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首页> 外文期刊>American Journal of Applied Mathematics >Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts
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Trisection of Any Angle and Consequentially the Division of Any Angle Into Any Number of Equal Parts

机译:任意角度的三等分并因此将任意角度分为任意数量的相等部分

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Historically, a contrived trisected line was used to trisect any other line, using the principle of projection. This is in essence about relationship and its accomplishment is about working backwards. Loosely speaking, any angle comprises two connecting lines. Attempts at trisecting any angle, which is dividing it into three equal parts, failed. In this paper any angle is defined as a unique pair of arc and chord of sector of a circle irrespective of arc radius. Two theorems viz. Equal arcs have equal central angles and equal chords have equal central angles are combined to establish a unique relationship between a pair of arc-chord and its composite of three identical pairs of arc-chord, thereby revealing a CYCLIC TRAPEZIUM, where the base defines the angle, and each equal edge defines each of the equal trisected parts of this angle. For a range of angles between 0o and 360o, this relationship is expressed as Lorna Graph, which becomes the practical tool for trisection of any angle, using the working backwards approach. This approach is extended to division of any angle into any number of equal parts.
机译:从历史上看,使用投影原理将人为设计的三等分线用于三等分。这本质上是关于关系的,其成就是关于倒退的事情。宽松地说,任何角度都包含两条连接线。尝试将任何角度均分为三等分的尝试均失败了。在本文中,任何角度都定义为唯一的圆弧和圆弧扇形对,与圆弧半径无关。两个定理,即。相等的弧线具有相等的中心角,相等的弦线具有相等的中心角,以在一对弧线弦及其三对相同的弧弦线的合成之间建立独特的关系,从而揭示出一个CYCLIC TRAPEZIUM,其底面定义了角,并且每个相等的边定义了该角的每个相等的三等分部分。对于介于0o和360o之间的角度范围,此关系表示为Lorna图,它成为使用向后加工方法进行任何角度三等分的实用工具。该方法扩展为将任意角度划分为任意数量的相等部分。

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