如果你的计算器上没有pi……

    下面是一个有趣的小把戏:拿出一个科学型计算器(就比如说 Windows 计算器),确认你的计算器使用的是角度制。然后,输入 55555555 ,按 1/x ,再按 sin ,然后看看你的屏幕……神奇吧!如果你觉得还不够精确,输入 55555555555555555555 ,再依次按下 1/x 和 sin 看看……
    事实上,sin( (1 / 55555555555555555555)° ) = 3.141592653589793238494059.. * 10-22 ,前 20 位都和 pi 的值一模一样。显然,这绝对不可能是一个巧合。那么,这究竟是为什么呢?

    注意到 1/180 = 0.00555555… ,换句话说 55555..55 (连续 n 个 5 )的倒数就近似于 180 * 10-n-2 。另外,当 x 很小很小的时候, sin(x) 会与 x 非常接近,但在角度制中,我们必须写作 sin(x) ≈ (pi / 180) x 。因此, sin(1 / 55555..555) ≈ (pi / 180) * (180 * 10-n-2) = pi * 10-n-2

来源:http://divisbyzero.com/2010/02/17/the-math-behind-a-neat-calculator-trick/

35 条评论

  • Phil

    想起了以前那篇愚人節算Pi的日誌.

  • sippey

    问题在于一般没有pi的计算器也没有sin
    sign~

  • daizhuo

    Interesting.. Did you figure it out? I am wondering how does my calculator compute sin functions.

  • 掌柜的马甲

    我一般直接用计算器了…

  • 严酷的魔王

    我猜我能背下更多的位数。。。

  • hplonline

    发掘帝啊。。。

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  • www.28.com

    我直接用口算的,嘻嘻

  • yumimao

    我以前都是用 90032221开根四次

  • www.3158.com

    有空试试,win7的计算机不错

  • yumimao

    我的这个方法可以给2L sippey 试试

  • mystery.wd

    arccos -1

  • 影子

    有趣,像变魔术

  • Earleen

    该题太白痴了。稍有数学知识的人能有不知道的吗?

  • jcvb

    我背背就一两百位了。。

  • 霜晚

    在我的手机计算器上,这个的结果是0,于是我不得不使用算式sin(180×10^(-10))×10^10,得到3.1415926535898,然而我又发现计算器原本在等号上面的按钮就是π,结论是我的手机太智能了。

  • www.28.cn

    我在iphone也算过,和楼上的结果一样,太智能了,哈哈

  • www.3158.cn

    博主用过新买的ipad试过吗?

  • Zn

    很好很强大

  • www.28

    嗯嗯,非常好非常大,哈哈

  • vieplivee

    这个小把戏很适合给我讲给学生来听。:) 我最近弄到一个新puzzle,有兴趣来解一下──http://vvpuzzle.wordpress.com/2010/04/30/board-puzzle-from-ira/

  • 小猫

    囧上次那个中文twitter又被墙了。。还有捷径没。。

  • 白左

    lim(x→0)【sinx】=x

  • XANA

    我能背很多……大概20位,应该够用了吧?

  • JEFF

    其实有一个式子
    426880根号10005
    再除以13591409

  • zodiac1111

    大概能背28位,小学课本里几位就几位,话说一直停留在小学水平啊…

  • orbea jersey

    恩 想法蛮不错的

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