十万个为什么

继续迷恋数学，这次读到了圆周率，就是pi。记得上中学历史课的时候，学到中国古代科学家祖冲之，他最突出的贡献就是把圆周率精确到小数点后7位，并自豪的说祖冲之最先计算出精确的圆周率。

这个说法是根据《隋书·律历志》中的记载。那上面 说：“古之九数，圆周率三，圆径率一，其术疏舛。自刘歆、张衡、刘徽、王蕃、皮延宗之徒，各设新率，未臻折衷。宋末，南徐州从事史祖冲之更开密法，以圆径 一亿为一丈，圆周盈数三丈一尺四寸一分五厘九毫二秒七忽，朒数三丈一尺四寸一分五厘九毫二秒六忽，正数在盈朒二限之间。密率，圆径一百一十三，圆周三百五 十五。约率，圆径七，周二十二。又设开差冪，开差立，兼以正圆参之。指要精密，算氏之最者也。所著之书，名为《缀术》，学官莫能究其深奥，是故废而不 理。”

“我国历史上首先用数学方法推算圆周率的，是汉代的大学者刘歆（公元二三年为王 莽所杀），他的圆周率是31547。张衡（公元七八年——公元一三九年）是我国著名的天文学家，他的周率是√10。刘徽（公元二六三年前后时人），他用割 圆术来推算，即圆内画一六边形，逐渐增加边数，这多边形与圆会越来越接近，计算多边形的边，算到九十六边形时，周率定为314。王蕃（公元二一九——公元 二五七年）是14245＝3155，皮延宗（公元四四五年前后时人）的周率考查不出来。据李俨的《中国算学史》中说，在祖冲之之前，还有一位何承天（公元 三七○——四四七年），周率为22/7，即31428。这些周率都不精密”。

其实人类历史上，不同的文明都先后计算出精度不等的圆周率，所谓圆周率就是一个圆的周长除以其直径，这是一个非常古老的问题，早在公元前2000年左右，古巴比伦人就知道一个圆的周长是其直径的大约3倍。到公元前225年，古意大利的阿基米德估算出圆周率是在223/71到220/70之间，简单的说就是pi等于22/7。之后就应该是中国的祖冲之所计算的3.1415926到3.1415927之间，以后一直到1768年，Johann Lambert算出小数点后20位，并声称这个pi是个不规则数，到1853年，William Shanks算到小数点后527位，1949年，美国的计算机ENIAC花费了70个小时算到2037位，2002年，超级计算机算到了1,241,100,000,000位，如果把这些数并排写到纸上，纸的长度可以绕地球62圈。

很多人一直怀疑圆周率是否真的是个随机的没有规则的数，例如0123456789这个序列是否存在，1950年，荷兰的数学家Brouwer说这个序列是在圆周率中是不可能存在的，但1997年，人们在小数点后17,387,594,880位发现了这个序列，在更远的地方还发现了连续的10个6。

圆周率的一些变种也产生了很多奇妙的数字组合，例如pi/4=1-1/3+1/5-1/7+1/9-1/11……，还有pi²/6=1+1/2²+1/3²+1/4²+1/5²……。

圆周率可以用来检测计算机的运行速度，也可以考验人的记忆力，据说有的人能记住小数点后几千位，中国不知道什么时候的几句诗非常能帮助人记住这个数，“山巅一寺一壶酒（3.14159）,尔乐苦煞吾（26535）,把酒吃（897）,酒杀尔（932）,杀不死（384）,乐尔乐（626）”。

而英文的一首诗则写出了小数点后的740位。

Poe, E.
Near a Raven

Midnights so dreary, tired and weary.
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap – the weirdest tap!
An ominous vibrating sound disturbing my chamber’s antedoor.
“This”, I whispered quietly, “I ignore”.

Perfectly, the intellect remembers: the ghostly fires, a glittering ember.
Inflamed by lightning’s outbursts, windows cast penumbras upon this floor.
Sorrowful, as one mistreated, unhappy thoughts I heeded:
That inimitable lesson in elegance – Lenore -
Is delighting, exciting…nevermore.

Ominously, curtains parted (my serenity outsmarted),
And fear overcame my being – the fear of “forevermore”.
Fearful foreboding abided, selfish sentiment confided,
As I said, “Methinks mysterious traveler knocks afore.
A man is visiting, of age threescore.”

Taking little time, briskly addressing something: “Sir,” (robustly)
“Tell what source originates clamorous noise afore?
Disturbing sleep unkindly, is it you a-tapping, so slyly?
Why, devil incarnate!–” Here completely unveiled I my antedoor–
Just darkness, I ascertained – nothing more.

While surrounded by darkness then, I persevered to clearly comprehend.
I perceived the weirdest dream…of everlasting “nevermores”.
Quite, quite, quick nocturnal doubts fled – such relief! – as my intellect said,
(Desiring, imagining still) that perchance the apparition was uttering a whispered “Lenore”.
This only, as evermore.

Silently, I reinforced, remaining anxious, quite scared, afraid,
While intrusive tap did then come thrice – O, so stronger than sounded afore.
“Surely” (said silently) “it was the banging, clanging window lattice.”
Glancing out, I quaked, upset by horrors hereinbefore,
Perceiving: a “nevermore”.

Completely disturbed, I said, “Utter, please, what prevails ahead.
Repose, relief, cessation, or but more dreary ‘nevermores’?”
The bird intruded thence – O, irritation ever since! -
Then sat on Pallas’ pallid bust, watching me (I sat not, therefore),
And stated “nevermores”.

Bemused by raven’s dissonance, my soul exclaimed, “I seek intelligence, Explain thy purpose, or soon cease intoning forlorn ‘nevermores’!”
“Nevermores”, winged corvus proclaimed – thusly was a raven named?
Actually maintain a surname, upon Pluvious seashore?
I heard an oppressive “nevermore”.

My sentiments extremely pained, to perceive an utterance so plain,
Most interested, mystified, a meaning I hoped for.
“Surely,” said the raven’s watcher, “separate discourse is wiser.
Therefore, liberation I’ll obtain, retreating heretofore -
Eliminating all the ‘nevermores’ “.

Still, the detestable raven just remained, unmoving, on sculptured bust.
Always saying “never” (by a red chamber’s door).
A poor, tender heartache maven – a sorrowful bird – a raven!
O, I wished thoroughly, forthwith, that he’d fly heretofore.
Still sitting, he recited “nevermores”.

The raven’s dirge induced alarm – “nevermore” quite wearisome.
I meditated: “Might its utterances summarize of a calamity before?”
O, a sadness was manifest – a sorrowful cry of unrest;
“O,” I thought sincerely, “it’s a melancholy great – furthermore,
Removing doubt, this explains ‘nevermores’ “.

Seizing just that moment to sit – closely, carefully, advancing beside it,
Sinking down, intrigued, where velvet cushion lay afore.
A creature, midnight-black, watched there – it studied my soul, unawares.
Wherefore, explanations my insight entreated for.
Silently, I pondered the “nevermores”.

“Disentangle, nefarious bird! Disengage – I am disturbed!”
Intently its eye burned, raising the cry within my core.
“That delectable Lenore – whose velvet pillow this was, heretofore,
Departed thence, unsettling my consciousness therefore.
She’s returning – that maiden – aye, nevermore.”

Since, to me, that thought was madness, I renounced continuing sadness.
Continuing on, I soundly, adamantly forswore:
“Wretch,” (addressing blackbird only) “fly swiftly – emancipate me!”
“Respite, respite, detestable raven – and discharge me, I implore!”
A ghostly answer of: “nevermore”.

” ‘Tis a prophet? Wraith? Strange devil? Or the ultimate evil?”
“Answer, tempter-sent creature!”, I inquired, like before.
“Forlorn, though firmly undaunted, with ‘nevermores’ quite indoctrinated,
Is everything depressing, generating great sorrow evermore?
I am subdued!”, I then swore.

In answer, the raven turned – relentless distress it spurned.
“Comfort, surcease, quiet, silence!” – pleaded I for.
“Will my (abusive raven!) sorrows persist unabated?
Nevermore Lenore respondeth?”, adamantly I encored.
The appeal was ignored.

“O, satanic inferno’s denizen — go!”, I said boldly, standing then.
“Take henceforth loathsome “nevermores” – O, to an ugly Plutonian shore!
Let nary one expression, O bird, remain still here, replacing mirth.
Promptly leave and retreat!”, I resolutely swore.
Blackbird’s riposte: “nevermore”.

So he sitteth, observing always, perching ominously on these doorways.
Squatting on the stony bust so untroubled, O therefore.
Suffering stark raven’s conversings, so I am condemned, subserving,
To a nightmare cursed, containing miseries galore.
Thus henceforth, I’ll rise (from a darkness, a grave) — nevermore!

– Original: E. Poe
– Redone by measuring circles.

这首诗的秘密是这样的，每个单词的字母长度就是所代表的阿拉伯数字，如果正好是10个字母，这个单词就代表0，如果超过10个字母，就代表2个数字，例如12个字母的单词，就是数字1和2。

真的是太神奇了！

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