CN102795030A - Template of pictorial diagram for simulating bimetric projection, picture constructing method thereof and use of template - Google Patents
Template of pictorial diagram for simulating bimetric projection, picture constructing method thereof and use of template Download PDFInfo
- Publication number
- CN102795030A CN102795030A CN2012103079660A CN201210307966A CN102795030A CN 102795030 A CN102795030 A CN 102795030A CN 2012103079660 A CN2012103079660 A CN 2012103079660A CN 201210307966 A CN201210307966 A CN 201210307966A CN 102795030 A CN102795030 A CN 102795030A
- Authority
- CN
- China
- Prior art keywords
- template
- ball
- circle
- audio
- positive
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Landscapes
- Toys (AREA)
Abstract
The invention provides a template of a pictorial diagram for simulating bimetric projection, a picture constructing method thereof and use of the template. The template is characterized in that an included angle between a projection line of the pictorial diagram and an x-axis, an included angle between the projection line and a y-axis, and the included angle between the projection line and the z-axis are respectively alpha, 90 degrees and 90 degrees-alpha, and when sin alpha is 0.2 or 0.15, the axial stretching ratio of a three-dimensional coordinate is 0.2:1:1 or 0.15:1:1. A great circle with a sphere outline is arranged at the center of the template, a key position line of geometry in common use is arranged on the outline of the great circle, an inscribed sphere outline circle with a sphere inscribed cube is arranged at the lower right part of the outline of the great circle, and an inscribed sphere outline circle with a sphere inscribed regular tetrahedron is arranged at the lower left part of the outline of the great circle; three ellipses are arranged on the two sides of the template, are respectively formed by the stretching and contracting of the circumscribed circles of squares on the upper surface and the lower surface of the sphere inscribed cube, the stretching and the contracting of the circumscribed circles of triangles on the bottom of sphere inscribed regular tetrahedron, and the stretching and the contracting of the great circle of the equator. Due to the adoption of the method and the template provided by the invention, various pictorial diagram for simulating biometric projection can be drawn.
Description
Technical field
The present invention relates to a kind of technique of painting and template thereof of intending positive two survey audio-visual pictures, particularly disclose a kind of use of intending positive two survey audio-visual picture templates and patterning process and template, is a kind of school school supply and stationery, is used to draw the tool palette of audio-visual picture.
Background technology
In decades, a popular wider mistake in middle school teaching thinks that promptly the oblique two survey audio-visual picture techniques of painting are parallel projection techniques of painting.This case inventor delivered " oblique two survey audio-visual pictures are not the proofs of parallel projection space diagram " on " mathematics circular ".
The oblique two survey coordinate systems that use now are through adjustment, and the essence of adjustment is that the x axle has been rotated counterclockwise about 3.59 °, and the y axle has been rotated counterclockwise about 7.18 °, and this rotation makes that the lower left quarter position of ball is too sagging, and the upper right position excess of ball is alarmmed.So the scope of application of " oblique two survey the technique of painting " should limit: it is only applicable to simple polyhedron, and is not suitable for rotary body.
Can't investigate now is oblique two to survey the techniques of painting and be referred to as the parallel projection technique of painting after whose first adjustment, but All the time thinks in whole secondary school education circle and mechanical drawing circle.For example:
1, existing regular senior secondary school curricular standard experiment textbook, mathematics, the people teaches the A version, required 2 (2007 February the 3rd edition), P
16, the 9th row: " the oblique two survey techniques of painting are a kind of special parallel projection techniques of painting "; P
18, the 7th row reciprocal: " seeing that from the angle of projection three-view diagram and the audio-visual picture that draws with the oblique two survey techniques of painting all are the space diagrams that under parallel projection, draws and ";
2, required 2 teaching materials of [Beijing Normal University version] high school mathematics, P
9, the 1st row reciprocal: " audio-visual picture of drawing with the oblique two survey techniques of painting is the figure that draws according to the principle of parallel projection ".
It all is the most influential teaching material in the present whole nation that the people teaches A version teaching material and Beijing Normal University version teaching material.To survey the techniques of painting be to be positioned over the four seas and all accurate truth, a kind of blanket rule so people think oblique two always.People are always at the audio-visual picture of all space diagrams of O-xyz rectangular coordinate system in space pilot scale picture; Even when drawing cylinder, circular cone, intuitively also do not believe firmly; In the time can't drawing ball, also turn a blind eye to, in teaching material, survey the picture ball at present and generally adopt the avoidance attitude oblique two.
On the existing textbook simple polyhedron, cylinder, circular cone, ball adopted the method for multiple different picture audio-visual picture; When in same width of cloth figure, having related to multiple solid; Confusion has just appearred in technique of painting rule, so various not audio-visual pictures intuitively just occurred.The purpose that should be known in the picture audio-visual picture is in order to cultivate student's space imagining ability, and it at first wants " intuitively ".Use oblique two to survey the technique of painting and be regardless of occasion ground at present, use same medicine prescription just as being regardless of indication scope ground.
Some teacher is not directly perceived for fear of rotary body, uses instead and just waits axle to survey a picture cylinder, circular cone, has thought in addition that again a method draws ball specially.Because the mistake on this understanding; Cause the confusion on relevant solid (polyhedron, circular cone, cylinder, ball) the audio-visual picture technique of painting; Cause in a figure to have multiple solid simultaneously, when for example ball is with its inpolyhedron, at a loss as to what to do on the technique of painting; Take the challenger that it is arranged, the flicker of drawing a picture carelessly survivor has it (it is a kind of helpless that this flicker is actually).This situation teaches the A version required 2 the people, and the related Sections of Beijing Normal University version required 2 is seen everywhere.This can't but be great regretting to cultivating student's space imagining ability, and this problem does not solve, this sorry will ceaselessly continuing.
The parallel projection audio-visual picture that the more various common techniques of painting draw (seeing accompanying drawing 1); Can find out; In fact at present popular " oblique two survey the technique of painting " though do not belong to parallel projection; But the simple polyhedron intuitive of drawing in this way is very good, but the audio-visual picture of the ball that draws in this way but is difficult to make us agreeing, because it is tangible in too far away from spherical " intuitively ".
Summary of the invention
The object of the invention solves in the prior art defective of " oblique two survey the techniques of painting " exactly, disclose a kind ofly to intend positive two and survey the patterning process of audio-visual pictures, and designs template corresponding, and compatible simple polyhedron can also be drawn the audio-visual picture of real ball.
The present invention is achieved in that a kind of use of intending positive two survey audio-visual picture templates and patterning process and template, and it is characterized in that described patterning process: the angle of the projection line of audio-visual picture and three axes x axle, y axle and z axle is followed successively by
α, 90 °, 90 °-
α, establish observation station plane top partially under the line under the line, then the axial stretching ratio of said three axes is followed successively by sin
α, sin90 °, sin (90 °-
α), work as sin
αBe 0.2 or 0.15 o'clock, the axial stretching ratio of three-dimensional is 0.2:1:0.98 or 0.15:1:0.99, and the axial stretching ratio of selecting three-dimensional is 0.2:1:1 or 0.15:1:1;
The circles that have three kinds of the evenly divided line different sizes: connect in the ball and connect leg-of-mutton circumscribed circle in positive tetrahedron bottom surface and equator great circle in the foursquare circumscribed circle of square upper and lower surfaces, the ball; Longitudinal extension is deformed into the ellipticity of 0.2:1 or 0.15:1 and is distributed in the template both sides, and these oval " evenly divided lines " are convenient to horizontal figure rotation to obtain third dimension;
Described template center is provided with three circles that vary in size; Wherein the ball profile is a maximum circle; Its profile circle is provided with the key position line of solid commonly used, in its lower right is ball, connects the inscribed sphere profile circle of square, its lower left be ball in connect the inscribed sphere profile circle of positive tetrahedron; Also be provided with three kinds of ellipses on the template; Be respectively and connect the ellipse that ellipse that the leg-of-mutton circumscribed circle dilatation in positive tetrahedron bottom surface becomes becomes with equator great circle dilatation in the ellipse that connects the foursquare circumscribed circle dilatation of square upper and lower surfaces in the ball and become, the ball; Magnification is 0.2:1 or 0.15:1, and the ellipse of these two groups different magnifications is distributed in the template both sides.
The use that said plan positive two is surveyed the audio-visual picture templates: the audio-visual picture when being used to make cylinder and relevant polyhedron, circular cone and relevant polyhedron thereof, ball and relevant polyhedron thereof and ball, cylinder, circular cone and relevant polyhedron high integrity thereof.
The positive two survey techniques of painting from accompanying drawing 1 can find out that it has concurrently and " is parallel to
YOzAppropriate section in the figure on plane (or cross section) and the audio-visual picture is that 1:1 shows, and any direction profile of ball all is round " the consistent advantage of approving of present people.But such technique of painting also has a very big shortcoming: intuitive is bad.
The present invention is through changing dimetric projection's direction, keeps its advantage and improves its deficiency, proposes a kind of " intending positive two surveys " audio-visual picture, and it defines as follows:
If the angle of the projection line of audio-visual picture and three axes (x axle, y axle, z axle) is followed successively by
α, 90 °, 90 °-
αGenerally, establish observation station top, plane partially under the line exactly.In this case, the axial stretching ratio of three axes is followed successively by sin
α, sin90 °, sin (90 °-
α), i.e. sin
α, 1, cos
α
Work as sin
α≤0.20 o'clock, cos
α>=0.98.This explanation, the minor axis of the ellipse that forms when " equatorial plane " are during with ratio≤0.20 of major axis, and the axial stretching ratio of z axle is in close proximity to 1.
If confirm as 0.2 (or littler): 1:1 to the axial stretching ratio of three axes (x axle, y axle, z axle), just claim that audio-visual picture at this moment is " intending positive two surveys " audio-visual picture, shown in accompanying drawing 2, accompanying drawing 3 than 0.2.
The advantage of the present invention " intends positive two surveys " audio-visual picture:
1, audio-visual picture has kept the advantage of " front view 1:1 demonstration " " to intend positive two surveys ", and makes polyhedron and rotary body in same audio-visual picture obtain perfect expression simultaneously.
2, z axle axial stretching ratio is in close proximity to 1, and " arctic point " can be drawn in topmost approx, meets the habit of painting of ball.
Though some restriction of graphing method of the audio-visual picture of " intending positive two surveys ", it still has uses the basis widely: the people teaches the A version, and the circular cone in the teaching materials such as Shanghai Edition, the habit of painting of cylinder are in close proximity to " intending positive two surveys " technique of painting.Blemish in an otherwise perfect thing be, their ellipse draw too fat (eccentricity is less), this contradict topmost with " arctic point " (ellipse draw too fat be eccentricity hour, the axial stretching ratio of z axle is less, thereby " arctic point " moved down).
3, audio-visual picture passes through polyhedral third dimension of angle representations of rotation " to intend positive two surveys ".
Thus it is clear that, intend positive two and survey the inadequate natural endowment that audio-visual picture has been avoided existing oblique two survey audio-visual pictures.
Except above-mentioned advantage, the patterning process that the present invention intends positive two survey audio-visual pictures also possesses other benefit:
1, regular senior secondary school's curricular standard experiment textbook, mathematics, the people teaches the A version, required 2 (2007 February the 3rd edition), P
17, the 3rd row: " in solid geometry, commonly used just the grade surveyed the circle that the technique of painting is drawn horizontal positioned ".
If only see the circle of horizontal positioned, describe as if proper above.If but be converted into problem " drawing a shaft section is foursquare cylinder "; Adopt and just waiting the method (seeing accompanying drawing 4) of surveying the picture ellipse to remove picture; Can find that in just waiting survey technique of painting, oval horizontal direction major axis has approximately been lengthened 1.155 times at once; The shaft section of this cylinder has become rectangle, shown in accompanying drawing 5.
If survey the techniques of painting to go to the painted scroll cross section is foursquare cylinder but adopt to intend positive two, or shaft section is the circular cone of equilateral triangle, and its expression almost is perfectly, sees accompanying drawing 6, accompanying drawing 7.
2, all as accompanying drawing 8, draw ball in the nearly all textbook.Although z axle axial stretching ratio is less, arctic point should have moving down of larger amt, but is drawn in arctic point topmost.Adopt and just waiting the survey technique of painting that similar problem is also arranged, like accompanying drawing 9.
Remove the picture ball if adopt plan positive two to survey the techniques of painting, its arctic point almost reaches topmost, sees accompanying drawing 10.
Description of drawings
Fig. 1 is the comparison sketch map that adopts the parallel projection audio-visual picture that the various common techniques of painting draw.
Fig. 2 is the definition figure that plan of the present invention positive two is surveyed audio-visual picture.
Fig. 3 is that the present invention intends the comparison sketch map that positive two survey audio-visual pictures and positive two are surveyed audio-visual pictures.
Fig. 4 adopts just to wait to survey the oval method sketch map of picture.
Fig. 5 adopts just to wait to survey the method sketch map that the technique of painting is drawn cylinder.
Fig. 6 is that the shaft section that adopts plan positive two to survey techniques of painting picture is foursquare cylinder sketch map.
Fig. 7 is that the shaft section that adopts plan positive two to survey techniques of painting picture is the circular cone sketch map of equilateral triangle.
Fig. 8 is the position view of arctic point in the present teaching material.
Fig. 9 is the position view that is just waiting arctic point on the ball of surveying technique of painting picture.
Figure 10 be intend positive two survey arctic point on the ball that the techniques of painting draw position view.
Figure 11 is that the present invention intends positive two survey audio-visual picture formwork structure sketch mapes.
Figure 12 be to use intend positive two survey the audio-visual picture templates do ball in connect regular polygon step 1 sketch map.
Figure 13 be to use intend positive two survey the audio-visual picture templates do ball in connect regular polygon step 2 sketch map.
Figure 14 be to use intend positive two survey the audio-visual picture templates do ball in connect regular polygon step 3 sketch map.
Figure 15 is the horizontal figure of equilateral triangle before the rotation.
Figure 16 is that the horizontal figure of equilateral triangle is made postrotational situation.
Figure 17 is a foursquare horizontal figure before the rotation.
Figure 18 is that foursquare horizontal figure is made postrotational situation.
Figure 19 is the horizontal figure of obtuse triangle before the rotation.
Figure 20 is that the horizontal figure of obtuse triangle is made postrotational situation.
Figure 21 be adopt ball that template of the present invention does in connect the square audio-visual picture.
Figure 22 be adopt ball that template of the present invention does in connect the positive tetrahedron audio-visual picture.
Figure 23 be adopt ball that template of the present invention does in connect the audio-visual picture of regular octahedron.
Figure 24 is the ball inscribed circle post audio-visual picture that adopts template of the present invention to do.
Figure 25 is the ball inscribed cone audio-visual picture that adopts template of the present invention to do.
Figure 26 is the positive tetrahedron audio-visual picture that adopts template of the present invention to do.
Figure 27 is the cylinder inscribed sphere audio-visual picture that adopts template of the present invention to do.
Figure 28 be adopt cylinder that template of the present invention does with in connect the audio-visual picture of falling the rectangular pyramid.
Figure 29 is square and the positive tetrahedron audio-visual picture that adopts template of the present invention to do.
Figure 30 is the imperial crown nut audio-visual picture that adopts template of the present invention to do.
Figure 31 is the not hexagonal (hexagon)nut audio-visual picture through rotating that adopts template of the present invention to do.
Figure 32 is the hexagonal (hexagon)nut audio-visual picture through rotation that adopts template of the present invention to do.
Figure 33 is the inscribed sphere audio-visual picture that adopts the square of template work of the present invention.
Figure 34 is the regular octahedron audio-visual picture that adopts template of the present invention to do.
Figure 35 adopts the imperial palace of hemisphere that template of the present invention does to connect positive rectangular pyramid audio-visual picture.
Figure 36 is the positive rectangular pyramid audio-visual picture that adopts template of the present invention to do.
The specific embodiment
A kind of use of intending positive two survey audio-visual picture templates and patterning process and template of the present invention, its patterning process: the angle of the projection line of audio-visual picture and three axes x axle, y axle and z axle is followed successively by
α, 90 °, 90 °-
α, establish observation station plane top partially under the line under the line, then the axial stretching ratio of said three axes is followed successively by sin
α, sin90 °, sin (90 °-
α), work as sin
αBe 0.2 or 0.15 o'clock, the axial stretching ratio of three-dimensional is 0.2:1:0.98 or 0.15:1:0.99, and the axial stretching ratio of selecting three-dimensional is 0.2:1:1 or 0.15:1:1.
The circles that have three kinds of the evenly divided line different sizes: connect in the ball and connect leg-of-mutton circumscribed circle in positive tetrahedron bottom surface and equator great circle in the foursquare circumscribed circle of square upper and lower surfaces, the ball; Longitudinal extension is deformed into the ellipticity of 0.2:1 or 0.15:1 and is distributed in the template both sides, and these oval " evenly divided lines " are convenient to horizontal figure rotation to obtain third dimension.
According to accompanying drawing 11; Template center is provided with three circles that vary in size; Wherein the ball profile is a maximum circle; Its profile circle is provided with the key position line of solid commonly used, in its lower right is ball, connects the inscribed sphere profile circle of square, its lower left be ball in connect the inscribed sphere profile circle of positive tetrahedron.Also be provided with three kinds of ellipses on the template; Be respectively and connect the ellipse that ellipse that the leg-of-mutton circumscribed circle dilatation in positive tetrahedron bottom surface becomes becomes with equator great circle dilatation in the ellipse that connects the foursquare circumscribed circle dilatation of square upper and lower surfaces in the ball and become, the ball; Magnification is 0.2:1 or 0.15:1, and the ellipse of these two groups different magnifications is distributed in the template both sides.After the round longitudinal extension that will have an evenly divided is deformed into ellipticity, also have evenly divided on the ellipse, and ellipse short shaft/major axis≤0.30 (two kinds of different magnifications that template of the present invention provides make z axle axial stretching ratio>=0.98 ≈ 1).Therefore, when three axes axial stretching ratio was 0.2:1:1, arctic point can be drawn in topmost.
The present invention intends positive two audio-visual pictures when surveying the audio-visual picture templates and being used to make cylinder and relevant polyhedron, circular cone and relevant polyhedron thereof, ball and relevant polyhedron thereof and ball, cylinder, circular cone and relevant polyhedron high integrity thereof.
According to accompanying drawing 12～14, use the present invention intend positive two survey the audio-visual picture templates do ball in connect the method for regular polygon:
1, uses template draw ball profile and equator great circle;
2, connect square in drawing in the great circle under the line, and utilize the template scale to do suitably rotation.The rotation principle is seen accompanying drawing 15～20;
3, connect Geophysical South Pole, arctic point and equator each summit of big inscribed square respectively, obtain ball with in connect the audio-visual picture of regular octahedron.
According to accompanying drawing 21～23, respectively expression use the present invention intend positive two survey the audio-visual picture templates make ball in connect square, ball in connect positive tetrahedron, ball in connect the audio-visual picture of regular octahedron.
According to accompanying drawing 24～36, employing the present invention intends the patterning process of positive two survey audio-visual pictures and intends positive two survey audio-visual picture templates and can make the positive two survey audio-visual pictures of various plans.
Claims (3)
- One kind intend positive two survey the audio-visual picture templates patterning process, it is characterized in that: the angle of the projection line of audio-visual picture and three axes x axle, y axle and z axle is followed successively by α, 90 °, 90 °- α, establish observation station plane top partially under the line under the line, then the axial stretching ratio of said three axes is followed successively by sin α, sin90 °, sin (90 °- α), work as sin αBe 0.2 or 0.15 o'clock, the axial stretching ratio of selecting three-dimensional is 0.2:1:1 or 0.15:1:1;The circles that have three kinds of the evenly divided line different sizes: connect in the ball and connect leg-of-mutton circumscribed circle in positive tetrahedron bottom surface and equator great circle in the foursquare circumscribed circle of square upper and lower surfaces, the ball; Longitudinal extension is deformed into the ellipticity of 0.2:1 or 0.15:1 and is distributed in the template both sides, and these oval " evenly divided lines " are convenient to horizontal figure rotation to obtain third dimension;Template center is provided with three circles that vary in size; The profile circle that a wherein maximum circle is a ball; Its profile circle is provided with the key position line of solid commonly used, in its lower right is ball, connects the inscribed sphere profile circle of square, its lower left be ball in connect the inscribed sphere profile circle of positive tetrahedron.
- 2. the plan of the said patterning process of claim 1 positive two is surveyed the audio-visual picture template; It is characterized in that: template center is provided with three circles that vary in size; Wherein the ball profile is a maximum circle; Its profile circle is provided with the key position line of solid commonly used, in its lower right is ball, connects the inscribed sphere profile circle of square, its lower left be ball in connect the inscribed sphere profile circle of positive tetrahedron; Also be provided with three kinds of ellipses on the template; Be respectively and connect the ellipse that ellipse that the leg-of-mutton circumscribed circle dilatation in positive tetrahedron bottom surface becomes becomes with equator great circle dilatation in the ellipse that connects the foursquare circumscribed circle dilatation of square upper and lower surfaces in the ball and become, the ball; Magnification is 0.2:1 or 0.15:1, and the ellipse of these two groups different magnifications is distributed in the template both sides.
- 3. the use of the said template of claim 2 is characterized in that: the audio-visual picture when being used to make cylinder and relevant polyhedron, circular cone and relevant polyhedron thereof, ball and relevant polyhedron thereof and ball, cylinder, circular cone and relevant polyhedron high integrity thereof.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210307966.0A CN102795030B (en) | 2012-08-28 | 2012-08-28 | Template of pictorial diagram for simulating bimetric projection, picture constructing method thereof and use of template |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210307966.0A CN102795030B (en) | 2012-08-28 | 2012-08-28 | Template of pictorial diagram for simulating bimetric projection, picture constructing method thereof and use of template |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN102795030A true CN102795030A (en) | 2012-11-28 |
| CN102795030B CN102795030B (en) | 2014-08-27 |
Family
ID=47194434
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201210307966.0A Expired - Fee Related CN102795030B (en) | 2012-08-28 | 2012-08-28 | Template of pictorial diagram for simulating bimetric projection, picture constructing method thereof and use of template |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN102795030B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105329032A (en) * | 2015-12-01 | 2016-02-17 | 唐文虎 | Sphere illustrative diagram, composition method of North Pole position thereof and used template |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB605647A (en) * | 1946-01-02 | 1948-07-28 | John Frederick Leete | An improved draughtsman's template |
| CN85201416U (en) * | 1985-04-23 | 1986-08-20 | 李公珏 | Multipurpose quick drawing template for mathematics learned in middle school |
| CN85204535U (en) * | 1985-10-31 | 1986-11-19 | 田志学 | Template for technical drawing |
| CN2127669Y (en) * | 1992-06-27 | 1993-03-03 | 马俊贵 | Multi-functional digital drawing ruler |
| CN2375476Y (en) * | 1999-04-15 | 2000-04-26 | 董俊道 | Stencil for students |
-
2012
- 2012-08-28 CN CN201210307966.0A patent/CN102795030B/en not_active Expired - Fee Related
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB605647A (en) * | 1946-01-02 | 1948-07-28 | John Frederick Leete | An improved draughtsman's template |
| CN85201416U (en) * | 1985-04-23 | 1986-08-20 | 李公珏 | Multipurpose quick drawing template for mathematics learned in middle school |
| CN85204535U (en) * | 1985-10-31 | 1986-11-19 | 田志学 | Template for technical drawing |
| CN2127669Y (en) * | 1992-06-27 | 1993-03-03 | 马俊贵 | Multi-functional digital drawing ruler |
| CN2375476Y (en) * | 1999-04-15 | 2000-04-26 | 董俊道 | Stencil for students |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105329032A (en) * | 2015-12-01 | 2016-02-17 | 唐文虎 | Sphere illustrative diagram, composition method of North Pole position thereof and used template |
Also Published As
| Publication number | Publication date |
|---|---|
| CN102795030B (en) | 2014-08-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN103258329B (en) | A kind of camera marking method based on ball one-dimensional | |
| Sun et al. | The application of 3D printing in STEM education | |
| CN102795030B (en) | Template of pictorial diagram for simulating bimetric projection, picture constructing method thereof and use of template | |
| CN204375266U (en) | A kind of mathematics probability demonstration teaching aid | |
| US5215467A (en) | Mathematical instruction board and method of use | |
| CN206242758U (en) | A kind of multifunctional ruler | |
| CN201304821Y (en) | Multi-purpose folding ruler for blackboard teaching | |
| CN102723021B (en) | Multifunctional movable space geometry analytical model | |
| CN104318812A (en) | View projection demonstrator | |
| CN109334308A (en) | A kind of Pattern plate ruler | |
| Yackel | Teaching temari: Geometrically embroidered spheres in the classroom | |
| Long | Painless geometry | |
| CN105329032B (en) | Sphere illustrative diagram, composition method of North Pole position thereof and used template | |
| CN201610023U (en) | Dotting type mathematical drawing board | |
| CN2338179Y (en) | Multi-functional curve ruler for teaching purpose | |
| CN203644262U (en) | Cartesian coordinate teaching aid for blind | |
| Wares | Problem solving through paper folding | |
| KR100843755B1 (en) | Multi purpose ruler | |
| McGraw | Quadrilaterals: Diagonals and area | |
| CN217331170U (en) | Temporary simple platform capable of being used for setting aerial image measurement control points | |
| CN214847408U (en) | Creative model of graticule | |
| CN210488961U (en) | Teaching aid for proving cone volume, ball volume and ball surface area formula by using ball bottom rectangular pyramid | |
| CN103075996A (en) | Globe longitude and latitude detector | |
| Arranz et al. | Realities from GeoGebra | |
| CN201501222U (en) | Mathematical drawing template |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20140827 Termination date: 20160828 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |