CN100393536C

CN100393536C - Trisectrix of angle drawing instrument

Info

Publication number: CN100393536C
Application number: CNB2006100143227A
Authority: CN
Inventors: 赵建科
Original assignee: Individual
Current assignee: Individual
Priority date: 2006-06-13
Filing date: 2006-06-13
Publication date: 2008-06-11
Anticipated expiration: 2026-06-13
Also published as: CN1861420A

Abstract

The present invention relates to a trisection angle drawing instrument. The present invention is characterized in that the trisection angle drawing instrument is composed of a T-square, an L-square and an auxiliary straight rule, wherein both ends of the head of the T-square are respectively provided with a cardinal axis, and a T-square body working side of the T-square and a midpoint of the axis center distance of the two cardinal axes are arranged on the same line; the upper end of a vertical side of the L-square is hinged on the cardinal axis on one end of the head of the T-square, and the vertical distance from the axis center of the cardinal axis on the vertical side of the L-square to the bottom edge of a horizontal side of the L-square is equal to one half of the axis center distance of the two cardinal axes of the T-square; the auxiliary straight rule is hinged on the other cardinal axis on the head of the T-square, and the working side of the auxiliary straight rule and the axis center of the cardinal axis are arranged on the same line. The present invention has the advantages that through the ingenious combination of the T-square, the straight rule and the L-square, a drawing instrument for the accurate and quick trisection of arbitrary angles without calculation is provided, and the present invention has the advantages of simple structure, easy operation and convenience for plane geometry drawing.

Description

Trisectrix of angle drawing instrument

Technical field

The present invention relates to a kind of drawing instrument, relate in particular to a kind of Trisectrix of angle drawing instrument.

Background technology

In plane geometry was drawn, trisection can be carried out with ruler in some special angle, as 90 ° of angles and 45.Usually, the ruler trisection can be used in the angle of 180/2n (n is a positive integer), but utilizing ruler and any angle of compasses construction trisection is the problem that mathematics circle is inquired into great concentration, this goes through more than 2000 year pendent always knotty problem, through countless mathematicians repeatedly feasibility study drawn the conclusion of generally acknowledging up to 1895, promptly any angle of trisection belongs to " construction with ruler and compasses can not problem ".There is not the exploration of the knotty problem of solution to come to an end thereby make more than 2,000 year.In plane geometry is drawn, generally adopt any angle of graphometer trisection at present, calculate but at first will pass through, and be subjected to graphometer scale accuracy limitations, inaccurate.

Summary of the invention

Main purpose of the present invention be at the problems referred to above provide a kind of can be accurately in plane geometry is drawn, the angle of any trisection of an angle of trisection promptly plotter.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of Trisectrix of angle drawing instrument is characterized in that being made up of T-square, square and auxiliary ruler, and the chi head two ends of T-square are respectively equipped with a hinge, the blade working edge of T-square and the distance of shaft centers of two hinges from mid point be positioned at same straight line; Square vertical edge top is articulated on the hinge of the first end of T-square chi, on the square vertical edge from the axle center of hinge to the outer peripheral vertical range of square horizontal sides equal T-square two hinge distances of shaft centers from 1/2nd; Auxiliary ruler is articulated on another hinge of chi head, and its working edge and hinge axle center are positioned at same straight line.

Described T-square chi head inward flange equates with the distance of hinge axle center, square vertical edge top to square horizontal sides outward flange vertical line with the distance and the square vertical edge inward flange of two hinge axial connecting lines.

Described square can be positive and negative L shaped or inverted T-shaped.

The invention has the beneficial effects as follows: by ingenious combination with T-square, ruler and square, provide a kind ofly need not calculate, the accurate plotter at any angle of trisection fast, simple in structure, processing ease is for the plane geometry drawing brings convenience.

Description of drawings

Fig. 1 is a structural representation of the present invention;

Fig. 2 is a difformity square structural representation;

Fig. 3 is an operation chart of the present invention;

Fig. 4 is the equivalent schematic diagram of Fig. 3.

Among the figure: 1 auxiliary ruler, 1-1 ruler working edge, 2-1 hinge, the 2-2 hinge, 3 T-squares, 3-1 chi head, 3-2 hinge distance of shaft centers is from (axial connecting line), and the 3-3 distance of shaft centers is from mid point, the 3-4 blade, 3-5 blade working edge, 3-6 chi head inward flange, 4 squares, the 4-1 axle center is to horizontal sides outward flange vertical range, 4-2 square horizontal sides, 4-3 horizontal sides outward flange, 4-4 square vertical edge, 4-5 vertical edge inward flange.

Below in conjunction with drawings and Examples to the detailed description of the invention.

The specific embodiment

As shown in Figure 1, it is a kind of Trisectrix of angle drawing instrument, it is characterized in that forming by T-square 3, square 4 and auxiliary ruler 1, the chi head 3-1 two ends of T-square 3 are respectively equipped with a hinge 2-1 and a 2-2, and the distance of shaft centers of the blade working edge 3-5 of T-square 3 and two hinge 2-1 and 2-2 is positioned at same straight line from the mid point 3-3 of 3-2; Square vertical edge 4-4 top is articulated on the hinge 2-2 of T-square chi head 3-1 one end, and the vertical range 4-1 that square vertical edge 4-4 goes up from the axle center of hinge 2-2 to square horizontal sides outward flange 4-3 equals the distance of shaft centers of 3 liang of hinge 2-1 of T-square and 2-2 from 1/2nd of 3-2; Auxiliary ruler 1 is articulated on another hinge 2-1 of chi head, and its working edge 1-1 and hinge 2-1 axle center are positioned at same straight line.Described T-square 3 chi head inward flange 3-6 equate with the distance of hinge 2-2 axle center, square vertical edge top to square horizontal sides outward flange 4-3 vertical line with distance and the square 4 vertical edge inward flange 4-5 of two hinge axial connecting line 3-2.Described square 4 can be positive and negative L shaped or inverted T-shaped.Adopted anti-L shaped in this example.(a) and (b) show the square 4 of the just L shaped or inverted T-shaped of employing respectively among Fig. 2.T-square 3, square 4 and auxiliary ruler 1 adopt the material such as the making such as plastic plate, corrosion resistant plate of same thickness in actual fabrication.

Using method and principle: △

As shown in Figure 3, trisection one any angle ∠ AOB at first, places the O left side, ∠ AOB summit with the blade 3-4 of the T-square 3 of Trisectrix of angle drawing instrument, will assist the working edge 1-1 of ruler 1 to aim at the OA limit then, and move down (shown in arrow among Fig. 3) along the OA limit; Square horizontal sides outward flange 4-3 is aimed at the OB limit, and move right along the OB limit (shown in arrow among Fig. 3), because auxiliary ruler 1 is articulated on the hinge 2-1 of T-square chi head 3-1, square vertical edge 4-4 top is articulated on the T-square chi head hinge 2-2, therefore the Cheng Zhongneng of moving past on the throne does the adaptability rotation, when the blade working edge 3-5 that moves to T-square 3 overlaps with the summit O of ∠ AOB, at this moment, draw to connect the straight line that O orders (also promptly connecting the straight line of ordering apart from mid point 3-3 and O in the axle center) L1 along blade working edge 3-5, then, determine chi head inward flange 3-6 and vertical edge inward flange 4-5 intersection point 3-7, and draw to connect the straight line L2 that intersection point 3-7 and O are ordered, promptly finish the trisection of ∠ AOB.

Fig. 4 is the equivalent schematic diagram of Fig. 3, wherein F represents hinge 2-1 axle center, D represents hinge 2-2 axle center, E is the mid point 3-3 of the distance of shaft centers of two hinge 2-1 and 2-2 from 3-2, the extended line of crossing EO is the blade working edge 3-5 of T-square 3, DC is to the vertical range 4-1 of square horizontal sides outward flange 4-3 from the axle center of hinge 2-2, HC is square horizontal sides outward flange 4-3, F ' D ' is T-square chi head inward flange 3-6, E ' is D ' F ' and OE intersection point, D ' C ' is square 4 vertical edge inward flange 4-5, and D ' is the intersection point 3-7 of T-square chi head inward flange 3-6 and square 4 vertical edge inward flange 4-5.At first proof utilizes T-square 3 blade working edge 3-5 (OE) and hinge 2-2 axle center D to determine the angular bisector of trisection of an angle ∠ AOB: connect OD, ∵ E is the FD mid point, DC=DE, OD is a common edge, DC ⊥ OC, OE ⊥ FD ∴ right angled triangle DEO ≌ right angled triangle DCO, ∴ ∠ EOD=∠ COD (being ∠ BOD); ∵ FE=DE again, OE is a common edge, OE ⊥ FD, ∴ right angled triangle DEO ≌ right angled triangle FEO, ∴ ∠ DOE=∠ FOE (being ∠ AOE); ∴ ∠ FOE=∠ EOD=∠ DOC, that is: ∠ AOE=∠ EOD=∠ DOB, ∠ AOB trisection is set up.In the above-mentioned proof, L2 draws by connecting O and hinge 2-2 axle center D, during practical operation, because of chi has certain width, so the point of determining is D ', L2 is drawn by OD ', D ' is the intersection point 3-7 of chi head inward flange 3-6 (F ' D ') and vertical edge inward flange 4-5 (D ' C '), ∵ chi head inward flange 3-6 equates with the distance of hinge 2-2 axle center, square vertical edge top to square horizontal sides outward flange 4-3 vertical line with distance and the square 4 vertical edge inward flange 4-5 of two hinge axial connecting line 3-2, ∵ OE ⊥ FD again, OC ⊥ DC, ∴ E ' E=C ' C, ∵ OE=OC again, ∴ OE '=OC ', OE ' they are common edge, ∴ right angled triangle D ' OE ' ≌ right angled triangle D ' OC ', ∠ E ' OD '=∠ C ' OD ', i.e. ∠ EOD '=∠ COD ', ∴ OD ' and OD (L2) are on same straight line.Utilize accurately trisection of an angle ∠ AOB of T-square 3 blade working edge 3-5 (OE) and intersection point 3-7 (D ').

Claims

1. Trisectrix of angle drawing instrument is characterized in that being made up of T-square, square and auxiliary ruler, and the chi head two ends of T-square are respectively equipped with a hinge, the blade working edge of T-square and the distance of shaft centers of two hinges from mid point be positioned at same straight line; Square vertical edge top is articulated on the hinge of the first end of T-square chi, on the square vertical edge from the axle center of hinge to the outer peripheral vertical range of square horizontal sides equal T-square two hinge distances of shaft centers from 1/2nd; Auxiliary ruler is articulated on another hinge of chi head, and its working edge and hinge axle center are positioned at same straight line.

2. a kind of Trisectrix of angle drawing instrument according to claim 1 is characterized in that described T-square chi head inward flange equates with the distance of hinge axle center, square vertical edge top to square horizontal sides outward flange vertical line with the distance and the square vertical edge inward flange of two hinge axial connecting lines.

3. a kind of Trisectrix of angle drawing instrument according to claim 1 and 2 is characterized in that described square can be positive and negative L shaped or inverted T-shaped.