CN208954437U

CN208954437U - A kind of central angle and angle of circumference relation demonstration teaching aid

Info

Publication number: CN208954437U
Application number: CN201820192562.4U
Authority: CN
Inventors: 史可晗
Original assignee: Individual
Current assignee: Individual
Priority date: 2018-02-05
Filing date: 2018-02-05
Publication date: 2019-06-07
Anticipated expiration: 2028-02-05

Abstract

A kind of central angle and angle of circumference relation demonstration teaching aid.The utility model includes central angle dial, center guide pillar, elastic tightrope, and center guide pillar is fixedly mounted on the center point of central angle dial, and the disk of central angle dial is provided with annular T-slot；Angle of circumference dial is installed, angle of circumference dial is using center guide pillar as axis rotation on center guide pillar；It is carved with curved scale line in the disk of angle of circumference dial, the radius of curved scale line is the center line of annular T-slot to the distance in the central angle dial center of circleTimes；2 central angle pointers are installed on the center guide pillar in the disk of angle of circumference dial.The beneficial effect is that exquisite composition, design is rationally, intuitive to show central angle variation synchronous with angle of circumference, and guarantees that angle can be read at any time；Convenient for operation, the geometrical relationship of central angle and angle of circumference can be demonstrated, allows the dynamic change of student's visual understanding central angle and angle of circumference, improves the cognition degree to relevant knowledge.

Description

A kind of central angle and angle of circumference relation demonstration teaching aid

Technical field

The utility model relates to a kind of middle school mathematics teaching aids, teach more particularly, to a kind of central angle and angle of circumference relation demonstration Tool, belongs to teaching aid design field.

Background technique

Circumference angle theorem be an arc to angle of circumference be equal to it to the half of central angle.Theorem reflection is circumference The relationship at angle and central angle.In teaching, theorem needs point three kinds of situations to be proved, it may be assumed that

1, central angle and angle of circumference are overlapped on one side, fall in the ipsilateral of center of circle O on one side；

2, the both sides of central angle and angle of circumference respectively fall in the two sides of center of circle O；

3, the both sides of angle of circumference fall in the ipsilateral of center of circle O.

Since its method of proof is cumbersome, intuitive is poor, and the dynamic for artificially having isolated central angle and angle of circumference is closed System, the student for being is not deep to theorem understanding impermeable, and the acquisition of knowledge is not secured enough.

In middle school geometry teaching, it is related to the geometric proof topic and calculation question of central angle, angle of circumference, has 70% topic type to need It to be calculated using circumference angle theorem or conversion, many students are due to cannot quickly have found central angle and circle in numerous geometry angles The corresponding relationship of round angle, or the conversion at two kinds of property angles cannot be accurately carried out, it causes not proving to solve a problem or calculate mistake, this is It is observed since student lacks, fails to set up the dynamic corresponding relationship in whole circumference between central angle and angle of circumference, it cannot be quick It was found that caused by positive connection between them.

Utility model content

In order to overcome student present in existing middle school geometry teaching due to cannot quickly find in numerous geometry angles The corresponding relationship of central angle and angle of circumference, or the conversion at two kinds of property angles cannot be accurately carried out, it causes not proving to solve a problem or count The deficiency of mistake is calculated, the utility model provides a kind of central angle and angle of circumference relation demonstration teaching aid.

The technical scheme adopted by the utility model to solve the technical problem is as follows: a kind of central angle and angle of circumference relation demonstration Teaching aid, including central angle dial, center guide pillar, elastic tightrope, center guide pillar are fixedly mounted on the center of circle of central angle dial Place, the upper end of the center guide pillar protrudes from the disk of the central angle dial；The disk of the central angle dial is set It is equipped with annular T-slot；Angle of circumference dial is installed, the angle of circumference dial is with the center guide pillar on the center guide pillar For axis rotation；Curved scale line is carved in the disk of the angle of circumference dial, the radius of the curved scale line is annular T The center line of type groove to the central angle dial center of circle distanceTimes；In in the disk of the angle of circumference dial 2 central angle pointers are installed on heart guide post.

Further, guide post is installed, the guide post is slided along the annular T-slot in the annular T-slot.The guide post Quantity be 3, in which: 1 be circumference guide post, 2 be center of circle guide post；2 center of circle guide posts respectively with 2 centers of circle The other end of angle pointer connects；Around flexible tightrope on the circumference guide post, the both ends of the elasticity tightrope respectively with described 2 The center of circle guide post connection.

Further, there is 0 ~ 360 ° of graduation mark along the disk edge of the central angle dial；In the circular scale disk disk Curved scale line on face is 0 ~ 90 °；Longitudinal centre line along the central angle pointer is carved with groove.

The central angle pointer selects the production of transparent organic glass material.

Further, bearing is installed between the center guide pillar and the angle of circumference dial.

Further, the both ends of the elastic tightrope are provided with ring set, and the ring set covers on the center of circle guide post.

The utility model has the beneficial effects that exquisite composition, design is rationally, intuitive to show central angle change synchronous with angle of circumference Change, and guarantees that angle can be read at any time；Convenient for operation, the geometrical relationship of central angle and angle of circumference can be demonstrated, makes student straight The dynamic change of understanding central angle and angle of circumference is seen, the cognition degree to relevant knowledge is improved.

Detailed description of the invention

Fig. 1 is the front schematic view of the utility model central angle and angle of circumference relation demonstration teaching aid.

Fig. 2 is the A-A cross-sectional view (structural representation of the utility model central angle and angle of circumference relation demonstration teaching aid of Fig. 1 Figure).

Fig. 3 is elastic tightrope schematic diagram in the utility model.

Fig. 4 is the utility model embodiment schematic diagram.

In figure: 1. central angle dials, 2. angle of circumference dials, 3. center guide pillars, 4. center of circle guide posts, 5. elastic tightropes, 6. central angle pointer, 7. bearings, 8. annular T-slots, 9. curved scale lines, 10. ring sets, 11. central angles, 12. angles of circumference, 13. Circumference guide post.

Specific embodiment

The utility model is described in further detail with reference to the accompanying drawings and examples.But those skilled in the art should Know, the utility model is not limited to listed specific embodiment all should include as long as meeting spirit of the invention In in the protection scope of the utility model.

Referring to attached drawing 1,2.A kind of central angle of the utility model and angle of circumference relation demonstration teaching aid, including central angle dial 1, angle of circumference dial 2, central angle pointer 6, elastic tightrope 5, center guide pillar 3 are fixedly mounted on the center of circle of central angle dial 1 Place；The upper end of the center guide pillar 3 protrudes from the disk of the central angle dial 1；Above 1 disk of central angle dial The center guide pillar 3 on angle of circumference dial 2 is installed, the angle of circumference dial 2 can be that axis turns with center guide pillar 3 It is dynamic.It is annular groove among the central angle dial 1 in the present embodiment, the angle of circumference dial 2 is located in groove.

Further, there is 0 ~ 360 ° of graduation mark along the disk edge of the central angle dial 1；The central angle dial 1 Disk on be additionally provided with annular T-slot 8, usually annular T-slot 8 is located at the inside of 0 ~ 360 ° of graduation mark in disk.

Further, curved scale line 9, the radian of the curved scale line 9 are carved in the disk of the angle of circumference dial 2 It is 0 ~ 90 °；The radius of the curved scale line 9 be annular T-slot 8 center line to 1 center of circle of central angle dial away from FromTimes；

Further, guide post is installed, the guide post can be slided along the annular T-slot 8 in the annular T-slot 8.Institute The quantity for stating guide post is 3, in which: it is center of circle guide post 4 that 1, which is circumference guide post 13,2,.

Further, 6 quantity of central angle pointer be 2, central angle pointer 6 select transparent organic glass or other thoroughly Bright material production.There is circular mounting hole at the both ends of the central angle pointer 6, and one end is mounted on the disk of the angle of circumference dial 2 On center guide pillar 3 on face, the other end is mounted on the center of circle guide post 4 in annular T-slot, the central angle pointer 6 with the center guide pillar 3 be axis rotation.Longitudinal centre line along the central angle pointer 6 is carved with groove, which represents the center of circle Two sides at angle.

Further, the both ends of the elastic tightrope 5 are provided with ring set 10(referring to attached drawing 3), the ring set 10 is respectively fitted over On 2 center of circle guide posts 4；The middle part of the elasticity tightrope 5 is wound on circumference guide post 13.2 of elasticity tightrope 5 formation Line represents 2 sides of angle of circumference.

It, can also be in the center guide pillar 4 and the angle of circumference dial for the ease of rotating the angle of circumference dial 2 Bearing 7 is installed between 2.

Referring to attached drawing 4.A kind of application method of the utility model central angle and angle of circumference relation demonstration teaching aid, step is such as Under:

A, the central angle pointer 6 is stirred, so that 2 central angle pointers 6 form any angle；

B, the ring set 10 at 5 both ends of elastic cord is respectively fitted on two center of circle guide posts 4, pulls the elasticity The middle part set of flexible cord 5 hangs on the circumference guide post 13 and tightens；

C, it stirs central angle pointer 6 and forms a central angle 11,6 groove of central angle pointer and central angle dial on right side 0 ° of line alignment on 1 rotates 270 ° in the instruction of another angle of circumference pointer 6 any angle 11(such as Fig. 4), central angle 11 is 90°；The two lines of the elastic cord 5 are formed by angle and are and angle of circumference 12 corresponding to central angle 11 at this time；

D, certain of 1, the right side of the elastic cord 5 line and the curved scale line 9 on the angle of circumference dial 2 One scale is overlapped, which is reading I (being 55 ° in attached drawing 4)；Another 1 line of the elastic cord 5 and the circumference angle index Another scale of the curved scale line 9 on disk 2 is overlapped, which is reading II (being 10 ° in attached drawing 4)；Reading I and reading 45 ° of difference of II are angle of circumference angle.

On the basis of above step, central angle pointer 6 can be slided and indicate any position, increased or reduce in central angle While angle of circumference also change therewith, and remain that central angle is 2 times of relationships of angle of circumference, thus drill and show central angle With the dynamic change of angle of circumference, angular values are read by dial, times angular dependence of central angle and angle of circumference can be verified.

The utility model central angle and angle of circumference relation demonstration teaching aid, exquisite composition, rationally, two dials are distinguished for design After zero, no matter central angle is increased or reduced, angle of circumference correspondingly synchronous variation, and guarantees that angle can be read at any time, and It is capable of the geometrical relationship of demonstration and verification central angle and angle of circumference, assisted geometric teaching；Students' response can be allowed to central angle and circle Round angle dynamic change between the two deepens student's cognition degree.

It should be noted that be not intended to limit the utility model the above is only the preferred embodiment of the utility model, it is right For those skilled in the relevant art, various modifications and changes may be made to the present invention.All spirit in the utility model With any modification made within principle, equivalent substitute, improvement etc., should be included within the scope of protection of this utility model.

Claims

1. a kind of central angle and angle of circumference relation demonstration teaching aid, including central angle dial, center guide pillar, elastic tightrope, center Guide post is fixedly mounted on the center point of central angle dial, it is characterized in that:

The upper end of the center guide pillar protrudes from the disk of the central angle dial；The disk of the central angle dial is set It is equipped with annular T-slot；

Angle of circumference dial is installed, the angle of circumference dial turns by axle center of the center guide pillar on the center guide pillar It is dynamic；

Curved scale line is carved in the disk of the angle of circumference dial, the radius of the curved scale line is annular T-slot Center line to the central angle dial center of circle distanceTimes；

2 central angle pointers are installed on the center guide pillar in the disk of the angle of circumference dial.

2. central angle and angle of circumference relation demonstration teaching aid according to claim 1, it is characterized in that: peace in the annular T-slot Equipped with guide post, the guide post is slided along the annular T-slot.

3. central angle and angle of circumference relation demonstration teaching aid according to claim 2, it is characterized in that: the quantity of the guide post is 3 It is a, in which: 1 is circumference guide post, and 2 are center of circle guide post；

2 center of circle guide posts are connect with the other end of 2 central angle pointers respectively；

Around flexible tightrope on the circumference guide post, the both ends of the elasticity tightrope connect with described 2 center of circle guide posts respectively It connects.

4. central angle and angle of circumference relation demonstration teaching aid according to claim 3, it is characterized in that: along the central angle dial Disk edge have 0 ~ 360 ° of graduation mark；Curved scale line in the angle of circumference dial disk is 0 ~ 90 °；Along the circle The longitudinal centre line of heart angle pointer is carved with groove.

5. central angle and angle of circumference relation demonstration teaching aid according to claim 4, it is characterized in that: the central angle pointer is selected The production of transparent organic glass material.

6. central angle and angle of circumference relation demonstration teaching aid according to claim 5, it is characterized in that: the center guide pillar with it is described Bearing is installed between angle of circumference dial.

7. central angle and angle of circumference relation demonstration teaching aid according to claim 6, it is characterized in that: the both ends of the elasticity tightrope It is provided with ring set, the ring set covers on the center of circle guide post.