CN102795030B - 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
- CN102795030B CN102795030B CN201210307966.0A CN201210307966A CN102795030B CN 102795030 B CN102795030 B CN 102795030B CN 201210307966 A CN201210307966 A CN 201210307966A CN 102795030 B CN102795030 B CN 102795030B
- 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.)
- Expired - Fee Related
Links
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 positive two uses of surveying audio-visual picture templates and patterning process and template of intending, is a kind of school school supply and stationery, for drawing the tool palette of audio-visual picture.
Background technology
In decades, a popular wider mistake in middle school teaching, thinks that the oblique two survey audio-visual picture techniques of painting are parallel projection techniques of painting.It is not the proof > > of projection space figure that this case inventor had delivered the oblique two survey audio-visual pictures of < < on < < mathematics circular > >.
The oblique two survey coordinate systems that use are now through adjusting, and the essence of adjustment is that x axle has been rotated counterclockwise to approximately 3.59 °, and y axle has been rotated counterclockwise to approximately 7.18 °, and this rotation makes the position, lower-left of ball too sagging, position, the upper right excess towering-up of ball.So the scope of application of " oblique two survey the technique of painting " should be limited: it is only applicable to simple polyhedron, and is not suitable for rotary body.
Cannot investigate is now 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, people teaches 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: " from the angle of projection, three-view diagram and be all the space diagram drawing under parallel projection with the audio-visual picture that the oblique two survey techniques of painting draw ";
2, required 2 teaching materials of [Beijing Normal University version] high school mathematics, P
9, the 1st row reciprocal: " being the figures that draw according to the principle of parallel projection with oblique two audio-visual pictures of surveying technique of painting picture ".
It is all the most influential teaching material in the current whole nation that people teaches A version teaching material and Beijing Normal University version teaching material.So people think that the oblique two survey techniques of painting are to be positioned over the four seas and all accurate truth, a kind of blanket rule 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 intuitively also do not believe firmly when drawing cylinder, circular cone, in the time cannot drawing ball, also turn a blind eye to, in teaching material, to oblique two, survey picture ball at present and generally adopt avoidance attitude.
On existing textbook, simple polyhedron, cylinder, circular cone, ball have been adopted the method for multiple different picture audio-visual picture, when having related to multiple solid in same width figure, just there is confusion in technique of painting rule, so just there are various not audio-visual pictures intuitively.The object that it should be known that picture audio-visual picture is in order to cultivate student's space imagining ability, and first it want " intuitively ".And at present regardless of occasion use oblique two to survey the techniques of painting, just as regardless of indication scope use same medicine prescription.
Some teacher is not directly perceived for fear of rotary body, just uses instead and to wait axle to survey picture cylinder, circular cone, has thought in addition that again a method draws ball specially.Due to the mistake in this understanding, cause the confusion on relevant solid (polyhedron, circular cone, cylinder, ball) the audio-visual picture technique of painting, cause in a figure and have multiple solid simultaneously, for example, during the inpolyhedron of ball and it, at a loss as to what to do on the technique of painting, take challenger to have it, the flicker of carelessly drawing a picture survivor has it (it is a kind of helpless that this flicker is actually).This situation, teaches A version required 2 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 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 " although do not belong to parallel projection, but the simple polyhedron intuitive drawing is in this way very good, but the audio-visual picture of the ball drawing in this way is but difficult to make us agreeing, because it is tangible away from too from spherical " intuitively ".
Summary of the invention
Object of the present invention solves in prior art the defect of " oblique two survey the techniques of painting " exactly, disclose a kind of patterning process of intending positive two survey audio-visual pictures, and designs corresponding template, and compatible simple polyhedron, can also draw the audio-visual picture of real ball.
The present invention is achieved in that a kind of positive two uses of surveying audio-visual picture template and patterning process and template of intending, and it is characterized in that described patterning process: the angle of the projection line of audio-visual picture and three axes x-axis, y-axis and z-axis is followed successively by
α, 90 °, 90 °-
α, establish observation station plane top partially under the line under the line, the axial stretching ratio of described 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 with three kinds of evenly divided line different sizes: connect in ball and connect the leg-of-mutton circumscribed circle in positive tetrahedron bottom surface and equator great circle in the foursquare circumscribed circle of square upper and lower surface, ball, longitudinal extension is deformed into the ellipticity of 0.2:1 or 0.15:1 and is distributed in template both sides, and " the evenly divided line " of these ellipses is convenient to horizontal figure and rotated to obtain third dimension;
Described template center is provided with three circles that vary in size, wherein ball profile is a maximum circle, its profile circle is provided with the key position line of conventional solid, connects the inscribed sphere profile circle of square in its lower right is ball, connects the inscribed sphere profile circle of positive tetrahedron in its lower left is ball; In template, be also provided with three kinds of ellipses, be respectively and in the ellipse that connects the foursquare circumscribed circle dilatation of square upper and lower surface in ball and become, ball, 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, magnification is 0.2:1 or 0.15:1, and the ellipse of these two groups different magnifications is distributed in template both sides.
The use that described plan positive two is surveyed audio-visual picture templates: the audio-visual picture when making cylinder and relevant polyhedron thereof, circular cone and relevant polyhedron thereof, ball and relevant polyhedron thereof and ball, cylinder, circular cone and relevant polyhedron high integrity thereof.
Positive two surveying the techniques of painting and can find out from accompanying drawing 1, it has concurrently and " is parallel to
yOzappropriate section in the figure of plane (or cross section) and audio-visual picture is that 1:1 shows, and any direction profile of ball is all round " the advantage of the consistent approval of current people.But such technique of painting also has a very large shortcoming: intuitive is bad.
The present invention is by changing dimetric projection's direction, retains its advantage and improves its deficiency, proposes a kind of " intending positive two surveys " audio-visual picture, and it is defined 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 °-
α.Generally, establish exactly observation station plane top partially under the line.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, when the oval minor axis of " equatorial plane " formation and ratio≤0.20 of major axis, the axial stretching ratio of z axle is in close proximity to 1.
If be 0.2 (or less than 0.2): 1:1 the axial stretching ratio-dependent of three axes (x axle, y axle, z axle), just claim that audio-visual picture is at this moment " intending positive two surveys " audio-visual picture, as shown in accompanying drawing 2, accompanying drawing 3.
The advantage of the present invention " intends positive two surveys " audio-visual picture:
1, audio-visual picture has retained 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.
Although some restriction of the graphing method of the audio-visual picture of " intending positive two surveys ", it still has uses basis widely: people teaches 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, their ellipse drawing obtains too fat (eccentricity is less), this contradict topmost with " arctic point " (ellipse drawing obtain 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 a polyhedral third dimension of angle representations of rotation " to intend positive two surveys ".
Visible, 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 present invention intends positive two patterning process of surveying audio-visual picture and also possesses other benefit:
1, regular senior secondary school's curricular standard experiment textbook, mathematics, people teaches A version, required 2 (2007 February the 3rd edition), P
17, the 3rd row: " in solid geometry, the conventional circle of surveying technique of painting picture horizontal positioned that just waiting ".
If only see the circle of horizontal positioned, describe and seem proper above.If but problem is converted into " drawing a shaft section is foursquare cylinder ", the method (seeing accompanying drawing 4) of survey picture ellipse such as just adopt to remove picture, can find at once, in just waiting survey technique of painting, oval horizontal direction major axis has approximately been lengthened 1.155 times, the shaft section of this cylinder has become rectangle, as shown in Figure 5.
If survey the techniques of painting to go to painted scroll cross section be foursquare cylinder but adopt to intend positive two, or shaft section is the circular cone of equilateral triangle, and its expression is almost perfectly, sees accompanying drawing 6, accompanying drawing 7.
2, in nearly all textbook, all as accompanying drawing 8, draw ball.Although z axle axial stretching ratio is less, arctic point should have moving down of larger amt, but arctic point is drawn in topmost.The survey technique of painting such as just adopt also to have similar problem, as accompanying drawing 9.
If adopt plan positive two to survey the techniques of painting, remove picture ball, its arctic point almost reaches topmost, sees accompanying drawing 10.
Accompanying drawing explanation
Fig. 1 is the comparison schematic diagram 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 schematic diagram that positive two survey audio-visual pictures and positive two are surveyed audio-visual pictures.
Fig. 4 adopts just to wait the method schematic diagram of surveying picture ellipse.
Fig. 5 adopts just to wait to survey the method schematic diagram that the technique of painting is drawn cylinder.
Fig. 6 is that the shaft sections that adopt plan positive two to survey techniques of painting picture are foursquare cylinder schematic diagrames.
Fig. 7 is that the shaft sections that adopt plan positive two to survey techniques of painting picture are circular cone schematic diagrames of equilateral triangle.
Fig. 8 is the position view of arctic point in current teaching material.
Fig. 9 is just waiting the position view of arctic point on the ball of surveying technique of painting picture.
Figure 10 intends positive two position views of surveying arctic point on the ball that the techniques of painting draw.
Figure 11 is that the present invention intends positive two survey audio-visual picture formwork structure schematic diagrames.
Figure 12 use to intend positive two and surveys audio-visual picture templates and make to connect in ball regular polygon step 1 schematic diagram.
Figure 13 use to intend positive two and surveys audio-visual picture templates and make to connect in ball regular polygon step 2 schematic diagram.
Figure 14 use to intend positive two and surveys audio-visual picture templates and make to connect in ball regular polygon step 3 schematic diagram.
Figure 15 is the horizontal figure of equilateral triangle before rotation.
Figure 16 is that the horizontal figure of equilateral triangle is made postrotational situation.
Figure 17 is foursquare horizontal figure before rotation.
Figure 18 is that foursquare horizontal figure is made postrotational situation.
Figure 19 is the horizontal figure of obtuse triangle before 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 square audio-visual picture.
Figure 22 be adopt ball that template of the present invention does in connect 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 and in connect the audio-visual picture of falling 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 hexagonal (hexagon)nut audio-visual picture through over-rotation that do not have that adopts template work of the present invention.
Figure 32 is the hexagonal (hexagon)nut audio-visual picture through over-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 positive two uses of surveying audio-visual picture template and patterning process and template, its patterning process: the angle of the projection line of audio-visual picture and three axes x-axis, y-axis and z-axis is followed successively by intended of the present invention
α, 90 °, 90 °-
α, establish observation station plane top partially under the line under the line, the axial stretching ratio of described 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 with three kinds of evenly divided line different sizes: connect in ball and connect the leg-of-mutton circumscribed circle in positive tetrahedron bottom surface and equator great circle in the foursquare circumscribed circle of square upper and lower surface, ball, longitudinal extension is deformed into the ellipticity of 0.2:1 or 0.15:1 and is distributed in template both sides, and " the evenly divided line " of these ellipses is convenient to horizontal figure and rotated to obtain third dimension.
With reference to the accompanying drawings 11, template center is provided with three circles that vary in size, wherein ball profile is a maximum circle, its profile circle is provided with the key position line of conventional solid, in its lower right is ball, connect the inscribed sphere profile circle of square, in its lower left is ball, connect the inscribed sphere profile circle of positive tetrahedron.In template, be also provided with three kinds of ellipses, be respectively and in the ellipse that connects the foursquare circumscribed circle dilatation of square upper and lower surface in ball and become, ball, 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, magnification is 0.2:1 or 0.15:1, and the ellipse of these two groups different magnifications is distributed in template both sides.Round longitudinal extension with evenly divided is deformed into after ellipticity, on ellipse also with evenly divided, and two kinds of different magnifications that ellipse short shaft/major axis≤0.30(template of the present invention provides make z axle axial stretching ratio >=0.98 ≈ 1).Therefore,, when three axes axial stretching ratio is 0.2:1:1, arctic point can be drawn in topmost.
The present invention intends positive two and surveys the audio-visual picture of audio-visual picture templates when making cylinder and relevant polyhedron thereof, circular cone and relevant polyhedron thereof, ball and relevant polyhedron thereof and ball, cylinder, circular cone and relevant polyhedron high integrity thereof.
With reference to the accompanying drawings 12～14, use the present invention intend positive two survey audio-visual picture templates do ball in connect the method for regular polygon:
1, use template to draw ball profile and equator great circle;
2, connect square in drawing in great circle under the line, and utilize template scale to do suitably rotation.Principle of Rotating is shown in accompanying drawing 15～20;
3, connect respectively each summit of the large inscribed square of Geophysical South Pole, Dian He equator, the arctic, obtain ball with in connect the audio-visual picture of regular octahedron.
With reference to the accompanying drawings 21～23, represent respectively to use the present invention intend positive two survey audio-visual picture templates make ball in connect square, ball in connect positive tetrahedron, ball in connect the audio-visual picture of regular octahedron.
With reference to the accompanying drawings 24～36, adopt the present invention to intend positive two and survey the patterning process of audio-visual pictures and intend positive two and survey audio-visual picture templates and can make various plans positive two and survey audio-visual pictures.
Claims (3)
1. a patterning process of intending positive two survey audio-visual picture templates, is characterized in that: the angle of the projection line of audio-visual picture and three axes x-axis, y-axis and z-axis is followed successively by
α, 90 °, 90 °-
α, establish observation station plane top partially under the line under the line, the axial stretching ratio of described 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 with three kinds of evenly divided line different sizes: connect in ball and connect the leg-of-mutton circumscribed circle in positive tetrahedron bottom surface and equator great circle in the foursquare circumscribed circle of square upper and lower surface, ball, longitudinal extension is deformed into the ellipticity of 0.2:1 or 0.15:1 and is distributed in template both sides, and " the evenly divided line " of these ellipses is convenient to horizontal figure and rotated to obtain third dimension;
Template center is provided with three circles that vary in size, the profile circle that wherein a maximum circle is ball, its profile circle is provided with the key position line of conventional solid, connects the inscribed sphere profile circle of square in its lower right is ball, connects the inscribed sphere profile circle of positive tetrahedron in its lower left is ball.
2. described in a claim 1, the plan of patterning process positive two is surveyed audio-visual picture template, it is characterized in that: template center is provided with three circles that vary in size, wherein ball profile is a maximum circle, its profile circle is provided with the key position line of conventional solid, in its lower right is ball, connect the inscribed sphere profile circle of square, in its lower left is ball, connect the inscribed sphere profile circle of positive tetrahedron; In template, be also provided with three kinds of ellipses, be respectively and in the ellipse that connects the foursquare circumscribed circle dilatation of square upper and lower surface in ball and become, ball, 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, magnification is 0.2:1 or 0.15:1, and the ellipse of these two groups different magnifications is distributed in template both sides.
3. a using method for template described in claim 2, is characterized in that: the audio-visual picture when making cylinder and relevant polyhedron thereof, 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 CN102795030A (en) | 2012-11-28 |
| CN102795030B true 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) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105329032B (en) * | 2015-12-01 | 2017-03-22 | 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 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN102795030A (en) | 2012-11-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN103258329B (en) | A kind of camera marking method based on ball one-dimensional | |
| CN102795030B (en) | Template of pictorial diagram for simulating bimetric projection, picture constructing method thereof and use of template | |
| CN201304821Y (en) | Multi-purpose folding ruler for blackboard teaching | |
| CN102723021B (en) | Multifunctional movable space geometry analytical model | |
| Araújo | A fisheye gyrograph: Taking spherical perspective for a spin | |
| Yackel | Teaching temari: Geometrically embroidered spheres in the classroom | |
| CN105329032B (en) | Sphere illustrative diagram, composition method of North Pole position thereof and used template | |
| TWM478889U (en) | Inflatable celestial globe | |
| CN109334308A (en) | A kind of Pattern plate ruler | |
| Long | Painless geometry | |
| CN107909896B (en) | Teaching device and application thereof | |
| CN2338179Y (en) | Multi-functional curve ruler for teaching purpose | |
| CN205508257U (en) | Lan bote map projection presentation device | |
| CN203644262U (en) | Cartesian coordinate teaching aid for blind | |
| CN210488961U (en) | Teaching aid for proving cone volume, ball volume and ball surface area formula by using ball bottom rectangular pyramid | |
| KR100843755B1 (en) | Multi purpose ruler | |
| CN205508256U (en) | Gauss ke lvge map projection presentation device | |
| Arranz et al. | Realities from GeoGebra | |
| CN201501222U (en) | Mathematical drawing template | |
| CN203217832U (en) | Polygon dynamic demonstration teaching aid | |
| CN214847408U (en) | Creative model of graticule | |
| CN216435261U (en) | Mathematics teaching aid for mathematical thinking training | |
| CN201055680Y (en) | Dice | |
| McGraw | Quadrilaterals: Diagonals and area | |
| CN115691277A (en) | Teaching tool for Lagrange point concept |
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 | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20140827 Termination date: 20160828 |