CN108062888A - A kind of central angle and angle of circumference relation demonstration teaching aid and its demenstration method - Google Patents
A kind of central angle and angle of circumference relation demonstration teaching aid and its demenstration method Download PDFInfo
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- CN108062888A CN108062888A CN201810111360.7A CN201810111360A CN108062888A CN 108062888 A CN108062888 A CN 108062888A CN 201810111360 A CN201810111360 A CN 201810111360A CN 108062888 A CN108062888 A CN 108062888A
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- 238000000034 method Methods 0.000 title claims abstract description 9
- 239000011521 glass Substances 0.000 claims description 3
- 239000000463 material Substances 0.000 claims description 3
- 238000003756 stirring Methods 0.000 claims description 3
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- 230000008859 change Effects 0.000 abstract description 5
- 230000019771 cognition Effects 0.000 abstract description 3
- 239000000203 mixture Substances 0.000 abstract description 3
- 230000001360 synchronised effect Effects 0.000 abstract description 2
- 230000000007 visual effect Effects 0.000 abstract 1
- 238000006243 chemical reaction Methods 0.000 description 3
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- 230000015572 biosynthetic process Effects 0.000 description 1
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Classifications
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
- G09B23/04—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics for geometry, trigonometry, projection or perspective
Abstract
A kind of central angle and angle of circumference relation demonstration teaching aid and its demenstration method.The present invention includes central angle dial, center guide pillar, elastic tightrope, and center guide pillar is fixedly mounted on the circle centre position 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.Its advantage is exquisite composition, and design is reasonable, directly perceived to show central angle variation synchronous with angle of circumference, and ensures that angle can be read at any time；It is easy to 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
Technical field
The present invention relates to a kind of middle school mathematics teaching aid, more particularly, to a kind of central angle and angle of circumference relation demonstration teaching aid and
Its demenstration method belongs to teaching aid design field.
Background technology
Circumference angle theorem be an arc angle of circumference is equal to it to the half of central angle.Theorem reflection is circumference
Angle and the relation of central angle.In teaching, theorem needs point three kinds of situations to be proved, i.e.,：
1st, central angle and angle of circumference are while overlap, while falling the homonymy in center of circle O；
2nd, the both sides of central angle and angle of circumference respectively fall in the both sides of center of circle O；
3rd, the both sides of angle of circumference fall the homonymy in 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
Circumference angle theorem or conversion to be applied to calculate, many students in numerous geometry angles due to cannot quickly have found central angle and circle
The correspondence of round angle or the conversion that cannot accurately carry out two kinds of property angles cause not proving to solve a problem or calculate mistake, this is
It is observed since student lacks, fails to set up the dynamic correspondence between central angle and angle of circumference in whole circumference, it is impossible to is quick
It was found that caused by positive connection between them.
The content of the invention
In order to overcome student present in existing middle school geometry teaching due to cannot quickly be found in numerous geometry angles
The correspondence of central angle and angle of circumference or the conversion that cannot accurately carry out two kinds of property angles, cause not proving to solve a problem or count
The deficiency of mistake is calculated, the present invention provides a kind of central angle and angle of circumference relation demonstration teaching aid and its demenstration method.
The technical solution adopted by the present invention to solve the technical problems is：A kind of central angle and the religion of angle of circumference relation demonstration
Tool, including central angle dial, center guide pillar, elastic tightrope, center guide pillar is fixedly mounted on the circle centre position of central angle dial,
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 provided with
Annular T-slot；Angle of circumference dial is installed, the angle of circumference dial is using the center guide pillar as axis on the center guide pillar
The heart rotates；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；It leads at center in the disk of the angle of circumference dial
2 central angle pointers are installed on column.
Further, guide post is installed, the guide post is slided along the annular T-slot in the annular T-slot.The guide post
Quantity for 3, wherein：1 is circumference guide post, and 2 are center of circle guide post；2 center of circle guide posts respectively with 2 centers of circle
The other end connection of angle pointer；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 °；Groove is carved with along the longitudinal centre line of the central angle pointer.
The central angle pointer selects transparent organic glass material to make.
Further, bearing is installed between the center guide pillar and the angle of circumference dial.
Further, the elastic tightrope is provided at both ends with ring set, and the ring set is sleeved on the center of circle guide post.
The demenstration method of a kind of central angle and angle of circumference relation demonstration teaching aid, its step are as follows：
A, the central angle pointer is stirred so that 2 central angle pointers form any angle；
B, the ring set at the elastic cord both ends is respectively fitted on two center of circle guide posts, pulled in the elastic cord
Portion's set hangs on the circumference guide post and tightens；
C, stir central angle pointer and form a central angle, the angle that the two lines of the elastic cord are formed at this time is and circle
Angle of circumference corresponding to heart angle；
D, rotate the angle of circumference dial so that 1 line of the elastic cord with it is described on the angle of circumference dial
The a certain scale of curved scale line overlaps, which is reading I；Another 1 line of the elastic cord and the circumference angle index
Another scale of the curved scale line on disk overlaps, which is reading II；The difference of reading I and reading II is angle of circumference
Angle.
The invention has the advantages that exquisite composition, design is reasonable, directly perceived to show central angle variation synchronous with angle of circumference,
And ensure that angle can be read at any time；It is easy to operation, the geometrical relationship of central angle and angle of circumference can be demonstrated, student is allowed intuitively to recognize
Know the dynamic change of central angle and angle of circumference, improve the cognition degree to relevant knowledge.
Description of the drawings
Fig. 1 is the front schematic view of central angle and angle of circumference relation demonstration teaching aid of the present invention.
Fig. 2 is the A-A sectional views of Fig. 1（The structure diagram of central angle and angle of circumference relation demonstration teaching aid of the present invention）.
Fig. 3 is elastic tightrope schematic diagram in the present invention.
Fig. 4 is schematic diagram of the embodiment of the present invention.
In figure：1. central angle dial, 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 invention will be further described with reference to the accompanying drawings and examples.But those skilled in the art should know
, the invention is not restricted to listed specific embodiment, as long as meeting the spirit of the present invention, should all be included in the present invention
Protection domain in.
Referring to attached drawing 1,2.A kind of central angle of the present invention and angle of circumference relation demonstration teaching aid, including central angle dial 1, circle
Round angle dial 2, central angle pointer 6, elastic tightrope 5, center guide pillar 3 are fixedly mounted on the circle centre position of central angle dial 1；Institute
The upper end for stating center guide pillar 3 protrudes from the disk of the central angle dial 1；Institute above 1 disk of central angle dial
State center guide pillar 3 on angle of circumference dial 2 is installed, the angle of circumference dial 2 can be that axis is rotated with center guide pillar 3.
In the present embodiment, it is located among the central angle dial 1 for annular groove, the angle of circumference dial 2 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
For 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.It is described to lead
The quantity of column is 3, wherein：1 is that circumference guide post 13,2 is center of circle guide post 4.
Further, 6 quantity of central angle pointer be 2, central angle pointer 6 select transparent organic glass or other thoroughly
Bright material makes.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 are rotated with the center guide pillar 3 for axis.Groove is carved with along the longitudinal centre line of the central angle pointer 6, which represents the center of circle
Two sides at angle.
Further, the elastic tightrope 5 is provided at both ends 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 embodiment of the demenstration method of central angle of the present invention and angle of circumference relation demonstration teaching aid, step
It is rapid as follows：
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 elastic cord
5 middle part set hangs on the circumference guide post 13 and tightens；
C, stir central angle pointer 6 and form a central angle 11,6 groove of central angle pointer on right side on central angle dial 1
0 ° of line alignment, rotate another angle of circumference pointer 6 instruction any angle 11（Such as 270 ° in Fig. 4）, central angle 11 is 90 °；
The angle that the two lines of the elastic cord 5 are formed at this time is and the angle of circumference 12 corresponding to central angle 11；
D, certain a moment of 1, the right side of the elastic cord 5 line and the curved scale line 9 on the angle of circumference dial 2
Degree overlaps, which is reading I（It is 55 ° in attached drawing 4）；Another 1 line of the elastic cord 5 and the angle of circumference dial 2
On the curved scale line 9 another scale overlap, the scale be reading II（It is 10 ° in attached drawing 4）；Reading I and reading II
45 ° of difference be 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 relations of angle of circumference, thus drill and show central angle
With the dynamic change of angle of circumference, angular values are read by dial, can verify times angular dependence of central angle and angle of circumference.
Central angle and angle of circumference relation demonstration teaching aid of the present invention, exquisite composition, design is reasonable, and two dials are respectively to zero
After, no matter central angle increases or reduces, and angle of circumference correspondingly synchronously changes, and ensures that angle can be read at any time, and can
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 angle of circumference
Therebetween dynamic change deepens student's cognition degree.
It it should be noted that these are only the preferred embodiment of the present invention, is not intended to limit the invention, is led for correlation
For the technical staff in domain, the invention may be variously modified and varied.Made within the spirit and principles of the invention
Any modification, equivalent substitute, improvement etc., should all be included in the protection scope of the present invention.
Claims (8)
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 circle centre position 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 2, 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 3, it is characterized in that：The quantity of the guide post is 3
It is a, wherein：1 is circumference guide post, and 2 are center of circle guide post；
The other end of 2 center of circle guide posts respectively with 2 central angle pointers is connected；
Connect respectively with described 2 center of circle guide posts around flexible tightrope, the both ends of the elasticity tightrope on the circumference guide post
It connects.
4. according to any central angles of claim 1-3 and angle of circumference relation demonstration teaching aid, it is characterized in that：Along the central angle
There is 0 ~ 360 ° of graduation mark at the disk edge of dial；Curved scale line in the circular scale disk disk is 0 ~ 90 °；Along institute
The longitudinal centre line for stating central 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
Transparent organic glass material makes.
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
Ring set is provided with, the ring set is sleeved on the center of circle guide post.
8. the demenstration method of central angle described in a kind of claim 1 and angle of circumference relation demonstration teaching aid, its step are as follows：
A, the central angle pointer is stirred so that 2 central angle pointers form any angle；
B, the ring set at the elastic cord both ends is respectively fitted on two center of circle guide posts, pulled in the elastic cord
Portion's set hangs on the circumference guide post and tightens；
C, stir central angle pointer and form a central angle, the angle that the two lines of the elastic cord are formed at this time is and circle
Angle of circumference corresponding to heart angle；
D, rotate the angle of circumference dial so that 1 line of the elastic cord with it is described on the angle of circumference dial
The a certain scale of curved scale line overlaps, which is reading I；Another 1 line of the elastic cord and the circumference angle index
Another scale of the curved scale line on disk overlaps, which is reading II；The difference of reading I and reading II is angle of circumference
Angle.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810111360.7A CN108062888A (en) | 2018-02-05 | 2018-02-05 | A kind of central angle and angle of circumference relation demonstration teaching aid and its demenstration method |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810111360.7A CN108062888A (en) | 2018-02-05 | 2018-02-05 | A kind of central angle and angle of circumference relation demonstration teaching aid and its demenstration method |
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| CN108062888A true CN108062888A (en) | 2018-05-22 |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109559599A (en) * | 2018-12-13 | 2019-04-02 | 中国农业大学烟台研究院 | A kind of economic analysis model system and method |
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| CN203910090U (en) * | 2014-05-27 | 2014-10-29 | 郝佳琪 | Demonstrating board for central angles and circumferential angles |
| CN107067896A (en) * | 2017-06-28 | 2017-08-18 | 张艺胧 | A kind of central angle theorem demonstrator |
| CN208954437U (en) * | 2018-02-05 | 2019-06-07 | 史可晗 | A kind of central angle and angle of circumference relation demonstration teaching aid |
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2018
- 2018-02-05 CN CN201810111360.7A patent/CN108062888A/en active Pending
Patent Citations (8)
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|---|---|---|---|---|
| KR200343851Y1 (en) * | 2003-12-05 | 2004-03-09 | (주) 수학사랑 | a teaching implement for explanation of geometry |
| CN201655097U (en) * | 2010-04-16 | 2010-11-24 | 王敏 | Circumferential angle demonstration device |
| CN201829092U (en) * | 2010-10-28 | 2011-05-11 | 李雪松 | Model for demonstrating central angle theorem |
| CN202331983U (en) * | 2011-11-23 | 2012-07-11 | 陈长虹 | Circumference angle theorem demonstration instrument |
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