CN105291659A - Method for equally dividing circumference - Google Patents

Abstract

The invention provides a method for equally dividing a circumference. A new tool deformed and improved on the basis of an existing common drawing tool is utilized, the circumference with the radius of r/n is rolled on the perimeter of a circumference with the known radius of r by n circles, a point is marked every time the circumference is rolled by one circle, and therefore the equal division points of the known circumference are found, and the known circumference is equally divided into any n parts, wherein n is a natural number. The mathematical problem of equally dividing the known circumference into any n parts is solved, and errors are avoided in theory. Meanwhile, the problems that a known arc and a known angle are equally divided into any n parts, a n-regular polygon is drawn in a known round, an externally tangent n-regular polygon is drawn in the known round, the position of phi is drawn on a number axis, and the round with the know perimeter is drawn out are solved. The angle measurement mode is changed, the theoretic 1/n degree can be drawn out, n can be any natural number, and the process cannot be achieved by a protractor.

Description

A kind of method of circumference in equal parts

Technical field

The invention belongs to drawing technique field, relate to a kind of drawing practice known circumference being carried out to any n (natural number) decile, a kind of specifically method of circumference in equal parts.

Background technology

At present, in fields such as scientific research, teaching, mapping, mechanical engineerings, the n decile to a known circular often can be related to, or the n decile to a known angle, arc, connect positive n limit shape or circumscribed n positive n limit shape etc. in doing in a known circular.These problems are (containing Software tool) in existing drawing tool, any single instrument or combination tool, all can not realize arbitrary n decile theoretically, only has part to realize, e.g., when n=2n, 3,4, the minorities such as 5 can realize.

N(natural number to circumference) decile in theory also do not have a kind of theoretical or real operation can by a known circular n(natural number) decile; Equally, do not have a kind of theoretical or real operation can by a known circular arc n(natural number yet) decile; Equally, do not have a kind of theoretical or real operation can by a known angle n(natural number yet) decile.

Summary of the invention

Object of the present invention is just to provide a kind of method of circumference in equal parts, utilize the new instrument carrying out being out of shape and improving on existing common drawing tool basis, realize carrying out any n(natural number to known circumference) decile, complete world's drawing and historically once to change.

The technical scheme that the present invention is adopted to achieve these goals is: a kind of method of circumference in equal parts, comprises the steps:

Step 1, finds out the center of circle of known round P;

Step 2, determines that a radius is the roundlet of r, is defined as the dynamic circle of facade;

Step 3, with the center of circle of known round P for the center of circle, is that radius is a round P ' with R, and the radius R of circle P ' equals facade and moves the n of radius of a circle r doubly, and described n is random natural number;

Step 4, rolls the circumference of dynamic for facade circle along circle P ', and the dynamic circle of facade, often from circling, circumferentially does a gauge point namely at circle P ', until the dynamic circle of facade to roll a circle along the circumference of circle P ';

Step 5, by the line of the center of circle with circle P ' n gauge point circumferentially, divide into n part by known round P, have found the n Along ent of known round P circumference simultaneously.

The invention solves the sciences problems of any for known circle n decile, achieve theoretic error free; Also naturally solve known arc and any n decile of known angle simultaneously, positive n limit shape is done in known circular, circumscribed positive n limit shape is done in known circular, number axis draws the position of π, draw the problems such as the circle of known circumferential length, the present invention also changes the pattern of angular surveying, can draw theoretic 1/n degree, n can be random natural number, and this cannot realize with protractor.

Accompanying drawing explanation

Fig. 1 is a kind of schematic diagram realizing used tool of the present invention;

Fig. 2 is the schematic diagram that Fig. 1 neutral surface moves circle and index device;

Fig. 3 is a kind of enforcement schematic diagram of the present invention;

In figure 1, ruler; 2, movable leg; 3, the dynamic circle of facade; 4, index device; 5, cylinder; 6, spiral shell clasp; 7, pin is pushed up; 8, vertical circle frame; 9, vertical circular shaft; 10, ridge is convex; 11, penholder; 12, pen; 13, resetting means; 14, P is justified; 15, P ' is justified.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention will be further described:

Principle analysis of the present invention:

Girth due to a known circular equal 2 π r(wherein r be the radius of known circular); To the n decile of known circular, namely to the n decile of the girth (2 π r) of known circular, namely the arc of each n decile equals 2 π r/n; We regard 2 π r/n as the product of 2 π and r/n as, and the girth according to circle equals 2 π r, then: the circle that the girth (2 π r) of known circular is made up of the circumference that n take r/n as radius, i.e. and n × { 2 π (r/n) }=2 π r.Can be regarded as: n is the circle of radius with r/n, the girth along known circular rolls one week, and the track that known circle is formed, still can be regarded as: one take r/n as the track of circle along the girth rolling n week formation of known circular of radius;

The arc length at above-mentioned adjacent point of contact is 2 π r/n, suppose separately to have one to take r/n as the roundlet of radius, can roll along the girth of known circular, namely roundlet often rolls one week starting point circumferentially in known circular: 2 π (r/n), is just in time the great circle arc length 2 π r/n at two adjacent point of contacts.So, this roundlet is after great circle rolling n week, and the position of the starting point that known circular stays is just in time the point of the n decile of known circular.

The instrument that the inventive method is used:

Facade moves round rule, and as shown in Figure 1, comprise ruler 1, movable leg 2, the dynamic circle 3 of facade, index device 4, ruler 1 is provided with scale, and centre is processed with groove, and movable leg 2 is arranged in the groove of ruler 1, and facade moves one end that circle 3 and index device 4 are arranged at ruler 1; Described movable leg 2, be made up of cylinder 5, spiral shell clasp 6 and top pin 7, cylinder 5 outer setting has screw thread, and it is outside that spiral shell clasp 6 is socketed in cylinder 5, and cylinder 5 lower end is fixed with top pin 7, and top pin 7 is for determining that facade moves the center of circle of round programming bowlder; The dynamic circle 3 of facade also comprises vertical circle frame 8, vertical circular shaft 9, and vertical circle frame 8 top is fixed on ruler 1, and vertical circular shaft 9 is fixed on the bottom of vertical circle frame 8, and the dynamic circle of facade 3 centers are through on vertical circular shaft 9, and the dynamic circle of facade 3 outer ledges are also provided with a ridge convex 10; Index device 4 comprises penholder 11, pen 12 and resetting means 13, penholder 11 one end is fixed on ruler 1, other end fixating repositor 13, and resetting means 13 adopts spring design, resetting means 13 is connected and fixed pen 12, and the pen head part of pen 12 and facade move the outer close contact of circle 3.

Embodiments of the invention,

As shown in Figure 3, step comprises:

Step 1, finds out the center of circle of known round P14;

The center of circle of known round P can be found with common construction with ruler and compasses;

Step 2, determines that a radius is the roundlet of r, is defined as the dynamic circle 3 of facade;

The described facade vertical circle moved in round rule moves the roundlet that face 3 is radii fixus r;

Step 3, with the center of circle of known round P14 for the center of circle, is that radius is a round P ' 15 with R, and circle P ' 15 radius R equals facade and moves the n of circle 3 radius r doubly, and described n is random natural number;

Adjustment facade moves the position of movable leg 2 on ruler 1 in groove in round rule, makes movable leg 2 be n times that founds circle dynamic face 3 radius r to the distance in vertical round dynamic face 3;

Step 4, the circumference of dynamic for facade circle 3 along circle P ' 15 is rolled, the dynamic circle 3 of facade often from circling, under the effect of ridge convex 10 and resetting means 13, pen 12 can circumferentially do a gauge point at circle P ', until the dynamic circle 3 of facade to roll a complete circle along the circumference of circle P ';

Be specially and the top pin 7 of movable leg 2 is fixed on the center of circle of known circumference, rotate ruler 1, the dynamic circle 3 of facade rolls in the plane, the round P ' 15 that a radius is the radius of n times of r drawn by 12, the pen simultaneously moving circle 3 close contacts with facade, the dynamic circle 3 of facade is often from circling simultaneously, ridge convex 10 contacts once with pen 12, due to the effect of resetting means 13, pen 12 can make a graticule on circle P ' 15, a complete circle until the circumference of facade dynamic circle 3 edge circle P ' rolls, circle P ' 15 has circumferentially also had n gauge point simultaneously;

Step 5, by the line of n gauge point on the center of circle and circle P ' 15, can find the n Along ent of known round P14; Namely have found any Along ent of known circumference, achieve circumference in equal parts.

The invention solves the sciences problems of any for known circumference n decile, achieve theoretic error free; Also naturally solve known arc and any n decile of known angle simultaneously, positive n limit shape is done in known circular, circumscribed positive n limit shape is done in known circular, number axis draws the position of π, draw the problems such as the circle of known circumferential length, the present invention also changes the pattern of angular surveying, can draw theoretic 1/n degree, n can be random natural number, and this cannot realize with protractor.

The invention provides a kind of theoretic drawing technique and realize the process route of this technology, method and path, all meet this technology any making and reach the method realizing this technical purpose and be of the present invention original; The present invention relates to a class (multiple) multifunctional drawing technology and the instrument realizing this technology, is the multifunctional application science toolses such as a class (multiple) collection drawing, measurement, drawing, calculating, principle application, scientific research, teaching, test.It changes current drawing, the idea of graphics field instrument, thinking and present situation, utilize carry out being out of shape on existing common drawing tool basis, improvement and bring new ideas, change the plane thoughtcast of existing any instrument, being the innovative tool that rule is drawn, is the revolution in drawing, drawing world history; Any component combination application of the present invention all should belong to protection scope of the present invention; The present invention includes and imagine in the technology of the application (as: software, films and television programs, computer, video, animation etc.) of any media with the realization of core technology of the present invention and principle, and according to the application software etc. that its central principle is worked out.

Claims (1)

1. a method for circumference in equal parts, is characterized in that: comprise the steps:

Step 1, finds out the center of circle of known round P;

Step 2, determines that a radius is the roundlet of r, is defined as the dynamic circle of facade;

Step 3, with the center of circle of known round P for the center of circle, is that radius is a round P ' with R, and the radius R of circle P ' equals facade and moves the n of radius of a circle r doubly, and described n is random natural number;

Step 4, rolls the circumference of dynamic for facade circle along circle P ', and the dynamic circle of facade, often from circling, circumferentially does a gauge point namely at circle P ', until the dynamic circle of facade to roll a complete circle along the circumference of circle P ';

Step 5, by the line of the center of circle with circle P ' n gauge point circumferentially, divide into n part by known round P, have found the n Along ent of known round P circumference simultaneously.