CN102788541A

CN102788541A - Protractor

Info

Publication number: CN102788541A
Application number: CN2012100116723A
Authority: CN
Inventors: 周华
Original assignee: Individual
Current assignee: Individual
Priority date: 2012-01-16
Filing date: 2012-01-16
Publication date: 2012-11-21

Abstract

The invention provides a protractor (shown as figure) by utilizing an established mathematical model with one-to-one corresponding two sides and two inscribed circle radiuses and two central angles of two inner angles and inscribed circles of a triangle. The protractor is used for measuring angles (for measuring the sizes of the angles as well as the lengths of the sides). A tool is supplied for learning, living and researching; a mode is also supplied for visual field expansion and manual exploratory development; a use method for the protractor is simple; and by only aligning a point B or C at a vertex and utilizing the sliding of a slide block to cause the two sides of the protractor to be superposed with the two sides of an angle, the size of the angle is read from the angle degree indicated on the slide block and the lengths of the two sides of the angle can be directly read on the two sides of the protractor.

Description

New drawing instrument with the functions of compasses, protractor and set square

Make a=collude=3 long measures, b=thigh=4 long measure, the c=string=?

Supposing a horizontal fixed, is radius with the length of b, is that circle is drawn in the center of circle around the node C with a; Length with a+b is radius again, is that circle is drawn in the center of circle with the node B of c and a, and two circles are inscribed within the A` point, connects two center of circle B and C and prolongation must be passed through point of contact A`, and this line must be axis of symmetry, and according to symmetry, we study the first half (like Fig. 1) of axis of symmetry.At this moment, when a and b angle are 180 °, c=string=a+b=3+4=7 long measure; C=string=5 long measures when a and b angle are 90 °, the famous burst string theorem (like Fig. 1) of colluding that Here it is; String=b-a=4-3=1 long measure of c=when a and b angle are 0 °; As can beappreciated from fig. 1, along with the variation of a and b angle, the length of c string is also along with variation, and when 90 °＜a and b angle＜180 °, 5＜c string＜7 long measure; When 0 °＜a and b angle＜90 °, 1＜c string＜5 long measure.Be the angle of a and b when in 180 °, changing, the length of c string changes in 1-7 long measure.See conversely; To on 1-7 the long measure of c string more arbitrarily; Constantly determined the length of string own; And decision is the central angle of the drawn circle of radius with the length of b, and determined that the length with a+b is the size of the central angle of the drawn circle of radius, and two the interior angle ∠ ACB of these two central angles and △ ABC and ∠ ABC are corresponding one by one.In other words, be exactly on the C string more arbitrarily, both determined that a+b was the length that radius winds up, also determined the size of another central angle that central angle that a and b are folded and a and c are folded.See again when a level is motionless, when the horizontal A of b overlaps with the A` point, rotation counterclockwise, central angle ∠ ACB is then from 180 ° → 0 °, then 0 ° → 180 ° of another central angle ∠ ABC, but these two central angles not complementary (0 ° with 180 ° except).

We are divided into 180 ° five equilibrium central angle (because angle of circumference is 360 °) to the semi arch that with a+b is long measure, are 0 ° with the starting point of A and A`, and then with b being all has not isometric section on the drawn arc of radius and 180 the central angle radius a+b.In like manner, being that the drawn semicircle of length radius also is divided into 180 ° five equilibrium central angle with b, the point that overlaps with A` at A; Then central angle ∠ ACB=180 °, when ∠ ACB then from 180 ° → 0 °, 180 Along ents also have 180 corresponding sections that do not wait on the circular arc on string a+b; Therefore, each point on the a+b string has triple identity, and the one, the length of c string itself; The 2nd, the size of central angle ∠ ABC, the 3rd, the size of central angle ∠ ACB.If c＞7 long measure promptly has a+b=3+4=7＜c, both sides and then can not constitute triangle less than the 3rd limit, promptly there is b-a=1＞c or c＜1, the difference on both sides can not constitute triangle greater than the 3rd limit.

Certainly, like a ≠ collude b ≠ thigh, but positive count; (for convenient understand for the purpose of, always be replaced into a limit to minor face), above our theory of inquiring into always set up, therefore; We have known a limit, and the angle that b limit and a and b are folded, c limit have just been determined by a certain section (long measure) on this radius of a+b; We can directly read out, in other words, and cosine law c ²=a ²+ b ²-2abCos ∠ C just can measure with a ruler, and now, we in the same way; We can design a measuring instrument, i.e. both energy point of view of this measuring instrument can measure the length (when not required) of two contained sides again simultaneously; We know the ruler amount of being length, and we are the narrow groove that cuts out a band circular hole (doing using of fixed point rotation) in the middle of the ruler, and this ruler can be drawn four scale marks; Two outer most edge scale length scales of ruler, as make 1 long measure=3cm, then a=9cm; B=12cm is on one side cut out the number of degrees that two narrow groove inner edges mark central angle ∠ ABC, the number of degrees (like Fig. 2) the C chi of another side standard ∠ ACB.Design a slide block again, this slide block band circular hole, this slide block are wanted and can be rotated around a certain fixed point, again can be along narrow groove linear slide.Therefore, we cut into plane (like Fig. 4) to the right cylinder two symmetrical limits of gong nail, and this moment, the gong nail both can freely rotate in circular opening; And can slide two tangent planes along narrow groove; And this gong nail slide block can also as pointer point out on the chi face scale (like Fig. 5) (enlarged drawing) (Fig. 6), for imagination and the manipulative ability of developing the user, we can also design straight fillet chi; Beat some holes in the above, let the user be unified into triangle or polygon (like Fig. 7) with drawing pin.We are in the same place the A chi among Fig. 2, B chi and C chi couplet now, have just constituted New drawing instrument with the functions of compasses, protractor and set square shown in Figure 5.Its usage: with the summit of B point alignment angle; The a limit overlaps with the one side at angle, lets the b limit rotate around the C point, and slide block is slided along the c groove; The c limit is overlapped with the another side at angle; Then can show length on one side on a chi, can show the length of another side on the c chi, and c chi top shoe can indicate the number of degrees of the upper left limit of ruler inner edge ∠ ABC; If with C point (on a chi) alignment angle summit, one side the overlapping of a limit and angle, the b limit overlaps with the another side at angle; Then the length on both sides, angle shows on a chi and b chi, is the number of degrees (Fig. 5) of ∠ ACB and can indicate c ruler inner edge lower right scale at c chi top shoe, and we can find out from Fig. 2 and Fig. 5: the even scale of the non-uniform scale of angle and length has bigger difference; During especially in ∠ ABC＜60 ° (∠ ACB＞120 ° time), the scale of angle is closeer, and error is bigger; In order to change this situation, we can be adjusted into Fig. 6 situation to New drawing instrument with the functions of compasses, protractor and set square, and A point, B point can only be rotated; And the b chi can only slide along the b chi at the C point; But the b chi is in the angle of two inner edge left side marking ∠ ABC, but the angle of the right marking ∠ ACB of inner edge, and this is an isosceles triangle.The ∠ ABC precision of measuring this moment high (but angle can not be too big)

In a word; We are with leg-of-mutton both sides and two inscribe radius of a circles, and the central angle of leg-of-mutton two interior angles and two incircles is set up relation one to one, utilizes this mathematical model to study the dynamic relationship between triangle edges, the angle; And then draw general conclusion; Utilize the conclusion of this quantitative model again, design concrete New drawing instrument with the functions of compasses, protractor and set square, and this New drawing instrument with the functions of compasses, protractor and set square can be widely used in measurement, check and research in our daily study, work, life.

Claims

1. utilize Pythagorean theorem set up corresponding with two inscribed circle radius respectively and leg-of-mutton two interior angles in leg-of-mutton both sides respectively with the central angle mathematical relation one to one of two circles, promptly get in touch into the dynamic mathematical model of integral body to triangle and two incircles.

2. be the central angle angle that the variation of triangle interior angle is gone up expression at a line segment (being a certain radius of circle), this method is directly perceived, image, simple, has fully reflected the overall picture that triangle changes, and sums up regularity (the mark rule of angle on radius).

3. the rule of utilizing above-mentioned mathematical model to draw is designed New drawing instrument with the functions of compasses, protractor and set square.

4. cut into the narrow groove of being with circular hole to ruler in the New drawing instrument with the functions of compasses, protractor and set square, can in narrow groove, slide along groove, can rotate in circular hole place fixed point again, the both sides of narrow groove are used for the scale of scale angle, and the angle index of narrow groove two inner edges is corresponding one by one with ruler outer rim length scale.

5. slide block is designed to nut shape; Plane cutting is made on the cylindrical both sides of punching in the centre, makes the narrow place of slide block only need rotate the direction of a sliding block at needs fixed point place along sliding in the narrow groove of chi; Right cylinder can only in circular hole, be rotated; Its hollow position is made fixed point usefulness, makes perpendicular line at the slide block center as pointer, the angle and the length of indicating narrow groove place.

6. on narrow ruler, beat some holes, ruler connection in twos, can connect easy triangle alive with screw, polygons such as quadrilateral supply the usefulness of study, research.

7. in computer, internet and other commodity design, use this model theory or New drawing instrument with the functions of compasses, protractor and set square, all should obtain the written agreement permission.