and can only be shown by twisting that its changes are needed for demonstration. This device can also more intuitively and appropriately show the shape changes of Möbius strips of different colors and splicing methods.

[0060] When the ring belt 2 needs to be longitudinally spliced, the bottom belt 1 is removed, the ring belt 2 is directly connected end to end according to the requirement, is firmly pasted through the ring tape 21, then can be deformed according to the requirement, when end to end, different colors of ring belt 2 and its spare parts should be selected, so that the color change can also be seen when twisting.

[0061] Although the specific embodiments of the present application are described above, those skilled in the art should understand that the specific embodiments described are only illustrative, not for limiting the scope of the present application, and equivalent modifications and changes made by those skilled in the art in accordance with the spirit of the present application should be covered within the scope of the claims of the present application.

Claims

1. A demonstration apparatus for the transformation of a Mobius strip, characterized in that, The utility model relates to a kind of variation demonstration teaching aids of Mobius ring, including: Bottom band (1) and ring band (2); The bottom band (1) is flexible long strip shape structure; The bottom band (1) is uniformly provided with a plurality of adhesive pieces (11) on one side, the adhesive piece (11) is double-sided adhesive patch, a plurality of the adhesive piece (11) can be separated and pasted on the bottom band (1); The bottom band (1) is provided with end strip (12) at both ends, and the bottom band (1) is pasted by end strip (12) at both ends to be detachable and connected in a ring shape; The ring band (2) is flexible sheet long strip, the ring band (2) has a plurality of different color spare parts, the ring band (2) is same as the width of spare part, and both ends of the ring band (2) are provided with ring strip (21);End strip (12) can also be pasted at both ends of the bottom band (1) and be detachable; Both ends of a single ring band (2) are pasted by ring strip (21) to be detachable and connected in a closed ring shape; The ring band (2) and spare part are also pasted by ring strip (21) to be detachable and connected in a closed ring shape; The ring band (2) and its spare part are pasted on the same side of the bottom band (1) by adhesive piece (11) and can be separated, and the ring band (2) and spare part are arranged in parallel on the bottom band (1);And the ring band (2) and its spare part on the same bottom band (1) are sequentially and side by side spliced, and the edge is aligned with each other; The closed ring structure pasted by the bottom band (1), ring band (2) and spare part is circular ring or Mobius ring.

2. The variation demonstration teaching aid of Mobius ring according to claim 1, wherein: The adhesive piece (11), end strip (12) and ring strip (21) are pressure-sensitive adhesive sheet or self-adhesive silicone sheet.

3. A demonstration apparatus of the variation of a Mobius strip according to claim 1, characterized in that: The bottom band (1) is transparent flexible PVC sheet; The adhesive piece (11) is uniformly distributed on the bottom band (1) on the same straight line; The bottom band (1) has a plurality of different width replacement parts, the width s of the bottom band (1) is multiple of the width d of the ring band (2), and the width of the bottom band (1) is 2, 3 or 4 times the width of the ring band (2).

4. The demonstration apparatus of claim 1, wherein: The ring band (2) and its spare part are colored PVC film, and the thickness of the ring band (2) is less than the thickness of the bottom band (1).

Images