CN2399227Y - Drawing/calculating instrument - Google Patents
Drawing/calculating instrument Download PDFInfo
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- CN2399227Y CN2399227Y CN 99253895 CN99253895U CN2399227Y CN 2399227 Y CN2399227 Y CN 2399227Y CN 99253895 CN99253895 CN 99253895 CN 99253895 U CN99253895 U CN 99253895U CN 2399227 Y CN2399227 Y CN 2399227Y
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Abstract
The utility model relates to a drawing/calculating instrument, mainly composed of a transparent plastic bottom board, fundamentally geometric shape holes on the bottom board, a big semi-circle meter, a small semi-circle meter, angle and radian scale lines, equant small circular holes, a straightedge rule, etc., wherein, the centers of circles of the big and the small semi-circle meters are coincident, axle wires are arranged on an identical straight line, and the straightedge rule is positioned at the periphery of the big semi-circle meter. The drawing/calculating instrument can quickly and accurately draw a plurality of plane geometry patterns, solid geometry patterns, analytic geometry patterns, plane triangles, and algebraic curves, can equally divide any circle, can look up the trigonometric function and the inverse trigonometric function of an arbitrary angle, can solve triangles, can quickly draw out parallel lines and vertical lines, etc., and can be widely used for students, teachers, and research and development personnel.
Description
The utility model relates to a kind of drawing, computational tool, relates in particular to a kind of plotter of drawing the various figures in the middle school mathematics and carrying out simple computation.
At present, drawing instrument is of a great variety, many combined type drawing instruments with the multi-functional student of being suitable for or teacher's use have appearred again in recent years, example Chinese patent CN94202607.1 middle school mathematics multipurpose drawing board, it is to be provided with multiple geometric figure and ruler, graphometer etc. on a transparent plastic sheet, can draw multiple figure more quickly, but for some problem that runs in the mapping, then seem powerless as any five equilibrium any circumference, and also do not possess computing function.The author had once proposed solution in patent CN96247144.5, and had obtained popularization.But still existing the globality of design not good enough, the figure coupling is very unreasonable, also is not very convenient in the use.
The purpose of this utility model is to provide a kind of function more complete more practical, easy to carry, draws quick and precisely and the drawing instrument with multiple computing function.
The technical solution of the utility model is achieved in that
A kind of calculation instrument of painting, mainly constitute by a transparent plastic base plate, basic geometry hole (1) is arranged on the base plate, it is the rectangle of two double-lengths of minor face that the middle part of base plate also has a long limit, a long limit of rectangle and the outer rim of two minor faces all have identical length tolerance scale, there is a greater part of round instrument (2) rectangle inside, the long limit of the base of large semicircle instrument (2) and the band scale of rectangle overlaps, the circular arc limit is tangential on other three limits of rectangle respectively, the circular arc limit inner edge of large semicircle instrument (2) has the angle index value, the part of outer rim has the radian scale value, the length scale value identical with the rectangle minor face arranged on the axis of large semicircle instrument (2), the small semicircle instrument (3) that one band angle index value is arranged in the large semicircle instrument (2), the center of circle of large semicircle instrument (2) and small semicircle instrument (3) overlaps, the axis is on same straight line, and there is graphometer hole (4) the angle index value inboard of small semicircle instrument (3); There is five equilibrium circular hole (5) left side of large semicircle instrument (2), and the folded acute angle in the base of the line in the center of circle of the center of each circular hole and large semicircle instrument and large semicircle instrument (2) equals the number of degrees with the folded central angle of every equal portions circular arc of this corresponding Equal round in hole; Rectangle minor face inner edge has the angle index line, and every graduation mark and large semicircle instrument (2), small semicircle instrument (3) are gone up the graduation mark that equates the number of degrees and be located along the same line; Basic geometry hole (1) proportionally size can be divided into large scale graphical set (A, B, C, D, E, F) and small size graphical set (A ', B ', C ', D ', E ', F ').Small sircle hole (a, b, c, d, e, f, g, h, I, j, k, l, m, n) several holes in are arranged on the transparent plastic sheet.Tan hole (G), parabola hole (H), hyperbola hole (I), SIN function hole (J), rectangular opening (K), diamond hole (L) are arranged on the transparent plastic sheet; The left hand edge in tan hole (G) is a hyperbola, and right hand edge is a tan.The length scale is arranged around the transparent plastic sheet.The edge of transparent plastic sheet is a waveform.Be evenly equipped with aperture on the graduation mark of the left side of the rectangle on the transparent plastic sheet.
Below in conjunction with accompanying drawing the utility model is described in further detail.
Fig. 1 is a structural representation of the present utility model.
By shown in Figure 1, the utility model mainly is made of a transparent plastic sheet, there are a greater part of round instrument (2) and small semicircle instrument (3) in the middle part of base plate, the center of circle of two graphometers overlaps, and the axis is located along the same line, and there is graphometer hole (4) the angle index inboard of small semicircle instrument (3), be used for conveniently measuring and drawing various angles, the great circle camber line inner edge of large semicircle instrument (2) is carved with the angle index value, and there is the radian scale value left side of outer rim, is convenient to and the contrast of the angle index of this circular arc inner edge.Can ask the known whole number of degrees and whole mark central angle to the radian number of arc (whole mark is an estimated value); Also can be conversely, ask known radian number arc right central angle, known angle is in 90 °, can directly find from the scale contrast, if an angle of looking into is above 90 °, then deduct 90 ° integral multiple, calibration contrast place again, and the number that will check in add pi/2=1.571 integer multiple (with deduct 90 ° the identical multiple of multiple).As ask 50 ° of central angles to the radian number of arc.Find out 50 ° of scales at the circular arc inner edge, finding pairing radian number in the outer rim at identical graduation place is 0.873 (last times is estimative figure); And for example ask 223 ° 15 at central angle ' to the radian of arc.Since 223 ° of 15 '=90 ° * 2+ (43.25) °, so the number of degrees of the arc of asking are 3.142+0.755=3.897.Again furtherly, known the radian number, just can be according to arc length formula L=R θ (L is an arc length, and R is a radius of circle, and θ is that arc length institute is to the radian number) and sectorial area formula S=R
2θ/2 (S is a sectorial area) are carried out arc length and sectorial area easily and have been calculated.
There are several to be used for the five equilibrium circular hole (5) of circumference in equal parts in the left side of large semicircle instrument (2), each five equilibrium circular hole is other all to be indicated and the same number of five equilibrium numeral of the five equilibrium of certain Equal round, and the folded acute angle in the base of the line in the center of circle of the center in this Equal round hole and large semicircle instrument and large semicircle instrument (2) equals the number of degrees (every length of side institute of inscribed regular polygon is to there being central angle) of the folded central angle of every equal portions circular arc.According to every equal portions circular arc in the Equal round the number of degrees of right central angle be 360 °/N, get N=5,6,7 ..., when then obtaining the different equal portions of circumference, the folded central angle number of degrees of every equal portions circular arc are respectively:
| Branch numbers such as circumference: | 5 | ?6 | ?7 | ?8 | ?9 | ?10 | ?…… |
| The central angle number of degrees: | 72° | 60° | 51.43° | 45° | 40° | 36° | ?…… |
Five equilibrium circular hole (5) in the accompanying drawing 1 be exactly the center of circle with the large semicircle instrument be the summit, left side with the base (straight flange) of large semicircle instrument is one side (true edge), make 72 °, 60 °, 51.43 ° respectively to the inboard of graphometer ... angle, this angle line and radius are the intersection point of the circular arc of 3.5cm, be exactly the center of circle of five equilibrium circular hole, wherein each five equilibrium circular hole is other all indicates and the same number of numeral of the five equilibrium of Equal round.(annotate: the line hereinafter to be referred as the center of circle of the center of five equilibrium circular hole and large semicircle instrument is the Equal round graduation mark, does not draw among the figure).
When certain circumference of need five equilibrium, the center of circle with large semicircle instrument (2) is the center of circle, with required five equilibrium radius of a circle is that radius is respectively on the base of large semicircle instrument (2) (true edge) with indicate on the Equal round graduation mark with five equilibrium number same numbers and make an arc, (for example, need circumference 10 equal portions are promptly drawn arc on the Equal round graduation mark that indicates numeral 10).Circular arc intersects respectively on two lines, the distance between intersect 2 be every equal portions arc length in the circumference in equal parts right chord length, be radius with this chord length, promptly available compasses are divided into required umber to circumference.Also available rule is measured: the center of circle with large semicircle instrument (2) is an end points, with rule respectively on the datum line and indicate on the Equal round graduation mark with five equilibrium number same numbers and measure the long line segment of radius (radius of a circle of required five equilibrium), article two, the distance between in addition two end points of line segment be every equal portions arc length in the circumference in equal parts the length of right string, be that available rule is divided into required equal portions to circle with the length of this string.
In the center of circle with large semicircle instrument (2) is the center of circle, with the radius is the semi arch inside of 10mm, being blank except that the axis that the large semicircle instrument is arranged, is for clearer when measuring angle and search scale on the axis (because graduation mark is too intensive in this circular arc inside, being difficult for explanation).
Having on the base of large semicircle instrument (2) with the millimeter is the length scale of unit, both sides in large semicircle instrument (2), have respectively vertical with the base, with semi arch tangent to have with the millimeter be the tangent line of unit scale, also have a millimeter scale on the axis of large semicircle instrument (2), the tangent line at the place, summit of excessive graphometer (2) and the base of large semicircle instrument (2) and the base of large semicircle instrument (2) and the tangent line of large semicircle instrument (2) two sideband scales are formed a rectangle, and the length of this rectangle is wide 2 times.
A width is respectively arranged is the ruler of 10mm around the rectangle, and the right outer rim of ruler is a waveform, is used to draw wave, and the outer rim on its excess-three limit and rectangular central portion are parallel to that all to indicate with the millimeter on the straight line on the long limit of rectangle be the length scale of unit.
Utilize above-mentioned all lengths graduation mark, parallel lines and vertical line easily can draw.
The inner edge of the right side tangent line of large semicircle instrument (2) (rectangle minor face) has 0-45 ° angle index, and the inner edge of the long limit of rectangle right-hand part has 45 °-90 ° angle index.This graduation mark and large semicircle instrument (2), the graduation mark with identical number of degrees on the small semicircle instrument (3) is located along the same line, utilize the angle index of rectangle minor face inner edge, the angle index of long limit right-hand part inner edge on the rectangle, the millimeter scale of outer rim, the millimeter scale on the base of the angle index of the circular arc inner edge of large semicircle instrument (2) and large semicircle instrument (2), can check in the sine of trigonometric function, cosine, tangent, cotangent value (annotate: the scale of the outer rim of long limit right-hand part is uneven on the rectangle, is to aim to search after the corresponding relation calculating of tangent value according to function of the angle between 45 °-90 ° to engrave).Otherwise, according to trigonometric function value, on figure, also can check in pairing angle value, the method for specifically looking into is summarized as follows:
On the orthodrome of the right-hand part of large semicircle instrument (2), definition according to trigonometric function, arbitrarily the sine value of acute angle equals on the circular arc ordinate of (corresponding to arbitrarily angled) and the ratio of this arc radius more arbitrarily, because this arc radius equals 100mm just, so, the Y value of this point dwindle 100 times be this point on the circular arc to the sine value of angle, and the ordinate value of this point can directly be read on the tangent line on more than half circular arc right side, (this point is made vertical line to tangent line from the circular arc, and the numerical value of intersection point point promptly equals the ordinate of this point on the circular arc).For example Sin20 °=0.342 (last position is an estimative figure), Sin34 °=0.559, as a same reason, the cosine value of certain angle equals one of percentage of the horizontal point coordinates value of certain point on the circular arc, (cosine value also can be tried to achieve by the sine value of the complementary angle at this angle), example: COs40 °=Sin50 °=0.766, Cos71 ° of 24 '=Sin18 ° 36 '=0.948, for the angle greater than 90 °, should turn to acute angle to the obtuse angle according to induced formulas, on figure, find again.
The angle of the number of degrees between 0-45 °, its tangent value can directly read on the tangent line of the right of large semicircle instrument (the angle index line that certain tangent value of putting pairing angle is this point on the circular arc of large semicircle instrument prolong after one of the percentage of the coordinate figure of intersection on the right the tangent line, for example, tg20 °=0.364 (last position is an estimative figure), when angle is between 45 °-90 °, can grow the outer rim of limit right-hand part on rectangle directly reads, as tg50 °=1.21 (last position is an estimative figure), (45 °+a)=(1+tga) calculate among the ÷ (1-tga) of also available formula tg.When asking greater than 90 ° tangent value, should turn to acute angle to the obtuse angle according to induced formulas and table look-up again and try to achieve, when asking the cotangent value at angle, can utilize (90 °-a) try to achieve of induced formulas ctga=tg.
Otherwise,, can obtain according to counter the pushing away of said method if the trigonometric function value of known certain angle is asked angle value.
GRAPHIC CALCULATION functional value, significant digits are three, can satisfy Preliminary design, and theory study sharpens understanding.
Utilize the millimeter scale value of right-hand part on scale value on the axis of large semicircle instrument (2) and the base can also diagram right angled triangle (diagram Pythagorean theorem: a
2+ b
2=c
2), on the axis of large semicircle instrument (2), intercept line segment with compasses (or ruler) and equal a right angle length of side (center of circle with the large semicircle instrument is an end points), another right angle length of side of intercepting on the base of large semicircle instrument (2), then the distance between two other end points of these two line segments is the length of hypotenuse; If ask the right angle length of side, can on the axis, the intercepting line segment length equal the known right angle length of side, be the center of circle with this end points again, with known hypotenuse length is radius, draw arc and hand over the right-hand part that is plotted in large semicircle instrument base, joint is the length of the unknown right-angle side of right angled triangle to the distance in the center of circle, when diagram, the length on three limits of right angled triangle can enlarge or dwindle identical multiple simultaneously.
Be provided with proportionally size in the inside of rectangle and can be divided into large scale graphical set (A, B, C, D, E, F) and small size graphical set (A ', B ', C ', D ', E ', F '), utilize this figure hole can draw various solid figures rapidly and accurately as (three, four, five, six) prism, pyramid, terrace with edge, cylinder, circular cone, round platform, spheroid, billiard table, spherical crown etc.
Also have in that rectangle is inner: 1, a plurality of small sircle holes (a, b, c, d, e, f, g, h, I, j, k, l, m n), is used for and regular polygon or rhombus (as shown in phantom in FIG.) are drawn in other each point combination; 2, tangent cutve hole (G), left hand edge is a hyperbola, right hand edge is a tangent cutve, can draw hyperbola and just (surplus) cut curve; 3, parabola hole (H), left-half is a square parabola, and right half part is a cubic parabola, and two kinds of parabolas can draw.4, hyperbola hole (I), hyperbola or conjugate hyperbolas can draw; 5, sine curve hole (J) can be used to draw two kinds of sine and cosine ripples, cosine wave anyway; 6, rectangular opening (K), rectangle, square, right-angled trapezium, isosceles trapezoid can be used to draw; 7, diamond hole (L) can be used to the picture computer flow chart; 8, elliptical aperture (F
1'), (F
2'), be used to make dissimilar ellipses.
Around parabola hole (H), rectangular opening (K), coordinate grid is arranged, can be used for fast drawing and sharpen understanding the analytic geometry content.
On the axis of three limits of the left side of rectangle and large semicircle instrument, be evenly equipped with aperture, be used for drawing fast various charts.With any aperture is the center of circle, is radius with this center of circle to the distance of another aperture, can draw the circle of various radiuses.
In the various holes of rectangle inside, wherein, the diameter of circular port (E, E ') is equal with the major axis of oval (F, F ') respectively.
Reverse side at transparent plastic sheet, several miniature roundlet projectioies (spherical crown shape) (diameter 1-2mm is advisable) are arranged, like this when being figure, plastic plate will leave paper (only having several small embossments to contact with paper) a little, both helped quick and precisely mapping, can solve behind the picture problem of band ink marks on paper again.
Claims (6)
1, a kind of calculation instrument of painting mainly is made of a transparent plastic base plate, and basic geometry hole (1) is arranged on the base plate, it is characterized in that:
A), it is the rectangle of two double-lengths of minor face that the middle part of base plate also has a long limit, a long limit of rectangle and the outer rim of two minor faces all have identical length tolerance scale, there is a greater part of round instrument (2) rectangle inside, the long limit of the base of large semicircle instrument (2) and the strip length scale of rectangle overlaps, the circular arc limit is tangential on other three limits of rectangle respectively, the circular arc limit inner edge of large semicircle instrument (2) has the angle index value, the part of outer rim has the radian scale value, the length scale value identical with the rectangle minor face arranged on the axis of large semicircle instrument (2), the small semicircle instrument (3) that one band angle index value is arranged in the large semicircle instrument (2), the center of circle of large semicircle instrument (2) and small semicircle instrument (3) overlaps, the axis is on same straight line, and there is graphometer hole (4) the angle index value inboard of small semicircle instrument (3);
B), there is five equilibrium circular hole (5) left side of large semicircle instrument (2), the folded acute angle in the line in the center of circle of the center of each circular hole and large semicircle instrument (2) and the base of large semicircle instrument (2) equals the number of degrees with the folded central angle of every equal portions circular arc of this corresponding Equal round in hole;
C), rectangle minor face inner edge has the angle index line, every graduation mark and large semicircle instrument (2), small semicircle instrument (3) are gone up the graduation mark that equates the number of degrees and are located along the same line;
D), basic geometry hole (1) proportionally size can be divided into large scale graphical set (A, B, C, D, E, F) and small size graphical set (A ', B ', C ', D ', E ', F ').
2, the calculation instrument of painting according to claim 1, it is characterized in that small sircle hole is arranged on the transparent plastic sheet (a, b, c, d, e, f, g, h, I, j, k, l, m, n) several holes in.
3, the calculation instrument of painting according to claim 1 is characterized in that having on the transparent plastic sheet tan hole (G), parabola hole (H), hyperbola hole (I), SIN function hole (J), rectangular opening (K), diamond hole (L); The left hand edge in tan hole (G) is a hyperbola, and right hand edge is a tan.
4, the calculation instrument of painting according to claim 1, it is characterized in that transparent plastic sheet around the length scale arranged.
5, the calculation instrument of painting according to claim 1, the edge that it is characterized in that transparent plastic sheet is a waveform.
6, the calculation instrument of painting according to claim 1 is characterized in that being evenly equipped with aperture on the graduation mark of the rectangle left side on the transparent plastic sheet.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 99253895 CN2399227Y (en) | 1999-11-11 | 1999-11-11 | Drawing/calculating instrument |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 99253895 CN2399227Y (en) | 1999-11-11 | 1999-11-11 | Drawing/calculating instrument |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN2399227Y true CN2399227Y (en) | 2000-10-04 |
Family
ID=34037691
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN 99253895 Expired - Fee Related CN2399227Y (en) | 1999-11-11 | 1999-11-11 | Drawing/calculating instrument |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN2399227Y (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105856922A (en) * | 2015-08-24 | 2016-08-17 | 周德明 | Drawing device for function graphs and use method thereof |
| CN115008930A (en) * | 2022-06-28 | 2022-09-06 | 中国地质大学（北京） | Finger ring and bracelet hand-painted design template ruler |
-
1999
- 1999-11-11 CN CN 99253895 patent/CN2399227Y/en not_active Expired - Fee Related
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105856922A (en) * | 2015-08-24 | 2016-08-17 | 周德明 | Drawing device for function graphs and use method thereof |
| CN115008930A (en) * | 2022-06-28 | 2022-09-06 | 中国地质大学（北京） | Finger ring and bracelet hand-painted design template ruler |
| CN115008930B (en) * | 2022-06-28 | 2023-06-02 | 中国地质大学（北京） | Finger ring and bracelet hand-painting design template ruler |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| C19 | Lapse of patent right due to non-payment of the annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |