第17章 割圆之法
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87_87010计侨心中无数头羊驼驼飞奔而过，居然被无恤算出来了！还算对了！
“这么快？”
“怎么可能这么快！”
他连忙想再去细看赵无恤演算的那些奇异符号和竖式，却见赵无恤脚一动，将它们统统抹去！
计侨心疼得直捂肚子，他感觉自己已经接近了一种前所未有的算法技巧，一旦学得，将开启数科新的时代！
也许，古算经中所记述的，“夫天可不阶而升，地不可得尺寸而度”的经天纬地之术，就不再会是传说！
他立刻换上了笑脸讨好道：“小君子不要胡闹，快将这算法说与我听听。”
赵无恤却偏要为难他一下：“先生已经考校过小子了，不知道小子能不能考校考校先生？”
“这个……”
“若是先生能答上小子的题目，小子定将这新颖算法拱手献上，毫不保留。”
计侨对筹算之术引以为傲，放眼晋国没有多少敌手，少有算题能将他难住，于是他今天脾气也上来了，稀里糊涂地就答应了赵无恤的挑战。
赵无恤在沙盘上画了个圆，口中道：“圆，一中同长也，这圆的直径长一尺，周长未知，先生能求得此圆的精确面积是多少么？”
计侨看罢，气呼呼地回答：“算经有载，周三径一，周长是直径的三倍，而半周半径相乘得积步，如此简单的问题，小君子是在小觑我么？”
赵无恤摸了摸无须的下巴嘿嘿笑道：“先生啊先生，枉你被称为赵氏算学第一，你觉得所谓周三径一真的准确么？”
计侨心中突突直跳，看赵无恤的眼神顿时就不一样了，周三径一是此时计算圆面积的普遍算法，实际上却有很大偏差，这也是困扰诸多算学专家和制车轮、陶轮工匠的大难题。
但其中的奥妙，也只有他这种数科大神能得窥一二。用“周三径一”计算出来的圆周长，实际上不是圆的周长而是圆内接正六边形的周长，其数值要比实际的圆周长小得多。
但那个神秘的比例到底如何求得，这是自从计侨八岁学数科以来，一直苦思不得其解的问题。
“请小君子教我！”对于计侨来说，什么师道尊严，都没有追求数科真理重要，他只差跪地稽首了！
赵无恤也不再难为他，继续在地上画画：“先生请看，如果我们可以在圆内接正六边形把圆周等分为六条弧的基础上，再继续等分，把每段弧再分割为二，做出一个圆内接正十二边形，这个正十二边形的周长不就要比正六边形的周长更接近圆周了吗？”
“所以，如果把圆周分割得细，误差就越少，其内接正多边形的周长就越是接近圆周。如此不断地分割下去，一直到圆周无法再分割为止，它的周长就与圆周几乎完全一致了！”
计侨如同一个小学蒙童般，听得如痴如醉，不住地头，心中直叹赵无恤才是真正的算学天才，竟然能想到如此巧妙的方法。
可恨自己刚才还想用那道“简单”的题难住他，还想指他……真是，真是羞愧难当啊，计侨只想找个地缝钻进去。
赵无恤展示的，其实就是割圆术，后世初中生都会的东西……但在此时，这个理论还得经过七百多年的发展，到魏晋时期才会被刘徵、祖冲之等人发现。欧洲人则要早一些，大科学家阿基米德在两百年后得出了相近的结果，但要精确到小数后六位数，就得等到十六、十七世纪了。
所以，计侨这位春秋数学家要能知道，那才有鬼。
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