JP6802406B1 - Angle N equal division drawing method and angle N equal division - Google Patents
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Abstract
【課題】作図工程がより簡略化でき、角の３以上のＮ等分にも対応できる角のＮ等分作図方法及び角のＮ等分器を提供する。【解決手段】原点（Ｏａ）を通る第１線（Ｌａ）及び第２線（Ｌｂ）によって規定される角（θ）を、１及び２を除く自然数（Ｎ）でＮ等分する角のＮ等分方法であって、基準円（１１）を引く基準円作図工程と、第２の基準円（１３）の円弧を引く第２の基準円作図工程と、第Ｎ原点（Ｏｎ）を定めるように印をつける第Ｎ原点決定工程とを含み、一方の２分角線（１４）を引く一方の２分角線作図工程と、他方の２分角線（１５）を引く他方の２分角線作図工程とのうちの少なくともいずれかの工程を含み、一方のＮ分角線（１６）を引く一方のＮ分角線作図工程と、他方のＮ分角線（１７）を引く他方のＮ分角線作図工程とのうちの少なくともいずれかの工程を含むことを特徴とする。【選択図】図４PROBLEM TO BE SOLVED: To provide an N equal division method for an angle and an N equal division device for an angle, which can further simplify the drawing process and can handle N equal divisions of three or more angles. SOLUTION: An angle (θ) defined by a first line (La) and a second line (Lb) passing through an origin (Oa) is divided into N equal parts by a natural number (N) excluding 1 and 2. An evenly bisector method to determine a reference circle drawing process that draws a reference circle (11), a second reference circle drawing process that draws an arc of a second reference circle (13), and an Nth origin (On). Including the Nth origin determination step of marking, one bisector drawing step of drawing one bisector (14) and the other bisector of drawing the other bisector (15). Including at least one of the line drawing steps, one N-angle line drawing step of drawing one N-angle line (16) and the other N drawing of the other N-angle line (17). It is characterized by including at least one of the angle bisector drawing steps. [Selection diagram] Fig. 4
Description
この発明は、原点を通る第１線の線分及び第２線の線分によって規定される角（θ）を、１及び２を除く自然数（Ｎ）でＮ等分する角のＮ等分作図方法及び角のＮ等分器に関する。 In the present invention, the angle (θ) defined by the line segment of the first line and the line segment of the second line passing through the origin is divided into N equal parts by a natural number (N) excluding 1 and 2. Regarding the method and the N equalizer of the corner.
従来の角のＮ等分器としては、角の３等分作図補助器であって、任意角の３等分作図方法の、習得のため、容易に３等分の作図を行う際の補助となる器具を目的とするもので、ノートなどの用紙に任意角と４等分線と中心角が直角となる直線の一辺を書き入れた図面の上に、発案した３等分作図法の法則をつかって３等分線の印を書き入れられる基板１を置き指示針などを、操作することによって、任意角の４分の１である４等分線に、１２分の１の角度を加えることにより３等分線が引ける印を書き入れられる（特許文献１参照）構成のものが提案されている。なお、この従来の角の３等分作図補助器は、作図されたものを書き写すためのものであり、それ自体で、任意角を３等分するものではない。 The conventional N-equal division device for angles is an auxiliary tool for drawing three equal parts at an arbitrary angle, and it is an aid for easily drawing three equal parts for learning the method of drawing three equal parts at an arbitrary angle. The purpose is to use the law of the trisection drawing method that was devised on a drawing in which one side of a straight line with an arbitrary angle, a quadrant line, and a central angle is written on a sheet of paper such as a notebook. By placing the substrate 1 on which the mark of the trisection line can be written and operating the indicator needle, etc., the angle of 1/12 is added to the quadrant line, which is a quarter of the arbitrary angle. A structure has been proposed in which an equidistant line can be drawn (see Patent Document 1). It should be noted that this conventional angle trisection assisting device is for copying what has been drawn, and does not itself divide an arbitrary angle into three equal parts.
角のＮ等分作図方法及び角のＮ等分器に関して解決しようとする問題点は、前記従来の角の３等分作図補助器で書き写される任意角の３等分作図方法では、その手順（工程）が複雑であり、また、その角の３等分作図補助器自体で、任意角の３等分が作図されるものでないと共に、あくまで３等分のみであって、角の３以上のＮ等分に関するものでないことにある。 The problem to be solved with respect to the angle N equal division method and the angle N equal division device is that in the arbitrary angle trisection drawing method copied by the conventional angle trisection auxiliary device. The procedure (process) is complicated, and the angle trisection assisting device itself does not draw any angle trisection, and it is only trisection, and the angle is 3 or more. It is not related to the N equal division of.
そこで本発明の目的は、作図工程がより簡略化でき、角の３以上のＮ等分にも対応できる角のＮ等分作図方法及び角のＮ等分器を提供することにある。 Therefore, an object of the present invention is to provide an N-equal drawing method for angles and an N-equalizer for angles, which can further simplify the drawing process and can handle N equal divisions of three or more angles.
本発明は、上記目的を達成するために次の構成を備える。
本発明に係る角のＮ等分作図方法の一形態によれば、原点（Ｏａ）を通る第１線（Ｌａ）の線分及び第２線（Ｌｂ）の線分によって規定される任意の角（θ）を、１及び２を除く自然数（Ｎ）でＮ等分する角のＮ等分方法であって、 前記原点（Ｏａ）を中心に、基準円（１１）を引く基準円作図工程と、前記角（θ）を２等分して原点（Ｏａ）を通る中心線（１２）を引く中心線作図工程と、前記中心線（１２）の前記角（θ）の外側へ延びる線上であって、前記基準円（１１）と交わる２倍半径の中心点（Ｏｂ）を中心にして、前記基準円（１１）の２倍の半径で該基準円（１１）の反対側の円周に接するように構成される第２の基準円（１３）の少なくとも一部である円弧を引く第２の基準円作図工程と、前記中心線（１２）の前記角（θ）の外側へ延びる線上であって、前記原点（Ｏａ）から前記基準円（１１）の半径のＮ−１倍の位置となる点である第Ｎ原点（Ｏｎ）を定めるように印をつける第Ｎ原点決定工程とを含み、前記２倍半径の中心点（Ｏｂ）、及び前記第１線（Ｌａ）に前記基準円（１１）が交差する点である第１の交点（Ｓ１）を通ることで、２分角（θ／２）を規定する一方の線分である一方の２分角線（１４）を引く一方の２分角線作図工程と、前記２倍半径の中心点（Ｏｂ）、及び前記第２線（Ｌｂ）に前記基準円（１１）が交差する点である第２の交点（Ｓ２）を通ることで、２分角（θ／２）を規定する他方の線分である他方の２分角線（１５）を引く他方の２分角線作図工程とのうちの少なくともいずれかの工程を含み、前記第Ｎ原点（Ｏｎ）、及び前記一方の２分角線（１４）の延長線上で前記第２の基準円（１３）の円弧に交差する点である第３の交点（Ｓ３）を通ることで、Ｎ分角（θ／Ｎ）を規定する一方の線分である一方のＮ分角線（１６）を引く一方のＮ分角線作図工程と、前記第Ｎ原点（Ｏｎ）、及び前記他方の２分角線（１５）の延長線上で前記第２の基準円（１３）の円弧に交差する点である第４の交点（Ｓ４）を通ることで、Ｎ分角（θ／Ｎ）を規定する他方の線分である他方のＮ分角線（１７）を引く他方のＮ分角線作図工程とのうちの少なくとも前記一方の２分角線作図工程又は前記他方の２分角線作図工程に対応するいずれかの工程を含むことを特徴とする。
The present invention includes the following configurations in order to achieve the above object.
According to one form of the N-equal drawing method for angles according to the present invention, any angle defined by a line segment of the first line (La) and a line segment of the second line (Lb) passing through the origin (Oa). (Θ) is an N equal division method of an angle that divides (θ) into N equal parts by a natural number (N) excluding 1 and 2, and is a reference circle drawing process in which a reference circle (11) is drawn around the origin (Oa). A center line drawing step of dividing the angle (θ) into two equal parts and drawing a center line (12) passing through the origin (Oa), and a line extending outside the angle (θ) of the center line (12). Then, centering on the center point (Ob) having a double radius intersecting the reference circle (11), it touches the circumference on the opposite side of the reference circle (11) with a radius twice the reference circle (11). A second reference circle drawing step of drawing an arc which is at least a part of the second reference circle (13) configured as described above, and a line extending outside the angle (θ) of the center line (12). Including the Nth origin determination step of marking so as to determine the Nth origin (On), which is a point at a position N-1 times the radius of the reference circle (11) from the origin (Oa). By passing through the center point (Ob) having the double radius and the first intersection (S1) at which the reference circle (11) intersects the first line (La), the dichotomy (θ /) The process of drawing one halved circle line (14), which is one of the line segments defining 2), the center point (Ob) of the double radius, and the second line (Lb). ) Passes through the second intersection (S2), which is the point where the reference circle (11) intersects, and the other dichotomy line (θ / 2), which is the other line segment that defines the dichotomy angle (θ / 2). The second is on an extension of the Nth origin (On) and the one dichotomous line (14), including at least one of the other bisection line drawing steps of drawing 15). By passing through the third intersection (S3), which is a point that intersects the arc of the reference circle (13) of the above, one N-division line (θ / N) is one of the N-division lines (θ / N). It intersects the arc of the second reference circle (13) on the extension line of the Nth origin (On) and the other half angle line (15), which draws 16). The other N-division line that draws the other N-division line (17), which is the other line segment that defines the N-division angle (θ / N), by passing through the fourth intersection (S4), which is the point to be It is characterized by including at least one of the drawing steps corresponding to at least one of the two-quarter line drawing steps or the other half-angle line drawing step.
また、本発明に係る角のＮ等分器の一形態によれば、前記の角のＮ等分作図方法に用いる角のＮ等分器であって、作図が可能な平面（１０１）が形成されるように平盤状に設けられ、回転軸が差し込まれて回動できるように該回転軸を受ける軸受穴が、前記中心線（１２）に相当するように前記平面（１０１）に引かれる線分上に、前記基準円（１１）の半径を基準として前記原点（０ａ）に相当する点から該半径の１倍及びＮ−１倍の間隔をおいて、少なくとも２個以上が設けられた台盤（１００）と、長尺の定規状に設けられ、前記軸受穴の一つであって前記２倍半径の中心点（Ｏｂ）に相当する位置に設けられた第１の軸受穴（１１０）に差し込むことができる前記回転軸の一つである第１の回転軸（２１０）を備えると共に、該第１の回転軸（２１０）から端縁（２２１）までの長さが、前記基準円（１１）の半径の２倍に相当する長さであって、該端縁（２２１）に至る少なくとも一部で、前記一方の２分角線（１４）又は前記他方の２分角線（１５）に相当する線分のうちの少なくともいずれかと一致する定規直線辺（２２０）を備える第１の回動定規片（２００）と、長尺の定規状に設けられ、前記軸受穴の一つであって前記第Ｎ原点（Ｏｎ）に相当する位置に設けられた第Ｎの軸受穴（１２０）に差し込むことができる前記回転軸の一つである第２の回転軸（３１０）を備えると共に、少なくとも前記第１の回動定規片（２００）の前記端縁（２２１）に接する付近の一部で、前記一方のＮ分角線（１６）又は前記他方のＮ分角線（１７）に相当する線分のうちの少なくともいずれかと一致する定規直線辺（３２０）を備える第２の回動定規片（３００）とを具備することを特徴とする。 Further, according to one form of the angle N equal division according to the present invention, the angle N equal division used in the above-mentioned angle N equal division method, and a plane (101) capable of drawing is formed. provided flat disc shape as the rotating shaft is inserted in a bearing hole for receiving the rotary shaft so as to be rotated, the pulled flat (101) to correspond to the center line (12) At least two or more are provided on the line segment at intervals of 1 time and N-1 times the radius from the point corresponding to the origin (0a) with reference to the radius of the reference circle (11). A base plate (100) and a first bearing hole (110) provided in a long ruler shape and at a position corresponding to the center point (Ob) of the double radius, which is one of the bearing holes. ) Is provided with a first rotating shaft (210) that is one of the rotating shafts that can be inserted into the), and the length from the first rotating shaft (210) to the edge (221) is the reference circle. A length corresponding to twice the radius of (11), and at least a part of the edge (221), the one halved line (14) or the other halved line (15). A first rotating ruler piece (200) having a straight line side (220) of a ruler that matches at least one of the line segments corresponding to), and one of the bearing holes provided in a long ruler shape. It is provided with a second rotating shaft (310), which is one of the rotating shafts, which can be inserted into the Nth bearing hole (120) provided at a position corresponding to the Nth origin (On). At least a part of the first rotating ruler piece (200) in the vicinity of the edge (221), which corresponds to the one N-segment line (16) or the other N-segment line (17). It is characterized by comprising a second rotating ruler piece (300) having a ruler straight line side (320) that matches at least one of the line segments.
本発明に係る角のＮ等分作図方法及び角のＮ等分器によれば、作図工程がより簡略化でき、角の３以上のＮ等分にも対応できるという特別有利な効果を奏する。 According to the angle N equal division method and the angle N equal division according to the present invention, the drawing process can be further simplified, and a special advantageous effect of being able to deal with N equal divisions of three or more angles is obtained.
以下、本発明に係る角のＮ等分作図方法の手順例を図１〜４に基づいて説明する。
本発明に係る角のＮ等分作図方法は、コンパスと直線を引く定規のみを用いて作図する方法であって、図１に示す如く、原点（Ｏａ）を通る第１線（Ｌａ）の線分及び第２線（Ｌｂ）の線分によって規定される任意の角（θ）を、１及び２を除く自然数（Ｎ）でＮ等分する際に、簡便に用いることができる方法である。
Hereinafter, a procedure example of the N equal division drawing method for angles according to the present invention will be described with reference to FIGS. 1 to 4.
The N-equal drawing method for angles according to the present invention is a method of drawing using only a compass and a ruler that draws a straight line, and as shown in FIG. 1, a line of the first line (La) passing through the origin (Oa). This is a method that can be easily used when dividing an arbitrary angle (θ) defined by a line segment of a minute and a second line (Lb) into N equal parts by a natural number (N) excluding 1 and 2.
本発明に係る角のＮ等分作図方法では、先ず、図２に示すように、前記原点（Ｏａ）を中心に、基準円（１１）を引く基準円作図工程と、前記角（θ）を２等分して原点（Ｏａ）を通る中心線（１２）を引く中心線作図工程と、前記中心線（１２）の前記角（θ）の外側へ延びる線上であって、前記基準円（１１）と交わる２倍半径の中心点（Ｏｂ）を中心にして、前記基準円（１１）の２倍の半径で該基準円（１１）の反対側の円周に接するように構成される第２の基準円（１３）の少なくとも一部である円弧を引く第２の基準円作図工程と、前記中心線（１２）の前記角（θ）の外側へ延びる線上であって、前記原点（Ｏａ）から前記基準円（１１）の半径のＮ−１倍の位置となる点である第Ｎ原点（Ｏｎ）を定めるように印をつける第Ｎ原点決定工程とを含む。 In the N-equal drawing method for angles according to the present invention, first, as shown in FIG. 2, a reference circle drawing step of drawing a reference circle (11) around the origin (Oa) and the angle (θ) are performed. A center line drawing step of dividing into two equal parts and drawing a center line (12) passing through the origin (Oa), and a line extending outward from the angle (θ) of the center line (12), and the reference circle (11). ) Is centered on the center point (Ob) having a double radius and is configured to touch the circumference on the opposite side of the reference circle (11) with a radius twice the reference circle (11). A second reference circle drawing step of drawing an arc that is at least a part of the reference circle (13) of the above, and a line extending outward from the angle (θ) of the center line (12), the origin (Oa). The Nth origin determination step of marking so as to determine the Nth origin (On), which is a point at a position N-1 times the radius of the reference circle (11).
中心線作図工程は、説明するまでもないが、同径の二つの補助円（例えば、図２に示す１１ａと１１ｂ）を用いることで行うことができる。図２に示す例では、補助円１１ａは、第１の交点（Ｓ１）を中心とする基準円１１と同径の円であり、補助円１１ｂは、第２の交点（Ｓ２）を中心とする基準円１１と同径の円である。その二つの補助円１１ａ、１１ｂが交わる二つの交点を通るように直線を引くことで、中心線１２を得ることができる。 Needless to say, the center line drawing step can be performed by using two auxiliary circles having the same diameter (for example, 11a and 11b shown in FIG. 2). In the example shown in FIG. 2, the auxiliary circle 11a is a circle having the same diameter as the reference circle 11 centered on the first intersection (S1), and the auxiliary circle 11b is centered on the second intersection (S2). It is a circle having the same diameter as the reference circle 11. The center line 12 can be obtained by drawing a straight line so as to pass through the two intersections where the two auxiliary circles 11a and 11b intersect.
次の工程として、前記２倍半径の中心点（Ｏｂ）、及び前記第１線（Ｌａ）に前記基準円（１１）が交差する点である第１の交点（Ｓ１）を通ることで、２分角（θ／２）を規定する一方の線分である一方の２分角線（１４）を引く一方の２分角線作図工程と、前記２倍半径の中心点（Ｏｂ）、及び前記第２線（Ｌｂ）に前記基準円（１１）が交差する点である第２の交点（Ｓ２）を通ることで、２分角（θ／２）を規定する他方の線分である他方の２分角線（１５）を引く他方の２分角線作図工程とのうちの少なくともいずれかの工程を含む。 As the next step, by passing through the center point (Ob) having the double radius and the first intersection (S1) at which the reference circle (11) intersects the first line segment (La), 2 One half-angle line drawing process that draws one half-angle line (14), which is one line segment that defines the division angle (θ / 2), the center point (Ob) of the double radius, and the above. The other line segment that defines the dichotomy (θ / 2) by passing through the second intersection (S2), which is the point where the reference circle (11) intersects the second line (Lb). Includes at least one of the other half-segment drawing steps of drawing the half-section line (15).
そして、さらに次の工程として、前記第Ｎ原点（Ｏｎ）、及び前記一方の２分角線（１４）の延長線上で前記第２の基準円（１３）の円弧に交差する点である第３の交点（Ｓ３）を通ることで、Ｎ分角（θ／Ｎ）を規定する一方の線分である一方のＮ分角線（１６）を引く一方のＮ分角線作図工程と、前記第Ｎ原点（Ｏｎ）、及び前記他方の２分角線（１５）の延長線上で前記第２の基準円（１３）の円弧に交差する点である第４の交点（Ｓ４）を通ることで、Ｎ分角（θ／Ｎ）を規定する他方の線分である他方のＮ分角線（１７）を引く他方のＮ分角線作図工程とのうちの少なくとも前記一方の２分角線作図工程又は前記他方の２分角線作図工程に対応するいずれかの工程を含む。 Then, as a next step, a third point that intersects the arc of the second reference circle (13) on the extension line of the Nth origin (On) and the one bisector line (14). One N-angle line drawing step of drawing one N-segment line (16), which is one line segment defining the N-segment angle (θ / N) by passing through the intersection (S3) of By passing through the N origin (On) and the fourth intersection (S4), which is a point intersecting the arc of the second reference circle (13) on the extension of the other angle bisector (15). At least one of the other angle bisector drawing steps of drawing the other N segment line (17), which is the other line segment defining the N segment angle (θ / N). Alternatively, it includes any step corresponding to the other half-angle line drawing step.
なお、一方のＮ分角線（１６）、又は他方のＮ分角線（１７）のいずれかの線をひくことができれば、中心線（１２）は定まっているため、Ｎ分角（θ／Ｎ）の２分の１の角を得ることができる。そして、そのＮ分角（θ／Ｎ）の２分の１の角を、２倍することで得られるＮ分角（θ／Ｎ）は、コンパスと、直線を引く定規とによって、容易に規定することができる。従って、一方のＮ分角線（１６）、又は他方のＮ分角線（１７）のいずれかの線をひくことができれば、Ｎ分角（θ／Ｎ）を得ることができる。 If either one of the N-angle lines (16) or the other N-angle line (17) can be drawn, the center line (12) is fixed, so the N-angle (θ /). It is possible to obtain a half angle of N). Then, the N-division angle (θ / N) obtained by doubling the half-angle of the N-division angle (θ / N) is easily defined by a compass and a ruler that draws a straight line. can do. Therefore, if either one of the N-angle lines (16) or the other N-angle line (17) can be drawn, the N-angle (θ / N) can be obtained.
また、図１から４に示した作図例は、角の３等分の場合を示しているが、同様の工程によって、任意の角（θ）について、３より大きな自然数（Ｎ）等分を行うことができる。
この角のＮ等分作図方法によれば、作図工程がより簡略化でき、角の３以上のＮ等分にも対応できるという特別有利な効果を奏する。
Further, the drawing examples shown in FIGS. 1 to 4 show the case of dividing the angle into three equal parts, but by the same process, a natural number (N) larger than 3 is equally divided for an arbitrary angle (θ). be able to.
According to this method of drawing N equal parts of angles, the drawing process can be further simplified, and a special advantageous effect of being able to deal with N equal parts of three or more angles is obtained.
次に、本発明に係る角のＮ等分器の形態例について、図５〜１１に基づいて、詳細に説明する。図５〜７は、角の３等分器の部品構成（台盤（１００）、第１の回動定規片（２００）、第２の回動定規片（３００））を、それぞれ示した図である。また、図８〜１０は、以上に説明した角のＮ等分作図方法に用いる具体例として、角の３等分器としての使用方法を示す図である。 Next, a morphological example of the angle N equal division according to the present invention will be described in detail with reference to FIGS. 5 to 11. 5 to 7 are views showing the component configurations of the angle trisection (base plate (100), first rotating ruler piece (200), second rotating ruler piece (300)), respectively. Is. Further, FIGS. 8 to 10 are diagrams showing a method of using the angle as a trisection device as a specific example used in the above-described angle trisection drawing method.
（１００）は台盤であり、作図が可能な平面（１０１）が形成されるように平盤状に設けられ、回転軸が差し込まれて回動できるように該回転軸を受ける軸受穴が、前記中心線（１２）に相当するように前記平面（１０１）に引かれる線分上に、前記基準円（１１）の半径を基準として前記原点（０ａ）に相当する点から該半径の１倍及びＮ−１倍の間隔をおいて、少なくとも２個以上が設けられている。 (100) is a weighing table, drawing is provided in a flat disc-shaped so as to form a plane (101) capable of rotating shaft is inserted in a bearing hole for receiving the rotary shaft so as to be rotated, On a line segment drawn on the plane (101) so as to correspond to the center line (12), one time the radius from the point corresponding to the origin (0a) with reference to the radius of the reference circle (11). At least two or more are provided at intervals of N-1 times.
（２００）は第１の回動定規片であり、長尺の定規状に設けられ、前記軸受穴の一つであって前記２倍半径の中心点（Ｏｂ）に相当する位置に設けられた第１の軸受穴（１１０）に差し込むことができる前記回転軸の一つである第１の回転軸（２１０）を備えると共に、該第１の回転軸（２１０）から端縁（２２１）までの長さが、前記基準円（１１）の半径の２倍に相当する長さであって、該端縁（２２１）に至る少なくとも一部で、前記一方の２分角線（１４）又は前記他方の２分角線（１５）に相当する線分のうちの少なくともいずれかと一致する定規直線辺（２２０）を備える。 (200) is the first rotating ruler piece, which is provided in the shape of a long ruler, and is provided at a position corresponding to the center point (Ob) of the double radius, which is one of the bearing holes. It is provided with a first rotating shaft (210) which is one of the rotating shafts that can be inserted into the first bearing hole (110), and from the first rotating shaft (210) to the edge (221). The length is a length corresponding to twice the radius of the reference circle (11), and at least a part of the edge (221), the one half line segment (14) or the other. It is provided with a ruler straight line side (220) that coincides with at least one of the line segments corresponding to the dichotomous line (15).
また、（３００）は第２の回動定規片であり、長尺の定規状に設けられ、前記軸受穴の一つであって前記第Ｎ原点（Ｏｎ）に相当する位置に設けられた第Ｎの軸受穴（１２０）に差し込むことができる前記回転軸の一つである第２の回転軸（３１０）を備えると共に、少なくとも前記第１の回動定規片（２００）の前記端縁（２２１）に接する付近の一部で、前記一方のＮ分角線（１６）又は前記他方のＮ分角線（１７）に相当する線分のうちの少なくともいずれかと一致する定規直線辺（３２０）を備える。 Further, (300) is a second rotating ruler piece, which is provided in a long ruler shape and is provided at a position corresponding to the Nth origin (On), which is one of the bearing holes. The second rotating shaft (310), which is one of the rotating shafts that can be inserted into the bearing hole (120) of N, is provided, and at least the end edge (221) of the first rotating ruler piece (200) is provided. ), A ruler straight line side (320) that coincides with at least one of the one N-segment line (16) and the other N-segment line (17). Be prepared.
図８は、台盤（１００）、第１の回動定規片（２００）、第２の回動定規片（３００）の部品を組み合わせた図であり、角のＮ等分を行うための準備状態を示している。 FIG. 8 is a diagram in which the parts of the base plate (100), the first rotating ruler piece (200), and the second rotating ruler piece (300) are combined, and preparations for N equal division of the corners are performed. Indicates the state.
図９は、２個のバー（第１の回動定規片（２００）、第２の回動定規片（３００））によりθ／３を求めたもので、これにより∠θを３等分することが可能になる。
図１０は、∠θの３等分がなされた状態を示す拡大詳細図であり、前述の角のＮ等分作図方法で説明した工程を、この角のＮ等分器で行った状態を示している。
In FIG. 9, θ / 3 is obtained from two bars (first rotating ruler piece (200) and second rotating ruler piece (300)), thereby dividing ∠θ into three equal parts. Will be possible.
FIG. 10 is an enlarged detailed view showing a state in which ∠θ is divided into three equal parts, and shows a state in which the process described in the above-mentioned N equal division drawing method for an angle is performed by an N equal division device for this angle. ing.
図１１は、∠θのＮ等分の例として、θ／５を求めたもので、同様にθ／Ｎを求めることも可能なことを示している。なお、図６（ｂ）及び図７（ｂ）に示すとおり第１の回転軸（２１０）及び第２の回転軸（３１０）が第１の回動定規片（２００）または第２の回動定規片（３００）を貫通して両側に飛び出していることにより、それぞれを差し込む第１の軸受穴（１１０）または第Ｎの軸受穴（１２０）に、第１の回動定規片（２００）または第２の回動定規片（３００）の双方をともに反転して差し込むことで図示する側と対象となる反対側のθ／Ｎを同様に求めることが出来る。また、前記のとおり述べてきた実施例では回動定規片側に回転軸、本体側に軸受穴を構成しているが、回転軸を本体側に軸受穴を回動定規片側にしても、同様の効果が得られる。すなわち、前記回転軸と前記軸受穴との関係は、相対的なものであって、前記回転軸が前記台盤の側に設けられ、前記軸受穴が前記回動定規片の側に設けられている構成であっても、同様に角のＮ等分を行うことができる。但し、図５〜１１に示す形態例のように、軸受穴（１１０、１２０）が、台盤（１００）に設けられている構成の方が、その台盤（１００）の平面（１０１）上に突起物がない形態となるため、その平面上で作図が行い易く、さらに作図された線を写し易い利点がある。 FIG. 11 shows that θ / 5 is obtained as an example of N equal division of ∠θ, and it is also possible to obtain θ / N in the same manner. As shown in FIGS. 6 (b) and 7 (b), the first rotation shaft (210) and the second rotation shaft (310) are the first rotation ruler piece (200) or the second rotation. By penetrating the ruler piece (300) and protruding to both sides, the first rotating ruler piece (200) or the first rotating ruler piece (200) is inserted into the first bearing hole (110) or the Nth bearing hole (120) into which each is inserted. By inserting both of the second rotating ruler pieces (300) in reverse, the θ / N on the side shown and the opposite side to be the target can be obtained in the same manner. Further, in the embodiment described as described above, the rotating shaft is formed on one side of the rotating ruler and the bearing hole is formed on the main body side. However, the same applies when the rotating shaft is on the main body side and the bearing hole is on one side of the rotating ruler. The effect is obtained. That is, the relationship between the rotating shaft and the bearing hole is relative, and the rotating shaft is provided on the side of the base plate and the bearing hole is provided on the side of the rotating ruler piece. Even with the configuration, the corners can be divided into N equal parts in the same manner. However, as in the configuration example shown in FIGS. 5 to 11, the configuration in which the bearing holes (110, 120) are provided on the base plate (100) is on the plane (101) of the base plate (100). Since the bearing has no protrusions, it is easy to draw on the plane, and it is easy to copy the drawn line.
次に、本発明に係る角のＮ等分作図方法の原理について、図１２〜１８に基づいて説明する。
（弧のＮ等分による角のＮ等分）
古代より目盛のない直線を引くためだけの直定規とコンパスのみによる角の３等分の作図は、代数的な方法により不可能であることが証明されている。ここで論ずるのは、定規とコンパスがあれば単純な幾何学的な手法により、同心円の角の弧がＮ等分(Ｎ＝任意数。以下同じ)され、角のＮ等分が可能になることである。
角のＮ等分ができるのならば、角の３等分の作図が可能なことは当然である。
Next, the principle of the N equal division drawing method for angles according to the present invention will be described with reference to FIGS. 12 to 18.
(N equal division of the angle by N equal division of the arc)
Since ancient times, it has been proved that it is impossible to draw an angle trisection with a straightedge and a compass only to draw a straight line without a scale by an algebraic method. What we will discuss here is that if you have a ruler and a compass, the arcs of the corners of concentric circles are divided into N equal parts (N = arbitrary number; the same applies hereinafter) by a simple geometric method, and N equal parts of the corners become possible. That is.
If the angle can be divided into N equal parts, it is natural that the angle trisection can be drawn.
１．角と弧の関係
図１２の∠θの大きさは、円Ｌ1において、∠θの角度が変化するとき弧の長さは比例する。
言い換えると、角の大きさは、弧の長さが1/2になれば、θ/2、1/4の長さになればθ/4となる。
1. 1. Relationship between angle and arc The size of ∠θ in FIG. 12 is proportional to the length of the arc when the angle of ∠θ changes in the circle L1.
In other words, the size of the angle is θ / 2 when the arc length is halved, and θ / 4 when the arc length is 1/4.
２．角の弧の長さの表現
図１３の∠θの弧の長さＡ1−Ｂ1の長さは2×sinθ/2の弦の弧として表すことができる。
また∠θを２等分した∠θ/2の弧Ｏ1−Ａ１および弧Ｏ1−Ｂ1の長さは2×sinθ/4の長さの弦の弧となる。
弧Ａ1−Ｂ１は∠θ/2の弧の２倍の長さになるので２×（2×sinθ/4）＝4×sinθ/4の長さの弦を持つ弧として表すこともできる。
∠θの弧は（１）2×sinθ/2の弦の弧又は（２）4×sinθ/4の弦の弧の長さとして表すことが出来る。弦の長さ（１）と（２）は長さに違いがあるが、弧の長さはおなじである。
2. 2. Representation of the arc length of the angle The arc length A1-B1 of ∠θ in FIG. 13 can be expressed as the arc of the chord of 2 × sinθ / 2.
The length of the arc O1-A1 and the arc O1-B1 of ∠θ / 2, which is bisected by ∠θ, is the arc of the string having a length of 2 × sinθ / 4.
Since the arc A1-B1 is twice as long as the arc of ∠θ / 2, it can be expressed as an arc having a string having a length of 2 × (2 × sinθ / 4) = 4 × sinθ / 4.
The arc of ∠θ can be expressed as the length of the arc of (1) 2 × sinθ / 2 or the arc of (2) 4 × sinθ / 4. The chord lengths (1) and (2) are different, but the arc lengths are the same.
３．２倍の同心円
図１４において、∠θの2倍の同心円Ｌ２の弧はＬ１の弧の2倍の長さになるため、Ｌ２の∠θ/ 2の弧がＬ1の弧Ａ1−Ｂ1と同じ長さになる。Ｌ２の∠θ/2の弧は4×sinθ/4の長さの弦の弧となるので、Ｌ2の弧Ａ２−Ｂ２は4×sinθ/4の長さの弦の弧の2倍の長さになる。見方を変えるとＬ2の弧Ａ２−Ｂ２は、4×sinθ/4の長さの弦の弧により2等分することが出来る。これは∠θの同心円の弧が、中心円の半径の倍率に比例して4×sinθ/4の長さの弦の弧の長さ分ずつひろがることを示すもので、同心円の弧のＮ等分により角のＮ等分ができる要素となる。
3.2 Double concentric circles In Fig. 14, the arc of the concentric circle L2, which is twice the length of ∠θ, is twice as long as the arc of L1, so the arc of ∠θ / 2 of L2 is the arc A1-B1 of L1. It will be the same length. Since the arc of ∠θ / 2 of L2 is the arc of a string with a length of 4 × sinθ / 4, the arc A2-B2 of L2 is twice as long as the arc of a string with a length of 4 × sinθ / 4. become. From a different point of view, the arc A2-B2 of L2 can be bisected by the arc of a string having a length of 4 × sin θ / 4. This indicates that the arc of the concentric circle of ∠θ spreads by the length of the arc of the string with a length of 4 × sinθ / 4 in proportion to the magnification of the radius of the central circle. It is an element that can divide the angle into N equal parts by the minute.
４．４倍の同心円
図１５の４倍の同心円Ｌ4の弧Ａ4−Ｂ4は、２倍の同心円Ｌ2の弧Ａ2−Ｂ2の弧の２倍の長さになるため、（4×sinθ/4）の長さの弦の弧の4倍の長さになる。
図を見れば、Ｌ4の弧Ａ4−B４がｌ2の4×sinθ/4の長さの弦の弧p1−p2により４等分されていることがわかる。
4.4 times concentric circle Since the arc A4-B4 of the four times concentric circle L4 in Fig. 15 is twice as long as the arc of the double concentric circle L2 arc A2-B2 (4 × sin θ / 4) It is four times as long as the arc of the string.
From the figure, it can be seen that the arc A4-B4 of L4 is divided into four equal parts by the arc p1-p2 of the string of 4 × sin θ / 4 of l2.
５．角の３等分
図１６は図１５において４倍の同心円を４等分したのとおなじように、３倍の同心円の∠θの弧Ａ3−B３を4×sinθ/4の長さの弦の弧により３等分した図である。図１６の∠θの弧の弦の長さは
Ｌ1の弧の弦Ａ1−B１＝４×sinθ/4
Ｌ2の弧の弦Ａ2−B２＝２×（4×sinθ/4）
Ｌ3の弧の弦Ａ3−B３＝３×（4×sinθ/4） となる。
これにより図のようにＬ3の∠θの弧Ａ3−B3は、4×sinθ/4の弦の弧 p1−p2により３等分されることがわかる。
弧が３等分されたことにより、角は３等分されθ/3を得ることができる。
３等分されたＬ3の弧Ｅ3−F3の弦は6×sinθ/6となる。
以上が、定規とコンパスにより任意の角を３等分の証明である。
5. Angle trisection Fig. 16 shows the arc A3-B3 of ∠θ of the triple concentric circle divided into four equal parts in Fig. 15 of the string of 4 × sin θ / 4. It is the figure which divided into three equal parts by an arc. The length of the arc chord of ∠θ in FIG. 16 is L1 arc chord A1-B1 = 4 × sinθ / 4
L2 arc string A2-B2 = 2 × (4 × sinθ / 4)
The arc string A3-B3 of L3 = 3 × (4 × sin θ / 4).
As shown in the figure, it can be seen that the arc A3-B3 of ∠θ of L3 is divided into three equal parts by the arc p1-p2 of the string of 4 × sinθ / 4.
By dividing the arc into three equal parts, the angle can be divided into three equal parts to obtain θ / 3.
The string of the arc E3-F3 of L3 divided into three equal parts is 6 × sin θ / 6.
The above is the proof of dividing any corner into three equal parts with a ruler and a compass.
6．角のＮ等分
図１７は90度の範囲で角のＮ等分が可能であることを示したものである。
角θのＮ倍の同心円の弧の長さは、（4×sinθ/4）の弦の弧のＮ倍の長さに等しい長さになる。
図１７は７倍の同心円の∠θの、Ｌ1〜Ｌ7それぞれの弧が、4×sinθ/4の弦の弧によりＮ等分されることを表したものである。
７倍の同心円Ｌ7の弧Ａ7−Ｂ7は、4×sinθ/4の弦の弧の７倍の7×（4×sinθ/4）に等しい長さとなるため、4×sinθ/4の弦の弧p1−p2により７等分され、θ/7を得ることができる。
Ｎ倍の同心円の∠θの弧が、4×sinθ/4の弦の弧p1−p2によるＮ等分の作図が可能なのは、４倍の同心円を除き素数倍の同心円に限られる。
6. N equal division of angles FIG. 17 shows that N equal division of angles is possible within a range of 90 degrees.
The arc length of concentric circles N times the angle θ is equal to N times the arc of the (4 × sin θ / 4) string.
FIG. 17 shows that the arcs of L1 to L7 of ∠θ of a 7-fold concentric circle are divided into N equal parts by the arc of a string of 4 × sinθ / 4.
The arc A7-B7 of the 7-fold concentric circle L7 has a length equal to 7 × (4 × sinθ / 4), which is 7 times the arc of the 4 × sinθ / 4 string, so the arc of the 4 × sinθ / 4 string. It is divided into 7 equal parts by p1-p2, and θ / 7 can be obtained.
The arc of ∠θ of an N-fold concentric circle can be divided into N equal parts by the arc p1-p2 of a 4 × sin θ / 4 string only for prime-numbered concentric circles except for a 4-fold concentric circle.
図１８は、図１７を拡大して分かりやすくした図である。
Ｌ2は2倍の同心円である。
Ｌ3は3倍・ Ｌ4は4倍の同心円の∠θの弧を示す。
ｌ5は5倍の同心円の中心円、ｌ7は7倍の同心円の中心円を示す。
図をみれば同心円の∠θのそれぞれの弧が、4×sinθ/4の弦の弧p1−p2によりＮ等分され、θ/Ｎの角が得られることがわかる。
FIG. 18 is an enlarged view of FIG. 17 for easy understanding.
L2 is a double concentric circle.
L3 shows an arc of 3 times and L4 shows a 4 times concentric arc of ∠θ.
l5 is the central circle of 5 times concentric circles, and l7 is the central circle of 7 times concentric circles.
Looking at the figure, it can be seen that each arc of ∠θ of the concentric circle is divided into N equal parts by the arc p1-p2 of the string of 4 × sinθ / 4, and the angle of θ / N is obtained.
次に、図１９〜２４に基づいて、回転定規片（２００、３００）を台盤（１００）に仮に保持（仮固定）させる実施例を示す。
図１９及び２０の実施例１によれば、本体である台盤（１００）を左右にまたいで、押さえ板が有り、その中央付近には長さ方向に沿った押さえ板のスリット溝が形成されており、その押さえ板のスリット溝に沿って締付け具（ボルト）が、自在にスライドでき、回動定規片（２００、３００）付近で停止させてネジを締め付けることで、その回動定規片を仮固定できる。その締め付けは、台盤（１００）に前記押さえ板のスリット溝に対応する位置に台盤側のスリット溝が有り、ボルトはそれぞれのスリット溝を貫通しており、上下を、座金を介してボルトと蝶ナットで、締め付けることでなされる。
Next, an embodiment in which the rotating ruler pieces (200, 300) are temporarily held (temporarily fixed) on the base plate (100) based on FIGS. 19 to 24 will be shown.
According to the first embodiment of FIGS. 19 and 20, there is a holding plate straddling the base plate (100) which is the main body to the left and right, and a slit groove of the holding plate along the length direction is formed near the center thereof. The tightening tool (bolt) can slide freely along the slit groove of the holding plate, and by stopping near the rotating ruler piece (200, 300) and tightening the screw, the rotating ruler piece can be tightened. Can be temporarily fixed. For tightening, the base plate (100) has a slit groove on the base plate side at a position corresponding to the slit groove of the holding plate, and the bolt penetrates each slit groove, and the bolts are bolted up and down via washers. It is done by tightening with a wing nut.
図２１及び２２の実施例２によれば、回動定規片（２００、３００）の適宜な位置に穴が明けられている。ボルトが、台盤（１００）の裏側に位置して前記回動定規片の適宜な位置の穴の回動半径と同じ中心半径を持つスリット状の回り止め摺動部が設けられたボルト摺動部に、摺動可能に嵌合されて配されている。前記回動定規片の穴に挿通されて上部に突出した前記ボルトの螺子部に、上部より適宜座金を介して止めネジ（蝶ナット）を螺合して締め付けることで、任意の位置に前記回動定規片を仮固定させることができる。 According to the second embodiment of FIGS. 21 and 22, holes are drilled at appropriate positions of the rotating ruler pieces (200, 300). The bolt slides on the back side of the base plate (100) and is provided with a slit-shaped detent sliding portion having the same center radius as the turning radius of the hole at an appropriate position of the rotating ruler piece. It is slidably fitted and arranged in the portion. A set screw (wing nut) is screwed into the screw portion of the bolt that is inserted into the hole of the rotating ruler piece and protrudes upward from the upper portion via a washer as appropriate, and tightened. The moving ruler piece can be temporarily fixed.
図２３及び２４の実施例３によれば、本体（台盤（１００））側の回転軸の受け穴に回転軸が下方から上方に向かって固定されており、その先端側にネジが形成されている。一方、回動定規片（２００、３００）の回転軸部には前記回転軸に嵌合する回転穴が形成されている。該回転穴を、本体側に固定された回転軸に挿通して前記先端のネジを使用して蝶ナット等で締め付け仮固定する。
さらに、本体側を雌ネジとして、回動定規片の上からボルトで留めても良い。この場合は中心位置が正確に決まるよう本体側に適当な深さのネジのない嵌合孔を形成し、ボルトの先端側にも精密孔に嵌合して締め付けられる程度の長さでネジのないストレートな外形を形成する必要がある。
According to the third embodiment of FIG. 23 and 24, and the body (weighing table (100)) side rotating shaft receiving hole of the rotation shaft of fixed upward from below, the screw is formed on the distal end side ing. On the other hand, the rotating shaft portion of the rotating ruler piece (200, 300) is formed with a rotating hole that fits the rotating shaft . The rotary hole is inserted into a rotary shaft fixed to the main body side and tightened with a wing nut or the like using the screw at the tip to temporarily fix the rotary hole.
Further, the main body side may be a female screw and may be bolted from above the rotating ruler piece. In this case, a fitting hole without a screw of an appropriate depth is formed on the main body side so that the center position can be accurately determined, and the screw is long enough to fit into the precision hole and be tightened on the tip side of the bolt. It is necessary to form a straight outer shape.
また、回転定規片（２００、３００）を台盤（１００）に仮に保持（仮固定）させる方法としては、磁石の磁力を利用する等考えられる種々の方法の中から適宜選択できるのは勿論である。 Further, as a method of temporarily holding (temporarily fixing) the rotating ruler pieces (200, 300) on the base plate (100), it goes without saying that it can be appropriately selected from various conceivable methods such as using the magnetic force of a magnet. is there.
以上、本発明につき好適な形態例を挙げて種々説明してきたが、本発明はこの形態例に限定されるものではなく、発明の精神を逸脱しない範囲内で多くの改変を施し得るのは勿論のことである。 Although various examples of the present invention have been described above, the present invention is not limited to the examples of the present invention, and it goes without saying that many modifications can be made without departing from the spirit of the invention. That is.
Ｌａ 第１線
Ｌｂ 第２線
Ｎ １及び２を除く自然数
Ｏａ 原点
Ｏｂ ２倍半径の中心点
Ｏｎ 第Ｎ原点
Ｓ１ 第１の交差点
Ｓ２ 第２の交差点
Ｓ３ 第３の交差点
Ｓ４ 第４の交差点
θ 任意の角
θ／２ ２分角
θ／Ｎ Ｎ分角
１１ 基準円
１２ 中心線
１３ 第２の基準円
１４ 一方の２分角線
１５ 他方の２分角線
１６ 一方のＮ分角線
１７ 他方のＮ分角線
１００ 台盤
１０１ 平面
１１０ 第１の軸受穴
１２０ 第Ｎの軸受穴
２００ 第１の回動定規片
２１０ 第１の回転軸
２２０ 定規直線辺
２２１ 端縁
３００ 第２の回動定規片
３１０ 第２の回転軸
３２０ 定規直線辺
La 1st line Lb 2nd line N Natural numbers excluding 1 and 2 Oa Origin Ob Center point of double radius On Nth origin S1 1st intersection S2 2nd intersection S3 3rd intersection S4 4th intersection θ Arbitrary Angle θ / 2 Bisection angle θ / N N division angle 11 Reference circle 12 Center line 13 Second reference circle 14 One half angle line 15 One half angle line 16 One N division angle line 17 The other N division angle line 100 Base 101 Flat surface 110 First bearing hole 120 Nth bearing hole 200 First rotating ruler piece 210 First rotating shaft 220 Ruler straight side 221 Edge edge 300 Second rotating ruler piece 310 Second rotation axis 320 Ruler straight side
Claims (1)
前記原点（Ｏａ）を中心に、基準円（１１）を引く基準円作図工程と、
前記角（θ）を２等分して原点（Ｏａ）を通る中心線（１２）を引く中心線作図工程と、
前記中心線（１２）の前記角（θ）の外側へ延びる線上であって、前記基準円（１１）と交わる２倍半径の中心点（Ｏｂ）を中心にして、前記基準円（１１）の２倍の半径で該基準円（１１）の反対側の円周に接するように構成される第２の基準円（１３）の少なくとも一部である円弧を引く第２の基準円作図工程と、
前記中心線（１２）の前記角（θ）の外側へ延びる線上であって、前記原点（Ｏａ）から前記基準円（１１）の半径のＮ−１倍の位置となる点である第Ｎ原点（Ｏｎ）を定めるように印をつける第Ｎ原点決定工程とを含み、
前記２倍半径の中心点（Ｏｂ）、及び前記第１線（Ｌａ）に前記基準円（１１）が交差する点である第１の交点（Ｓ１）を通ることで、２分角（θ／２）を規定する一方の線分である一方の２分角線（１４）を引く一方の２分角線作図工程と、前記２倍半径の中心点（Ｏｂ）、及び前記第２線（Ｌｂ）に前記基準円（１１）が交差する点である第２の交点（Ｓ２）を通ることで、２分角（θ／２）を規定する他方の線分である他方の２分角線（１５）を引く他方の２分角線作図工程とのうちの少なくともいずれかの工程を含み、
前記第Ｎ原点（Ｏｎ）、及び前記一方の２分角線（１４）の延長線上で前記第２の基準円（１３）の円弧に交差する点である第３の交点（Ｓ３）を通ることで、Ｎ分角（θ／Ｎ）を規定する一方の線分である一方のＮ分角線（１６）を引く一方のＮ分角線作図工程と、前記第Ｎ原点（Ｏｎ）、及び前記他方の２分角線（１５）の延長線上で前記第２の基準円（１３）の円弧に交差する点である第４の交点（Ｓ４）を通ることで、Ｎ分角（θ／Ｎ）を規定する他方の線分である他方のＮ分角線（１７）を引く他方のＮ分角線作図工程とのうちの少なくとも前記一方の２分角線作図工程又は前記他方の２分角線作図工程に対応するいずれかの工程を含むことを特徴とする角のＮ等分作図方法に用いる角のＮ等分器において、
作図が可能な平面（１０１）が形成されるように平盤状に設けられ、回転軸が差し込まれて回動できるように該回転軸を受ける軸受穴が、前記中心線（１２）に相当するように前記平面（１０１）に引かれる線分上に、前記基準円（１１）の半径を基準として前記原点（０ａ）に相当する点から該半径の１倍及びＮ−１倍の間隔をおいて、少なくとも２個以上が設けられた台盤（１００）と、
長尺の定規状に設けられ、前記軸受穴の一つであって前記２倍半径の中心点（Ｏｂ）に相当する位置に設けられた第１の軸受穴（１１０）に差し込むことができる前記回転軸の一つである第１の回転軸（２１０）を備えると共に、該第１の回転軸（２１０）から端縁（２２１）までの長さが、前記基準円（１１）の半径の２倍に相当する長さであって、該端縁（２２１）に至る少なくとも一部で、前記一方の２分角線（１４）又は前記他方の２分角線（１５）に相当する線分のうちの少なくともいずれかと一致する定規直線辺（２２０）を備える第１の回動定規片（２００）と、
長尺の定規状に設けられ、前記軸受穴の一つであって前記第Ｎ原点（Ｏｎ）に相当する位置に設けられた第Ｎの軸受穴（１２０）に差し込むことができる前記回転軸の一つである第２の回転軸（３１０）を備えると共に、少なくとも前記第１の回動定規片（２００）の前記端縁（２２１）に接する付近の一部で、前記一方のＮ分角線（１６）又は前記他方のＮ分角線（１７）に相当する線分のうちの少なくともいずれかと一致する定規直線辺（３２０）を備える第２の回動定規片（３００）とを具備することを特徴とする角のＮ等分器。 Arbitrary angle (θ) defined by the line segment of the first line (La) and the line segment of the second line (Lb) passing through the origin (Oa) is divided into N equal parts by a natural number (N) excluding 1 and 2. It is a method of dividing the angle into N equal parts.
A reference circle drawing process in which a reference circle (11) is drawn around the origin (Oa), and
A center line drawing process in which the angle (θ) is bisected and a center line (12) passing through the origin (Oa) is drawn.
Of the reference circle (11), centered on a center point (Ob) having a double radius intersecting the reference circle (11) on a line extending outside the angle (θ) of the center line (12). A second reference circle drawing process that draws an arc that is at least a part of the second reference circle (13) configured to touch the opposite circumference of the reference circle (11) with a double radius.
The Nth origin, which is a line extending outward from the angle (θ) of the center line (12) and is a position N-1 times the radius of the reference circle (11) from the origin (Oa). Including the Nth origin determination step of marking to determine (On)
By passing through the center point (Ob) having the double radius and the first intersection (S1) at which the reference circle (11) intersects the first line (La), the dichotomy (θ /) The process of drawing one half-angle line (14), which is one of the line segments defining 2), the center point (Ob) of the double radius, and the second line (Lb). ) Passes through the second intersection (S2), which is the point where the reference circle (11) intersects, so that the other dichotomy line (θ / 2) is the other line segment that defines the dichotomy (θ / 2). Includes at least one of the other two-segment line drawing steps of drawing 15).
Passing through a third intersection (S3), which is a point intersecting the arc of the second reference circle (13) on the extension of the Nth origin (On) and one of the two arc minutes (14). The process of drawing one N-segment line (16), which is one of the line segments defining the N-intersection (θ / N), the N-th origin (On), and the above. By passing through the fourth intersection (S4), which is a point that intersects the arc of the second reference circle (13) on the extension line of the other half arc line (15), the N arc minutes (θ / N) At least one of the two N-segment drawing steps of drawing the other N-segment line (17), which is the other line segment defining the above, or the other two-division line. In the corner N equal division used in the corner N equal division method, which comprises any of the steps corresponding to the drawing process.
Drawing is provided in a flat disc shape as a plane (101) can be formed, the rotary shaft is inserted to the bearing hole for receiving the rotary shaft so as to be rotated, corresponding to the center line (12) On the line segment drawn on the plane (101) as described above, an interval of 1 times the radius and N-1 times the radius from the point corresponding to the origin (0a) with respect to the radius of the reference circle (11). And, with a base (100) provided with at least two
The said, which is provided in the shape of a long ruler and can be inserted into a first bearing hole (110) provided at a position corresponding to the center point (Ob) of the double radius, which is one of the bearing holes. A first rotating shaft (210), which is one of the rotating shafts, is provided, and the length from the first rotating shaft (210) to the edge (221) is 2 of the radius of the reference circle (11). A line segment having a length equivalent to twice that corresponding to the one dichotomy line (14) or the other bisection line (15) at least in a part leading to the edge (221). A first rotating ruler piece (200) having a ruler straight side (220) that matches at least one of them.
A rotating shaft provided in a long ruler shape and capable of being inserted into an Nth bearing hole (120) provided at a position corresponding to the Nth origin (On), which is one of the bearing holes. A second rotation axis (310) is provided, and at least a part of the first rotation ruler piece (200) in the vicinity of contact with the end edge (221) of the one N segmental line. (16) or a second rotating ruler piece (300) having a ruler straight line side (320) that matches at least one of the line segments corresponding to the other N segment angle line (17). A corner N equalizer characterized by.
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| CN113587761A (en) * | 2021-07-12 | 2021-11-02 | 上海外高桥造船有限公司 | Clamping plate for assembling and controlling ship structure and manufacturing method thereof |
| CN114604024A (en) * | 2022-03-25 | 2022-06-10 | 王兆民 | Triangular equi-divider |
| JP7187130B1 (en) * | 2022-10-20 | 2022-12-12 | 帰己二 五藤 | Plotter for angle 3 and 5 |
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| CN113587761A (en) * | 2021-07-12 | 2021-11-02 | 上海外高桥造船有限公司 | Clamping plate for assembling and controlling ship structure and manufacturing method thereof |
| CN114604024A (en) * | 2022-03-25 | 2022-06-10 | 王兆民 | Triangular equi-divider |
| JP7187130B1 (en) * | 2022-10-20 | 2022-12-12 | 帰己二 五藤 | Plotter for angle 3 and 5 |
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