January 10th, 2008领略数字之美

让我们先来看看看下面的算式:

1 x 8 + 1= 9
12 x 8 + 2= 98
123 x 8 + 3= 987
1234 x 8 + 4= 9876
12345 x 8 + 5= 98765
123456 x 8 + 6= 987654
1234567 x 8 + 7= 9876543
12345678 x 8 + 8= 98765432
123456789 x 8 + 9= 987654321

1 x 9 + 2= 11
12 x 9 + 3= 111
123 x 9 + 4= 1111
1234 x 9 + 5= 11111
12345 x 9 + 6= 111111
123456 x 9 + 7= 1111111
1234567 x 9 + 8= 11111111
12345678 x 9 + 9= 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7= 88
98 x 9 + 6= 888
987 x 9 + 5= 8888
9876 x 9 + 4= 88888
98765 x 9 + 3= 888888
987654 x 9 + 2= 8888888
9876543 x 9 + 1= 88888888
98765432 x 9 + 0= 888888888

1 x 1= 1
11 x 11= 121
111 x 111= 12321
1111 x 1111= 1234321
11111 x 11111= 123454321
111111 x 111111= 12345654321
1111111 x 1111111= 1234567654321
11111111 x 11111111= 123456787654321
111111111 x 111111111=12345678987654321

  现在让我们研究一下其他的问题吧!

  从数学角度出发,101%>1是毋庸置疑的。然而当一个人说想要付出101%的努力又意味着什么呢?

  我们都曾经历过这样的画面:有人站在你面前,信誓旦旦的说要付出超过100%的努力。然而这可能吗?

  这里有一个小小的数学公式可以帮助你回答这个问题:

如果用1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
来代替A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

那么单词 H A R D W O R K(努力工作)
即为 8+1+18+4+23+15+18+11= 98%

然后单词 K N O W L E D G E (知识)
即为 11+14+15+23+12+5+4+7+5= 96%

单词 A T T I T U D E(态度)
即为 1+20+20+9+20+21+4+5= 100%

短语 L-O-V-E-O-F-G-O-D(上帝之爱)
即为 12+15+22+5+15+6+7+15+4= 101%

  因此,由数字得出的结论是:努力工作和知识可以让你离成功很近,态度可以助你成功,而上帝之爱才可以真正的推你到顶峰。


恩,我承认,文章是摘抄的,仔细一看还是篇宗教学术文章,不过那态度决定成功的推理还是很不错的。

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我们把这个142857从1到6按顺序乘一下,就会出现如下6组数字:

142857×1=142857    142857×2=258714

142857×3=428571    142857×4=571428

142857×5=714825    148257×6=857142

不知道大家是否发现这6组数字神奇在什么地方,仔细看的朋友也许发现了,对,这6组数字竟然是同一个142857,只是数字之间位置改变了而已…

继续…

142857这个数字乘上7,142857×7=999999,你是否很惊讶?

再把142857这个数字分解成两组数字,142,857

这两个数字之和得出142+857=999

再把142857分解成三组数字,14,28,57

这三组数字之和得出,14+28+57=99

最后我们把142857再乘于142857,结果是142857×142857=20408122449

再把20408122449分解两组数字,20408和122449

它们之和是:20408+122449=142857

游戏结束!是不是觉得这些数字很神奇啊?也不知道谁发现的,真的了不起啊…

关于其中神奇的解答:

142857

它发现于埃及金字塔内,

它是一组神奇数字,

它证明一星期有7天,

它自我累加一次,就由它的6个数字,依顺序轮值一次,

到了第7天,它们就放假,由999999去代班,

数字越加越大,每超过一星期轮回,每个数字需要分身一次,

你不需要计算机,只要知道它的分身方法,就可以知道继续累加的答案,

它还有更神奇的地方等待你去发掘!

也许,它就是宇宙的密码,

如果您发现了它的真正神奇秘密┅┅

请与大家分享!

142857×1=142857(原数字)

142857×2=285714(轮值)

142857×3=428571(轮值)

142857×4=571428(轮值)

142857×5=714285(轮值)

142857×6=857142(轮值)

142857×7=999999(放假由9代班)

142857×8=1142856(7分身,即分为头一个数字1与尾数6,数列内少了7)

142857×9=1285713(4分身)

142857×10=1428570(1分身)

142857×11=1571427(8分身)

142857×12=1714284(5分身)

142857×13=1857141(2分身)

142857×14=1999998(9也需要分身变大)

继续算下去……

以上各数的单数和都是“9”。有可能藏着一个大秘密。

以上面的金字塔神秘数字举例:1+4+2+8+5+7=27=2+7=9;您瞧瞧,它们的单数和竟然都是“9”。依此类推,上面各个神秘数,它们的单数和都是“9”;怪也不怪!(它的双数和27还是3的三次方)

无数巧合中必有概率,无数吻合中必有规律。 何谓规律?大自然规定的纪律!科学就是总结事实,从中找出规律。

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December 15th, 2007酒吧里高凳的税收政策

原文地址:Barstool Tax Policy

An ec 10 student emails me the following parable:

一位经济学的学生用电子邮件发给我下面一则故事

Suppose that every day, ten men go out for beer and the bill for all ten comes to $100. If they paid their bill the way we pay our taxes, it would go something like this:

假设一下,每天,十个人出去喝啤酒,这个十个人的酒钱是100美金,如果他们是按照我们支付税收的方式支付他们的酒钱的话,就会如下面一样。

The first four men (the poorest) would pay nothing.
前四位(最穷的,)不用付钱,
The fifth would pay $1.
第五位将支付1美金
The sixth would pay $3.
第六位将支付3美金
The seventh would pay $7.
第七位将支付7美金
The eighth would pay $12.
第八位支付12美金
The ninth would pay $18.
第九位支付18美金
The tenth man (the richest) would pay $59.
第十位(也是最富有的一位)将支付59美金
So, that’s what they decided to do.
而且,他们也决定这样做了。

The ten men drank in the bar every day and seemed quite happy with the arrangement, until one day, the owner threw them a curve. "Since you are all such good customers," he said, "I’m going to reduce the cost of your daily beer by $20." Drinks for the ten now cost just $80.

这是个人每天在酒吧里面喝酒,似乎对这样的安排很满意,直到有一天,酒吧老板给他们出了道难题。"既然你们都是如此令人满意的顾客,"他说道,"我将给你们优惠20美金。"十个人的饮料现在只要花80美金。

The group still wanted to pay their bill the way we pay our taxes, so the first four men were unaffected. They would still drink for free. But what about the other six men - the paying customers? How could they divide the $20 windfall so that everyone would get his ‘fair share?’ They realized that $20 divided by six is $3.33. But if they subtracted that from everybody’s share, then the fifth man and the sixth man would each end up being paid to drink his beer. So, the bar owner suggested that it would be fair to reduce each man’s bill by roughly the same amount, and he proceeded to work out the amounts each should pay. And so:

这组人仍然想按照我们承担赋税的方式来支付他们的账单,因此,前四个人没有影响,他们喝酒仍然免费,但是,剩下的6个人(也就是付钱的顾客)怎么办?他们应该如何瓜分这20美金的意外横财?他们意识到20美金除以6的话是3.33美金。但是如果他们扣除掉每个人应该承担的酒钱后,第五个人和第六个人每次会有人花钱请他们喝酒并且自己不用支付酒钱(第5个人每次喝酒可以赚2.33美金,第六个人每次可以赚0.33美金)因此,酒吧老板建议给每个人大致相等的优惠会公平一些,并且他进而得出每个人应该支付的数额,所以

The fifth man, like the first four, now paid nothing (100% savings).
第五个人,就如前四个一样,不用付钱(全省了)
The sixth now paid $2 instead of $3 (33%savings).
第六个人现在只要支付2美金而非3美金(省了33%)
The seventh now pay $5 instead of $7 (28%savings).
第七个人现在支付5美金而非原先的7美金(省了28%)
The eighth now paid $9 instead of $12 (25% savings).
第八个人现在只用支付9美金而非12美金(省料25%)
The ninth now paid $14 instead of $18 (22% savings).
第九个人现在只用支付14美金而非原先的18美金(节省22%)
The tenth now paid $49 instead of $59 (16% savings).
第十个人现在只用支付49美金而非原先的59美金(节省16%)

Each of the six was better off than before. And the first four continued to drink for free. But once outside the restaurant, the men began to compare their savings.

这六个人都比以前要好些,并且,前四位人继续免费的喝酒。但一旦出了餐馆,他们开始争执起来,这些人都开始比较起来他们省了多少。

"I only got a dollar out of the $20," declared the sixth man. He pointed to the tenth man," but he got $10!"

"我从这20美金中止拿出1美金来,"第六个人宣称,他指着地10个人说"但是他拿了10美金"

"Yeah, that’s right," exclaimed the fifth man. "I only saved a dollar, too. It’s unfair that he got ten times more than I!"

"恩,是的"第五个人也惊叫道:"我也仅仅只省料1美金,他拿的比我多来哦10倍,这太不公平了。"

"That’s true!" shouted the seventh man. "Why should he get $10 back when I got only two? The wealthy get all the breaks!"

"的确这样!"第七个人也叫道"为什么它能拿回来10美金而我只拿到2美金?富人得到所有的好处了。"

"Wait a minute," yelled the first four men in unison. "We didn’t get anything at all. The system exploits the poor!"

"等下" 前四个人一致喊道:"我们什么也没得到,这个规则剥削我们穷人!"

The nine men surrounded the tenth and beat him up.

这九个人围住地十个人,揍了他一顿。

The next night the tenth man didn’t show up for drinks, so the nine sat down and had beers without him. But when it came time to pay the bill, they discovered something important. They didn’t have enough money between all of them for even half of the bill!

第二天晚上第十个人没用出来喝酒,因此其余9个人坐下,喝起酒来。但是当要付账单的时候,他们发现出问题,他们之间所有人都没有钱来支付哪怕是账单一半!

And that, boys and girls, journalists and college professors, is how our tax system works. The people who pay the highest taxes get the most benefit from a tax reduction. Tax them too much, attack them for being wealthy, and they just may not show up anymore. In fact, they might start drinking overseas where the atmosphere is somewhat friendlier.

孩子们,记者以及大学教授们,这就是我们的税收系统如何工作的,纳税最多的人从减税中获利也是最大的,对他们课税太重,攻击他们了富有,他们将不再出现。实际上他们可能在气氛更加友好点的海外喝酒去了。

Apparently, there is some dispute about the authorship of the story.

显然对,对于这个故事原作者存在一些争论。

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