CN112634715A - Circle cutting demonstration instrument by inscribed polygon method - Google Patents

Abstract

The invention discloses a circle cutting demonstration instrument by an inscribed polygon method, which comprises: support, synchronous gear separator, uncovered cask, elasticity rope and transparent stay cord, the main part of support is branch and round axle pipe, synchronous gear separator includes ring dish and pivot, the pivot of synchronous gear separator inserts in the round axle pipe of support, the opening cup joint of uncovered cask is on the support, the ring dish of synchronous gear separator is in the uncovered cask, elasticity rope shunting is in the barrel head outside of uncovered cask, transparent stay cord links together elasticity rope and synchronous gear separator. The invention discloses an inscribed polygon method cyclotomy demonstration instrument which has complete functions: the whole process and the reaction process from expanding the circle inscribed regular hexagon into the regular dodecagon and then expanding the regular dodecagon into the twenty tetragon to the forty octagon can be quickly finished. The structure is compact, the cost is low, and the carrying is convenient; the applicability is strong: can be used in any occasions. Is suitable for teaching, light exhibition, etc.

Description

Circle cutting demonstration instrument by inscribed polygon method

The technical field is as follows:

the invention relates to a teaching display device, in particular to a circle cutting demonstration instrument by an inscribed polygon method.

Background art:

the circle cutting is a method for solving the circumference ratio, namely, the area of a circle inscribed with a regular polygon is infinitely approximated to the area of the circle, and the circumference ratio is solved by the method, the approximation process is the best explanation of the limit thought, particularly, the series limit is always the key point and the difficulty point in mathematical teaching, and because no proper teaching aid or available physical situation exists, great difficulty is brought to the learning and understanding of students, and the teaching effect and the learning quality are influenced. In order to solve the above problems, a few devices regarding the limit have appeared in the near stage, for example, patent application No. 201220379498.3 discloses "a series limit demonstration instrument", in which a set of elliptical plates having an ellipse similarity ratio of 0.5 and two foci trisecting the major axis of the ellipse and a semi-elliptical plate are fixed on a rigid flat plate, the left focus of the first semi-elliptical plate coincides with the right focus of the elliptical plate, the left focus of the second semi-elliptical plate coincides with the right focus of the first semi-elliptical plate, so that a glass ball (or a laser beam) is emitted from the left focus and reflected by the peripheries of the elliptical plate, the first semi-elliptical plate and the second semi-elliptical plate, and the intersection (focus) of the trajectory of the reflected rays on the major axis is sequentially moved to the right at a ratio of the distance between two adjacent intersections of 0.5. The problem is solved by demonstrating a series limit concept by the law that a sphere (or a laser) advances through the intersection point of an elliptic peripheral reflection and a long axis. The demonstrator explains the limit problem by point motion, does not give visual explanation on the change of the overall shape, and has no obvious quantification process. Patent application No. 201520878836.1 discloses a "demonstration device of a limit principle", in which a plurality of area plates are placed in a housing, the housing inner area is S, the area plate areas are 1/21S, 1/22S, 1/23S … … 1/2nS in this order, the sum of the area plate areas is (1-1/2n) S, and the area plates are laid in the housing, and the sum of the area plate areas is (1-1/2n) times the housing inner area, so that the sum of the area plate areas approaches the housing inner area infinitely as the number of the area plates increases, and only by means of the limit process of the synthesis sum of the pattern areas, there is no leap that the passing amount of two patterns with completely different shapes becomes qualitative, and the pertinence is insufficient.

The invention content is as follows:

in order to solve the technical problem, the invention provides an inscribed polygon cyclotomy demonstration instrument, which comprises: support, synchronous gear separator, uncovered cask, elasticity rope and transparent stay cord, the main part of support is branch and round axle pipe, synchronous gear separator includes ring dish and pivot, the pivot of synchronous gear separator inserts in the round axle pipe of support, the opening cup joint of uncovered cask is on the support, the ring dish of synchronous gear separator is in the uncovered cask, elasticity rope shunting is in the barrel head outside of uncovered cask, transparent stay cord links together elasticity rope and synchronous gear separator.

In a further technical scheme, the synchronous gear shifting machine comprises a first shaft lever, a second circular shaft pipe and a third circular shaft pipe, wherein the left end of the first shaft lever is respectively provided with a third circular ring disc and a fourth circular ring disc which are sleeved, the right end of the first shaft lever is respectively provided with a pin and a first push rod, the first push rod is a bolt provided with a nut, a screw rod outside the nut is screwed on the left part of the pin on the first shaft lever, a second circular shaft pipe which is pivoted is arranged between the fourth circular ring disc in the middle of the first shaft lever and the first push rod, the left part of the second circular shaft pipe is respectively provided with a fifth circular ring disc and a sixth circular ring disc which are sleeved from left to right, the edge of the right end of the second circular shaft pipe is provided with a second push rod which is the same as the first push rod, a third circular shaft pipe which is pivoted is arranged between the sixth circular ring disc in the middle of the second circular shaft pipe and the second push rod, the left part and the right end of the third circular shaft pipe are respectively provided with a seventh, the seventh circular ring disc and the third push rod are arranged the same as the sixth circular ring disc and the second push rod respectively.

Further technical scheme, uncovered cask includes pipe, disc, ring pilot lamp, be equipped with circular arc scale and first hoop, second hoop, third hoop in the past backward respectively on the outer wall of pipe, it is equipped with first line hole to open between first hoop and circular arc scale, second line hole, third line hole, fourth line hole have been seted up respectively at the rear portion of first hoop, second hoop, third hoop, be equipped with the ring pilot lamp on the front end cross-section of pipe, be equipped with fixed inscription disc between intraductal first line hole of pipe front end and first hoop cross-section.

Compared with the prior art, the invention has the beneficial effects that:

1. the circle cutting demonstration instrument adopting the inscribed polygon method is simple to operate, and can complete all functions only by pushing and pulling the handle.

2. The invention discloses an inscribed polygon method cyclotomy demonstration instrument which has complete functions: the whole process from expanding the circle inscribed regular hexagon into the regular dodecagon and then expanding the regular dodecagon into the twenty-quadrilateral to the forty-octagonal and the reverse process can be rapidly completed. The structure is compact, the cost is low, and the carrying is convenient; the applicability is strong: can be used in any occasions. Is suitable for teaching, light exhibition, etc.

3. At present, no such product is available on the market, and the inscribed polygon cyclotomy demonstration instrument is compact in structure, low in cost, safe, reliable, light and handy.

Description of the drawings:

the accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:

fig. 1 is a schematic structural view of the present invention.

Fig. 2 is a schematic structural view of the stent of the present invention.

Fig. 3 is a schematic structural view of the synchronous stepper of the present invention.

Figure 4 is a schematic view of the construction of the uncovered drum of the present invention.

In the drawings: 1-bracket, 11-first circular shaft tube, 12-first circular ring disc, 13-support rod, 14-disc base, 15-first gap, 16-second gap, 17-third gap, 18-second circular ring disc; 2-synchronous gear shifting machine, 21-first shaft lever, 22-second circular shaft pipe, 23-third circular shaft pipe, 211-third circular ring disk, 212-fourth circular ring disk, 213-first push rod, 214-pin, 221-fifth circular ring disk, 222-sixth circular ring disk, 223-second push rod, 231-seventh circular ring disk and 232-third push rod; 3-uncovered barrel, 31-round tube, 32-round disc, 33-circular arc scale, 34-first hoop, 35-second hoop, 36-third hoop, 37-circular ring indicator light, 38-first line hole, 39-second line hole, 310-third line hole and 311-fourth line hole.

The specific implementation mode is as follows:

as shown in the figure, the inscribed polygon method secant circularity demonstration instrument comprises: support 1, synchronous gear separator 2, uncovered cask 3, elastic rope strip 4 and transparent stay cord 5, the main part of support 1 is branch and circle spool, synchronous gear separator 2 includes ring dish and pivot, synchronous gear separator 2's pivot is inserted in support 1's the circle spool, the opening of uncovered cask 3 is cup jointed on support 1, synchronous gear separator 2's ring dish is in uncovered cask 3, elastic rope strip 4 shunting is in uncovered cask 3's barrel head outside, transparent stay cord 5 links together elastic rope strip 4 and synchronous gear separator 2.

As shown in fig. 2, the bracket 1 includes a first circular shaft tube 11, a first circular ring plate 12, a support rod 13, a disc base 14, a first notch 15, a second notch 16, a third notch 17 and a second circular ring plate 18, the first circular shaft tube 11 is a hard circular tube with a smooth inner wall, the support rod 13 and the first circular ring plate 12 are respectively arranged outside the first circular shaft tube 11, the support rod 13 is fixed in the middle, the inner circumference of the first circular ring plate 12 is sleeved on the left portion of the support rod 13, the first notch 15, the second notch 16 and the third notch 17 perpendicular to the bus are respectively arranged on the upper right portion of the first circular shaft tube 11, the second circular ring plate 18 is arranged at the right end of the first circular shaft tube 11, and the outer circumference of the second circular ring plate 18 is fixed in the tube opening.

As shown in fig. 3, the synchronous gear shifting machine 2 includes a first shaft rod 21, a second circular shaft tube 22, and a third circular shaft tube 23, the left end of the first shaft rod 21 is respectively provided with a third circular ring disc 211 and a fourth circular ring disc 212, which are sleeved, the right end of the first shaft rod 21 is respectively provided with a pin 214 and a first push rod 213, the first push rod 213 is a bolt provided with a nut, a screw rod outside the nut is screwed on the left portion of the pin 214 on the first shaft rod 21, a second circular shaft tube 22, which is axially rotated, is arranged between the fourth circular ring disc 212 and the first push rod 213 in the middle of the first shaft rod 21, the left portion of the second circular shaft tube 22 is respectively provided with a fifth circular ring disc 221 and a sixth circular ring disc 222, which are sleeved, the right end edge of the second circular shaft tube 22 is provided with a second push rod 223, which is the same as the first push rod 213, and a third circular shaft tube 23, which is axially rotated, is arranged between the sixth circular ring disc 222 and the second push rod 223 in, the left part and the right end of the third circular shaft tube 23 are respectively provided with a seventh circular disc 231 and a third push rod 232, and the seventh circular disc 231 and the third push rod 232 are respectively arranged to be the same as the sixth circular disc 222 and the second push rod 223.

As shown in fig. 4, the uncovered barrel 3 includes a round tube 31, a circular disc 32, and a circular ring indicator light 37, the round tube 31 is a hard round tube with a thick wall, the outer wall of the round tube 31 is provided with a circular arc scale 33, a first hoop 34, a second hoop 35, and a third hoop 36 from front to back, the first hoop 34, the second hoop 35, and the third hoop 36 are circular rings with circular arcs surrounded by semicircular rods outside, and the outer circular arcs are provided with parallel wire slots. First line holes 38 are arranged between the first hoop ring 34 and the circular arc scale 33, at least forty-eight first line holes 38 are evenly distributed, and four are respectively positioned at 0 degree, 90 degree, 180 degree and 270 degree of the circular arc scale 33, the rear parts of the first hoop 34, the second hoop 35 and the third hoop 36 are respectively provided with a second string hole 39, a third string hole 310 and a fourth string hole 311, at least six fourth string holes 311 are respectively positioned at 30 degrees, 90 degrees, 150 degrees, 210 degrees, 270 degrees and 330 degrees, at least twelve third string holes 310 are positioned at 15 degrees, 45 degrees, 75 degrees, 105 degrees, 135 degrees, 165 degrees, 195 degrees, 225 degrees, 255 degrees, 285 degrees, 315 degrees and 345 degrees, the second line hole 39 is the same as the first line hole 38, a circular ring indicator light 37 is arranged on the front end section of the circular tube 31, the fixed inner circular disc 32 is arranged between the first wire hole 38 and the cross section of the first hoop 34 at the front end of the circular tube 31.

The invention discloses a circle cutting demonstration instrument by an inscribed polygon method. The method is characterized in that: the operation is simple, and all functions can be completed by only pushing and pulling the handle. The functions are complete: the whole process from expanding the circle inscribed regular hexagon into the regular dodecagon and then expanding the regular dodecagon into the twenty-quadrilateral to the forty-octagonal and the reverse process can be rapidly completed. The structure is compact, the cost is low, and the carrying is convenient; the applicability is strong: can be used in any occasions. Is suitable for teaching, exhibitions and the like.

The invention discloses a circle cutting demonstration instrument by an inscribed polygon method, which has the function of demonstrating that a regular polygon is expanded into a circle, and comprises the following operation steps:

firstly, assembling instruments, and 1] placing a support 1 on a platform to enable the support to be in a stable state. 2] the first push rod 213, the second push rod 223 and the third push rod 232 on the synchronous gear shifting machine 2 are dismounted, the sleeved third circular shaft tube 23 is inserted into the first circular shaft tube and locked by the pin 214. And 3, connecting the first push rod 213, the second push rod 223 and the third push rod 232 with the synchronous gear separator 2 from the first gap 15, the second gap 16 and the third gap 17 respectively and fixing the two by nuts. And 4, placing six elastic ropes 4 on the synchronous gear separator 2 to form a regular hexagon. Twenty-four transparent pull ropes 5 are taken to fix the rear ends on the third circular ring disc 211 respectively, the other ends penetrate out from the second line hole 39, twelve transparent pull ropes 5 are taken to fix the rear ends on the fifth circular ring disc 221 respectively, the other ends penetrate out from the third line hole 310, six transparent pull ropes 5 are taken to fix the rear ends on the seventh circular ring disc 231 respectively, and the other ends penetrate out from the fourth line hole 311. 6] the uncovered cylinder 3 is placed on the holder 1. Forty-two transparent pull ropes 5 are respectively connected with six elastic rope strips 4 through the first string holes 38.

Setting symbols: 1] Liu Anhui Semisery, the area of the circle inscribed regular hexagon M6 is recorded as A1, the area of the circle inscribed regular dodecagon M12 is recorded as A2, the area of the circle inscribed regular icosahedron M24 is recorded as A3, the area of the circle inscribed regular 6 x 2n-1 hexagon M is recorded as An, and the result is: the area of the regular polygon is gradually increased along with the increase of the number of edges of the regular polygon, and finally the regular polygon is close to a circle. 2] the ring indicator lamp 37 represents a circumscribed circle. The projection of the figure formed by the six elastic ropes 4 on the disc 32 is a regular hexagon, the circular ring indicator light 37 is an external circle, and the front and the back of the drawing are equivalent to the lines of the circular ring indicator light 37. 4] the transverse elasticity of the elastic cord 4 can pull back the transparent pull rope 5 without tension and still present a straight line segment. 5] the length of any one of the three transparent pull ropes 5 with long length, medium length and short length is equal.

Thirdly, adjusting the initial position: the first push rod 213, the second push rod 223 and the third push rod 232 are slightly rotated to tighten the transparent pull rope 5 without influencing the fixation of the six elastic ropes 4 in a linear state.

Fourthly, demonstration and analysis: and 1, loosening the nut to rotate the third push rod 232, tensioning the six long transparent pull ropes 5 to drive the middle points of the six elastic rope strips 4 to expand outwards, and changing the regular hexagon into a dodecagon. And 2, stopping rotating and screwing the nut to fix the third push rod 232 when the expansion angular point of the dodecagon reaches the circumcircle. The regular hexagon becomes a regular dodecagon. And 3, loosening the nut to rotate the second push rod 223, tensioning the twelve middle transparent pull ropes 5 to drive the middle points of the elastic rope strips 4 of the regular dodecagon to expand outwards, and changing the regular dodecagon into a twenty-quadrilateral. And 4, stopping rotating the tightening nut to fix the second push rod 223 when the expansion angular point of the twenty-square reaches the circumcircle. The regular dodecagon becomes a regular icosahedron. And 5, loosening the nut to rotate the first push rod 213, tensioning twenty-four short transparent pull ropes 5 to drive the middle points of the elastic rope strips 4 of the regular twenty-square shape to expand outwards, and changing the regular twenty-square shape into a forty-octagon shape. And 4, stopping rotating the tightening nut to fix the first push rod 213 when the expansion corner point of the forty-octagonal shape reaches the circumcircle. The regular twenty-square becomes a regular forty-octagon. The transparent pull rope 5 is almost close to the inner side of the round tube 31 and visually consistent with the line of the ring indicator lamp 37.

Fifthly, finishing the demonstration: 1] loosening the nut reversely rotates the first push rod 213 back to the initial position. 2] loosening the nut reversely rotates the second push rod 223 to return to the initial position. 3] loosening the nut reversely rotates the third push rod 232 to return to the initial position. And 4, restoring the device to the initial state.

The invention relates to an inscribed polygon method cyclotomy demonstration instrument, which has the following economic value and application prospect: along with the technical progress and economic development, advanced equipment is required to improve the teaching effect and the product quality, an inscribed polygon cyclotomy demonstration instrument which is simple to operate and convenient to use is urgently needed, only thousands of schools are shared in high education nationwide, the quantity is considerable, the market prospect is very wide, and good economic benefit and social benefit are achieved.

The parts not involved in the present invention are the same as or can be implemented using the prior art.

As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

The technical means disclosed by the scheme of the invention are not limited to the technical means disclosed by the technical means, and also comprise the technical scheme formed by equivalent replacement of the technical features. The present invention is not limited to the details given herein, but is within the ordinary knowledge of those skilled in the art.

Claims (3)

1. The inscribed polygon method secant circularity demonstration instrument is characterized by comprising: support, synchronous gear separator, uncovered cask, elasticity rope and transparent stay cord, the main part of support is branch and round axle pipe, synchronous gear separator includes ring dish and pivot, the pivot of synchronous gear separator inserts in the round axle pipe of support, the opening cup joint of uncovered cask is on the support, the ring dish of synchronous gear separator is in the uncovered cask, elasticity rope shunting is in the barrel head outside of uncovered cask, transparent stay cord links together elasticity rope and synchronous gear separator.

2. An inscribed polygon method cyclotomy demonstration instrument according to claim 1, characterized in that: the synchronous gear separator comprises a first shaft lever, a second shaft lever and a third shaft lever, wherein the left end of the first shaft lever is respectively provided with a third annular disc and a fourth annular disc which are sleeved, the right end of the first shaft lever is respectively provided with a pin and a first push rod, the first push rod is a bolt provided with a nut, a screw rod outside the nut is screwed on the left part of the pin on the first shaft lever, a second shaft lever which is pivoted is arranged between the fourth annular disc and the first push rod in the middle of the first shaft lever, the left part of the second shaft lever is respectively provided with a fifth annular disc and a sixth annular disc which are sleeved from left to right, the edge of the right end of the second shaft lever is provided with a second push rod which is the same as the first push rod, a third shaft lever which is pivoted is arranged between the sixth annular disc in the middle of the second shaft lever and the second push rod, the left end and the right end of the third shaft lever are respectively provided with a seventh annular disc and a third push rod which are fixed, the seventh circular ring disc and the third push rod are arranged the same as the sixth circular ring disc and the second push rod respectively.

3. An inscribed polygon method cyclotomy demonstration instrument according to claim 1, characterized in that: the uncovered cask includes pipe, disc, ring pilot lamp, be equipped with circular arc scale and first hoop, second hoop, third hoop in the past backward respectively on the outer wall of pipe, it is equipped with first line hole to open between first hoop and circular arc scale, second line hole, third line hole, fourth line hole have been seted up respectively at the rear portion of first hoop, second hoop, third hoop, the front end cross-section of pipe, be equipped with the ring pilot lamp on the pipe front end intraductal first line hole of pipe and first hoop cross-section, be equipped with fixed inscription disc between the pipe front end intraductal first line hole and first hoop cross-section.

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