CN2864861Y - Teaching apparatus for mathematics - Google Patents

Teaching apparatus for mathematics Download PDF

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Publication number
CN2864861Y
CN2864861Y CN 200520142342 CN200520142342U CN2864861Y CN 2864861 Y CN2864861 Y CN 2864861Y CN 200520142342 CN200520142342 CN 200520142342 CN 200520142342 U CN200520142342 U CN 200520142342U CN 2864861 Y CN2864861 Y CN 2864861Y
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China
Prior art keywords
coordinate
scale
pointer
base plate
line
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Expired - Fee Related
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CN 200520142342
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Chinese (zh)
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韩继伟
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韩继伟
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Abstract

The utility model discloses a mathematics teaching tool comprising a bottom board equipped with rectangular coordinates system and a round whose center is original point, wherein the round is marked with angle scale value and angle index line, the coordinate axis is marked with coordinate scale value and coordinate index line, the coordinate scale value, from the original point to the cross point of round and coordinate axis, is from zero to one, the original point of bottom board is pin jointed with needle pointer, the cross point of the needle pointer and round is equipped with a clarity staff gage, from the cross point to the radius distance, which is marked with staff gage index line and scale value from zero to one. The mathematics teaching tool can visually demonstrate different triangular functions and calculate triangular functions.

Description

The mathematical education apparatus
Technical field
The utility model relates to a kind of study middle school mathematics that can be used in, and particularly understands the teaching aid of trigonometric function, can also make stationery and use.
Background technology
Trigonometric function occupies the position of weight as the content of middle school mathematics in elementary mathematics.Trigonometric function has related to a plurality of theorems, definition and formula, because some students can not well understand these theorems, definition and formula, because of not remembering and using easily and meet difficulty, caused all undesirable of teacher's teaching and student's results of learning, and the enthusiasm that makes the student learn is affected, and has brought certain difficulty for student and teacher even the head of a family.
The utility model content
At the not intelligible problem that exists in the trigonometric function teaching process, the purpose of this utility model is to provide a kind of mathematical education apparatus, can be used in demonstration trigonometric function relation, to help the student trigonometric function is carried out perceptual knowledge.
The utility model adopts following technical scheme: a kind of mathematical education apparatus, comprise a base plate, rectangular coordinate system is set and is the circle in the center of circle at backplate surface with the initial point of directly separating coordinate system, described circle is marked with angle index value and angle index line, the positive and negative direction of the coordinate axis of coordinate system indicates coordinate scale value and coordinate scale line, from coordinate origin to coordinate axis with the coordinate scale value of circle joining from zero to one, coordinate origin place at base plate is articulated with pointer, this pointer and described round joining place are articulated with a transparent scale, transparent scale by the pivoting point place to the isometric distance of radius of a circle in be provided with scale label line and from zero to one scale label value.
Described pointer can be one, can also be for more than two even two.
Described base plate can be rectangular flat, and its edge is provided with scale value and the scale mark of measuring length, also can circular or oval, polygon.
For ease of teaching demonstration, described base plate can be iron plate, and magnet is equipped with in described pointer and scale end.Perhaps base plate adopts magnetic material, and on pointer or scale iron core is set.
Anyly in described angle index line, coordinate scale line, the scale label line all can be concave or convex line, or paint film.Anyly in same angle index value, coordinate scale value, the scale label value also can be concave or convex line, paint film.
Described coordinate system and fenestra can adopt the mode of the paint film of concave or convex line and printing formation to form.
Can there be through hole at the initial point place of the coordinate system of described base plate, and the bearing pin of fixing or pass described pointer is through in this through hole, and described pointer and base plate are articulated.Can also be distributed with the through hole that initial point distance a plurality of and coordinate system does not wait from the initial point of coordinate system to bottom edge on the described base plate, nib be inserted this through hole rotate the circle of the different radii that can draw, play the effect of compasses around bearing pin.
This mathematical education apparatus of the present utility model can be used in the multiple trigonometric function of demonstration, and can be used for the calculating and the tolerance of trigonometric function, is beneficial to the student and deeply understands trigonometric function knowledge.And can both be suitable for teachers ' teaching and use do the stationery use of drawing again, and be suitable for the student again and learn to use.
Description of drawings
Fig. 1 is a kind of mathematical education apparatus structural representation of the present utility model.
Fig. 2 and Fig. 3 are the syndeton synoptic diagram of mathematical education apparatus.
Fig. 4 to Fig. 6 is the use-pattern synoptic diagram of mathematical education apparatus.
Embodiment
Below in conjunction with the drawings and specific embodiments mathematical education apparatus of the present utility model is described further, to help understanding content of the present utility model.
As shown in Figure 1, on base plate 1 surface of a rectangle (also can be other shape), be provided with a rectangular coordinate system 4, initial point with rectangular coordinate system 4 is that the center of circle also is provided with a circle 5, the X-axis of rectangular coordinate system 4, Y-axis from initial point to the distances that intersect with circle 5 in positive negative direction be provided with from 0~1 and from 0~-1 coordinate scale value and coordinate scale line, on circle 5, also indicate 0 °~360 ° angle index value and horn craving scale mark equally, a pointer 3 also can rotate around this pivot by the initial point O place that pivot is articulated in the coordinate system on the base plate 1, be articulated with a transparent scale 2 at pointer 3 equally with the intersection point places that circle 5 intersects, on the transparent scale 2 by the pivoting point place to the isometric distance of radius of a circle in be provided with scale label line 6 and from 0~1 scale label value.
As shown in Figure 2, pointer 3 and base plate 1, and pointer 3 and scale 2 that the mode of opening circular hole above one of the circular shaft of projection is set on can adopting therein one is plug-in, formation can change mutually the pivot joint mode.Perhaps as shown in Figure 3, on base plate 1 and pointer 3, through hole is set all, passes this through hole with a bearing pin 9 both are articulated, so that they can be around these bearing pin 9 rotations.
Coordinate system 4, circle 5 and all scale mark, scale values both can form by the mode that intaglio goes out groove, also can directly be printed on lacquer or printing ink etc. to form on base plate or the scale, or be convex line.
When using as teaching aid, for convenient the suspension used, base plate 1 can adopt iron plate or be compounded with one deck iron plate or other permeability magnetic materials, simultaneously be embedded with magnet in scale 2 one or both ends even other position, perhaps in the constituent material of scale 2, add magnetic material, whole mathematical education apparatus was vertically placed, scale 2 is adsorbed on the base plate 1 to be positioned arbitrary position easily.The bearing pin magnetic material that for example pointer 3 ends can be connected usefulness with scale 2.
Base plate 1 edge both can be illustrated in figure 1 as straight flange, and can be provided with the ruler scale to use as ruler, also can be arc.
When pointer 3 and base plate 1 adopt a bearing pin 9 to articulate as shown in Figure 3, also can be with reference to Fig. 1 and shown in Figure 3, on base plate 1, process a plurality of through holes 7 in the mode different with the initial point O distance of coordinate system, it is interior when bearing pin 9 rotation base plates like this pen 8 to be inserted different through hole 7, the different circle of radius can draw, make compasses and use, between bearing pin 9 and pointer 3, spring can be housed.
The using method of mathematical education apparatus of the present utility model once is described with several concrete examples below.
1, measurement is arbitrarily angled: if degree plate 1 adopts clear sheet, can utilize circle 5 and scale thereof directly to take measurement of an angle, make protractor and use.
2, the demonstration of trigonometric function and calculating:
(1) demonstration of sine function and calculating: as shown in Figure 1, making scale 2 and sitting axle is that 4 X-axis is vertical, then pointer 3, scale 2 and X-axis have formed a right-angle triangle, 3 on pointer is the hypotenuse of this right-angle triangle, the length r of pointer is 1 unit, the sinusoidal sinA=y/r of angle A (being 45 °) then, because r=1>0, so sinA=y, therefore this sine value is the scale label value (i.e. projection on Y-axis) of scale 2 and X-axis joining, can directly read from scale label line on the scale 2 and scale label value, for example be about 0.71 among Fig. 1.
(2) demonstration of cosine function and calculating: because cosA=x/r, and r=1>0, so cosA=x, the cosine function value can directly be read by scale 2 and the coordinate scale line and the scale value of the X-axis at X-axis joining place, is about 0.71 equally.
(3) demonstration of tan and cotangent function and calculating: because tan tgA=y/x, cotangent function ctga=x/y can directly be calculated by scale label line on the scale 2 and the coordinate scale line on the X-axis.
3, the variation of demonstration trigonometric function:
As shown in Figure 5, because scale 3 no effects are therefore not shown.
(1) popularization of the notion at angle: with the X-axis of the coordinate axis initial line as the angle, pointer 3 is as the whole limit at angle, is the angle that the summit rotation at angle can form the different angles value with pointer 3 around the initial point O of coordinate system.
(2) identical angle, whole limit.During with the multiple of 360 ° of pointer 3 rotations, pointer always is parked in identical position, can demonstrate identical angle, whole limit { β | β=K360 °+α }.
(3) variation of sinusoidal, the cosine function value of demonstration:, pointer 3 is rotated to that included angle A with the X-axis positive dirction is 0, when pi/2, π, 3 pi/2s, can demonstrate the different angles sine, do the variation of string functional value with reference to shown in Figure 1.
(4) induced formulas of demonstration trigonometric function: as shown in Figure 6, adopt two mathematical education apparatus that have scale 2 and pointer 3, can demonstrate the induced formulas of trigonometric function.
As shown in Figure 6, as can be seen sin (α)=-sin α
cos(-α)=cosα
tg(-α)=-taα
ctg(-α)=-ctgα
As shown in Figure 4, when the angle value of two pointers 3 of change is respectively α and 180 °+α, and make scale 2 vertical, then can demonstrate the relational expression at α and 180 °+α angle and α angle with X-axis.As seen from Figure 4, sin (180 °+α)=-sin α
cos(180°+α)=-cosα
tg(180°+α)=tgα
ctg(180°+α)=ctgα
In like manner can also demonstrate other induced formulas.
(5) monotonicity and the parity of demonstration sine function.
The mathematical education apparatus that a pointer 3 is only arranged shown in Fig. 1 is rotated, by variation and the just variation of negative direction on Y-axis of observing the reading on the scale 2, the monotonicity of observing sine function.In first quartile, sine value is dull to be increased as can be seen, reduces at second quadrant and third quadrant dullness, in the dull increase of four-quadrant.Can demonstrate out the monotonicity of sine function intuitively.
Can also be demonstrated the parity of sine function equally by the demenstration method of induced formulas in (4), it is about former point symmetry as can be seen.
(6) monotonicity and the parity of demonstration cosine function.
Adopt the mode shown in Fig. 1, by observe different angles cosine function value promptly on X-axis the variation of the scale value of projection and positive negative direction observe its monotonicity.As can be seen, cosine function is descending variation at the projection value of first and second quadrant on X-axis, for dullness reduces, is ascending at the projection value of third and fourth quadrant on X-axis, for dullness increases.
Cosine function is about the Y-axis symmetry equally as can be seen.
4, making compasses uses.
With reference to Fig. 1 and shown in Figure 3, the bearing pin 9 in the middle of pressing can be drawn circle with through hole 7 rotations that pen 8 inserts on the base plate 1, makes compasses and uses.
5, making ruler uses.
Utilize the straight flange of base plate 1 can do the ruler use, be used to measure length and draw straight line.
When the scale of four straight flanges that utilize base plate 1 then can draw easily equidistant and parallel horizontal line and vertical line, to draw coordinate paper.
In addition, mathematical education apparatus of the present utility model can also be demonstrated other trigonometric function, illustrates no longer one by one at this.

Claims (9)

1, a kind of mathematical education apparatus, comprise a base plate, rectangular coordinate system is set and is the circle in the center of circle at backplate surface with the initial point of directly separating coordinate system, described circle is marked with angle index value and angle index line, the positive and negative direction of the coordinate axis of coordinate system indicates coordinate scale value and coordinate scale line, from coordinate origin to coordinate axis with the coordinate scale value of circle joining from zero to one, coordinate origin place at base plate is articulated with pointer, this pointer and described round joining place are articulated with a transparent scale, transparent scale by the pivoting point place to the isometric distance of radius of a circle in be provided with scale label line and from zero to one scale label value.
2, mathematical education apparatus as claimed in claim 1 is characterized in that: described pointer is two.
3, mathematical education apparatus as claimed in claim 1 or 2 is characterized in that: described base plate is a rectangular flat, and its edge is provided with scale value and the scale mark of measuring length.
4, mathematical education apparatus as claimed in claim 1 or 2 is characterized in that: described base plate is an iron plate, and magnet is equipped with in described pointer and/or scale end.
5, mathematical education apparatus as claimed in claim 1 or 2 is characterized in that: any in described angle index line, coordinate scale line, the scale label line is concave or convex line, or paint film.
6, mathematical education apparatus as claimed in claim 1 or 2 is characterized in that: anyly in described angle index value, coordinate scale value, the scale label value be concave or convex line, paint film.
7, mathematical education apparatus as claimed in claim 1 or 2 is characterized in that: the paint film that described coordinate system and circle employing concave or convex line, printing form.
8, mathematical education apparatus as claimed in claim 1 or 2 is characterized in that: there is through hole at the initial point place of the coordinate system of described base plate, and the bearing pin of fixing or pass described pointer is through in this through hole, and described pointer and base plate are articulated.
9, mathematical education apparatus as claimed in claim 8 is characterized in that: the initial point from coordinate system on the described base plate is distributed with the through hole that initial point distance a plurality of and coordinate system does not wait to bottom edge.
CN 200520142342 2005-12-07 2005-12-07 Teaching apparatus for mathematics Expired - Fee Related CN2864861Y (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN 200520142342 CN2864861Y (en) 2005-12-07 2005-12-07 Teaching apparatus for mathematics

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN 200520142342 CN2864861Y (en) 2005-12-07 2005-12-07 Teaching apparatus for mathematics

Publications (1)

Publication Number Publication Date
CN2864861Y true CN2864861Y (en) 2007-01-31

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101853594A (en) * 2010-05-19 2010-10-06 周维保 Function calculating disc
CN103680263A (en) * 2012-09-12 2014-03-26 周维保 Trigonometric-function demonstration plate
CN103730043A (en) * 2013-11-29 2014-04-16 周维保 Rectangular plane coordinate system presentation device
CN104794962A (en) * 2015-04-06 2015-07-22 邬苏婷 Apparatus for teaching demonstration of the angle
CN105427710A (en) * 2015-12-03 2016-03-23 程亮 Mathematics learning tool
CN107591058A (en) * 2017-09-25 2018-01-16 费海迪 A kind of application of mathematical teaching apparatus

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101853594A (en) * 2010-05-19 2010-10-06 周维保 Function calculating disc
CN103680263A (en) * 2012-09-12 2014-03-26 周维保 Trigonometric-function demonstration plate
CN103730043A (en) * 2013-11-29 2014-04-16 周维保 Rectangular plane coordinate system presentation device
CN104794962A (en) * 2015-04-06 2015-07-22 邬苏婷 Apparatus for teaching demonstration of the angle
CN105427710A (en) * 2015-12-03 2016-03-23 程亮 Mathematics learning tool
CN105427710B (en) * 2015-12-03 2017-11-14 刘笑岩 Mathematics teaching instrument
CN107591058A (en) * 2017-09-25 2018-01-16 费海迪 A kind of application of mathematical teaching apparatus
CN107591058B (en) * 2017-09-25 2019-12-17 萧县威辰机电工程设备有限公司 Application of mathematical teaching device

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GR01 Patent grant
C14 Grant of patent or utility model
TR01 Transfer of patent right

Effective date of registration: 20110621

Address after: 102500 Beijing city Fangshan District Yanshan north south wind building No. 11, 3 No. 203

Patentee after: Han Shenghua

Address before: Beijing City, Fangshan District Yanshan 102500 South Street north wind No. 11 building 3 unit 203 room

Patentee before: Han Jiwei

COR Change of bibliographic data

Free format text: CORRECT: ADDRESS; FROM: 102500 ROOM 203, UNIT 3, BUILDING 11, BEIZHUANG NANLI, YINGFENG STREET, YANSHAN, FANGSHAN DISTRICT, BEIJING TO: 102500 NO. 203, UNIT 3, BUILDING 11, BEIZHUANG NANLI, YINGFENG, YANSHAN, FANGSHAN DISTRICT, BEIJING

ASS Succession or assignment of patent right

Owner name: HAN SHENGHUA

Free format text: FORMER OWNER: HAN JIWEI

Effective date: 20110621

C41 Transfer of patent application or patent right or utility model
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20070131

Termination date: 20131207

C17 Cessation of patent right