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首页> 外文期刊>21st Century Science & Technology >On the Expression in Rational Numbers of The Exact Relationship of a Circle To Its Circumscribed Square
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On the Expression in Rational Numbers of The Exact Relationship of a Circle To Its Circumscribed Square

机译：圆与外接圆的精确关系的有理数表达

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Geometers have always worked to establish the relationship between curved and straight lines; yet even now that we have the help of algebra, we have still not gained a good mastery of this question, at least not by applying the methods in use today. For it is impossible to reduce these problems to algebraic equations; yet it is still wonderfully useful to apply geometric formulas in engineering, as some of the most eminent mathematicians who have investigated the problem have not failed to observe. It was Archimedes who, to all appearances, first found the relationship among the cone, sphere, and cylinder having the same height and base to be that of the numbers 1, 2, 3—the cylinder being three times the cone and one-and-a-half times the sphere—which gave him the idea of having a sphere and cylinder engraved on his tomb; he also discovered the quadrature of the parabola. In the course of this century, means have been found to measure a number of curvilinear figures, notably when the ordinates BC stand in multiple or sub-multiple [fractional] proportion of any given degree, direct or reciprocal, to the abscissas AB or DC. [As we would say, when Y = X~m where m is any integer or rational fraction other than -1.—LH] The relationship of the figure ABCA to the circumscribed rectangle ABCD will be that of unity to the number expressing the multiplicity [power] of the ratio, plus 1.
机译：几何图形一直致力于建立曲线和直线之间的关系。但是即使在有了代数的帮助下，我们仍然没有很好地掌握这个问题，至少没有通过应用当今使用的方法。因为不可能将这些问题简化为代数方程。然而，将几何公式应用到工程中仍然非常有用，因为一些研究问题的最杰出的数学家们并没有发现失败。是阿基米德，从所有出现开始，首先发现具有相同高度和底数的圆锥体，球体和圆柱体之间的关系是数字1、2、3的关系，圆柱体是圆锥体的三倍，而圆柱体是-球形的一半-使他想到在坟墓上刻一个球形和圆柱体。他还发现了抛物线的正交性。在本世纪的过程中，已经找到了测量许多曲线图形的方法，特别是当坐标BC与横坐标AB或DC的任意给定度数成正比或倒数时，其倍数或约数[分数]比例时。 [我们要说的是，当Y = X〜m时，m是除-1以外的任何整数或有理数。-LH]图形ABCA与外接矩形ABCD的关系将与表示多重性的数字的整数一致[功率]的比率，再加上1。

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