你的生日在圆周率第几位？

3月14日，今天是圆周率日。你的生日在圆周率第几位？

查询方法：直接在微信公众号后台发送你的生日日期8位数字就可以查询。注意，是微信公众号，不是视频号。

🤔️小作业：

1.「半径、直径、周长、面积」怎么表达？

2.「加、减、乘、除」怎么表达？

3. calculus是什么意思？

无注释原文：

It's Pi Day! But Don't Forget About These Other Amazing Numbers

From: Science Alert

March 14 is celebrated as Pi Day because the date, when written as 3/14, matches the start of the decimal expansion 3.14159… the most famous mathematical constant.

By itself, pi is simply a number, one among countless others between 3 and 4. What makes it famous is that it's built into every circle you see – circumference equals pi times diameter – not to mention a range of other, unrelated contexts in nature, from the bell curve distribution to general relativity.

The true reason to celebrate Pi Day is that mathematics, which is a purely abstract subject, turns out to describe our Universe so well. My book, The Big Bang of Numbers, explores how remarkably hardwired into our reality math is.

Perhaps the most striking evidence comes from mathematical constants: those rare numbers, including pi, that break out of the pack by appearing so frequently – and often, unexpectedly – in natural phenomena and related equations, that mathematicians like me exalt them with special names and symbols.

So, what other mathematical constants are worth celebrating? Here are my proposals to start filling out the rest of the calendar.

The Golden Ratio

For January, I nominate the Golden Ratio, phi. Two quantities are said to be in this ratio if dividing the larger by the smaller quantity gives the same answer as dividing the sum of the two quantities by the larger quantity. Phi equals 1.618…, and since there's no January 61, we could celebrate it on January 6.

First calculated by Euclid, this ratio was popularized by Italian mathematician Luca Pacioli, who wrote a book in 1509 extravagantly extolling its aesthetic properties. Supposedly, Leonardo da Vinci, who drew 60 drawings for this book, incorporated it into the dimensions of Mona Lisa's features, a choice some claim is responsible for her beauty.

The first inkling that phi occurs in nature came from another Italian, Fibonacci, while studying how rabbits multiply. A common reproductive assumption was that each pair of rabbits begets another pair every month.

Start with a single rabbit pair, and successive populations will then follow the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on – that is, get multiplied by a monthly "growth ratio" of 2.

What Fibonacci observed, though, was that rabbits spent the first cycle reaching sexual maturity and only began reproducing after that. A single pair now gives the new, slower progression 1, 1, 2, 3, 5, 8, 13, 21, 34… instead.

This is the famous sequence named after Fibonacci; notice that each population turns out to be the sum of its two predecessors.

The constant 'e'

February offers another blockbuster constant, Euler's number e, which has the value 2.718…. So mark next February 7 for the shindig.

To understand e, consider "doubling" growth again, but now in terms of the "population" of dollars in your bank account. By some miracle, your money in this example is earning you 100 percent interest, compounded each year. Each $1 invested becomes $2 at year's end.

Suppose, however, the interest is compounded semi-annually. Then 50 percent of the interest is credited midyear, giving you $1.50. You get the remaining 50 percent interest on this $1.50 at the end of the year, which works out to $0.75, giving you $2.25 ($1.50 + $0.75).

So your investment gets multiplied by 2.25, rather than 2.

What if a war broke out between banks, each offering to compound the same 100 percent interest over shorter and more frequent intervals? Would the sky be the limit in terms of your payout?

The answer is no. You could raise your growth ratio from 2 to about 2.718 – more precisely, to e – but no higher. Although you get more frequent credits, they have progressively diminishing returns.

In the late 17th century, the discovery of calculus led to a quantum leap in people's ability to grapple with the Universe. Math could now analyze anything that changed – which extended its domain to most phenomena in nature.

The constant e is famous because of its iconic role in calculus: It turns out to be the most natural growth factor to track change. Consequently, it shows up in laws describing many natural processes – from population growth to radioactive decay.

Next on our calendar of mathematical constants would come pi, of course, for March.

My nominee for April is Feigenbaum's constant delta, which equals 4.669… and measures how quickly growth processes spin off into chaos.

I'll wait for my first batch to achieve official holiday status before going any further – happy to consider any candidates you want to nominate.

- ◆ -

注：中文文本为机器翻译并非一一对应，仅供参考

含注释全文：

It's Pi Day! But Don't Forget About These Other Amazing Numbers

From: Science Alert

March 14 is celebrated as Pi Day because the date, when written as 3/14, matches the start of the decimal expansion 3.14159… the most famous mathematical constant.

3月14日被称为圆周率日（Pi Day），因为这个日期写成3/14时，与最有名的数学常数π展开后的3.14159开头一致。

1）作形容词，表示“十进制的”，英文解释为“A decimal system involves counting in units of ten.”举个🌰：

The mathematics of ancient Egypt were based on a decimal system. 古埃及数学以十进制为基础。

2）作名词，表示“小数”，英文解释为“A decimal is a fraction that is written in the form of a dot followed by one or more numbers which represent tenths, hundredths, and so on”如：simple maths concepts, such as decimals and fractions 简单的数学概念，如小数和分数。

作名词，熟词僻义，表示“常数；常量”，英文解释为“a number or quantity that does not vary”。

补充：

📍variable表示“可变情况；变量；可变因素”（a situation, number or quantity that can vary or be varied）。

By itself, pi is simply a number, one among countless others between 3 and 4. What makes it famous is that it's built into every circle you see – circumference equals pi times diameter – not to mention a range of other, unrelated contexts in nature, from the bell curve distribution to general relativity.

π本身只是一个数字，是3到4之间无数个数字中的一个。它之所以有名，是因为它内嵌于你所见到的每一个圆形中——周长等于π乘以直径——更不用说从钟型曲线分布到广义相对论等自然界中一系列其他不相关情境下的应用了。

circumference /səˈkʌmfərəns/ 表示“圆周；圆周长”，英文解释为“a line that goes around a circle or any other curved shape; the length of this line”举个🌰：

The earth is almost 25 000 miles in circumference. 地球的周长大约为25000英里。

times /taɪmz/ 表示“乘，乘以”，英文解释为“multiplied by”举个🌰：

Two times two equals four (2 × 2 = 4). 2乘2等于4。

The area of a rectangle is its height times its width. 长方形的面积等于长乘以宽。

表示“直径；对径”，英文解释为“a straight line going from one side of a circle or any other round object to the other side, passing through the centre”举个🌰：

The dome is 42.3 metres in diameter. 这个穹顶直径为42.3米。

补充：

📍radius：a straight line between the centre of a circle and any point on its outer edge; the length of this line 半径（长度）

表示“钟形曲线，贝尔曲线”，英文解释为“a line on a graph that is shaped like a bell”

表示“广义相对论；一般相对论”，英文解释为“the idea, proposed by Albert Einstein in 1915, that gravity is caused by a curving of space and time”

The true reason to celebrate Pi Day is that mathematics, which is a purely abstract subject, turns out to describe our Universe so well. My book, The Big Bang of Numbers, explores how remarkably hardwired into our reality math is.

庆祝圆周率日的真正原因是，作为一门极其抽象的学科，事实证明数学能很好地刻画我们的宇宙。我的书《数字大爆炸》（The Big Bang of Numbers）探讨了数学是如何与我们的现实紧密联系在一起的。

表示“（能力、方法、活动类型等）基本固定的；本能的（指不可改变的）”，英文解释为“If an ability, approach, or type of activity is hardwired into the brain, it is a basic one and cannot be changed.”举个🌰：

Others think that the rules for what is "musical" are hardwired into our brains to some degree. 其他人认为，我们的大脑对什么东西是“悦耳的”在某种程度上有其内在的标准。

Humans are hardwired to love fattening foods. 人会本能地喜欢那些令人发胖的食物。

🎬电影《女性思维》（The Female Brain）中的台词提到：So our brains are hardwired to produce dopamine. 所以我们的大脑天生产生多巴胺。

🎬还是电影《女性思维》（The Female Brain）：But even though we're hardwired to avoid danger, 但即便天性要我们避免危险，

📍he和be到底是什么意思？文中提到：This shows that the attraction to the final moments of an experience is hard wired in our brains, said the study, which was published in the Journal Of Neuroscience. 这项研究发表在《神经科学杂志》上，它表明，对经验的最后时刻的吸引在我们的大脑中是天生固有的。

Perhaps the most striking evidence comes from mathematical constants: those rare numbers, including pi, that break out of the pack by appearing so frequently – and often, unexpectedly – in natural phenomena and related equations, that mathematicians like me exalt them with special names and symbols.

也许最引人注目的证据来自于数学常数：那些罕见的数字，包括圆周率，由于频繁、而且往往出乎意料地出现在自然现象和相关方程中而脱颖而出，以至于数学家们会赋予其特殊的名字和符号来赞美它们。

1）表示“异乎寻常的，惊人的；引人注目的；显著的；不同寻常的”，英文解释为“Something that is striking is very noticeable or unusual.”举个🌰：

The most striking feature of those statistics is the high proportion of suicides. 那些统计数据最显著的特征是高自杀率。

2）表示“俊秀的；妩媚动人的；很有魅力的”，英文解释为“Someone who is striking is very attractive, in a noticeable way.”举个🌰：

She was a striking woman with long blonde hair. 她曾是一个留着金色长发的俊秀女子。

exalt /ɪɡˈzɔːlt/表示“盛赞”，英文解释为“To exalt someone or something means to praise them very highly.”举个🌰：

His work exalts all those virtues that we are taught to hold dear. 他的作品盛赞了所有那些我们被教导要珍视的美德。

So, what other mathematical constants are worth celebrating? Here are my proposals to start filling out the rest of the calendar.

那么，还有哪些值得庆祝的数学常数呢？以下是我的提议，可以填补日历上空缺的节日。

The Golden Ratio 黄金比例

For January, I nominate the Golden Ratio, phi. Two quantities are said to be in this ratio if dividing the larger by the smaller quantity gives the same answer as dividing the sum of the two quantities by the larger quantity. Phi equals 1.618…, and since there's no January 61, we could celebrate it on January 6.

对于一月份，我提名黄金比例φ（phi）。如果用较大的量除以较小的量的结果，与用较大的量除以两个量总和的结果相同，那么这两个量就是这个比例。φ等于1.618……，因为1月没有61日，我们可以在1月6日庆祝它。

表示“比率；比例”，英文解释为“the relationship between two groups of people or things that is represented by two numbers showing how much larger one group is than the other”举个🌰：

The school has a very high teacher-student ratio. 这所学校的师生比例很高。

表示“提名；推荐”，英文解释为“to formally suggest that sb should be chosen for an important role, prize, position, etc.”举个🌰：

He was nominated (as) best actor. 他获得了最佳男演员的提名。

熟词僻义，表示“除；除尽”，英文解释为“If you divide a larger number by a smaller number or divide a smaller number into a larger number, you calculate how many times the smaller number can fit exactly into the larger number.”举个🌰：

Measure the floor area of the greenhouse and divide it by five. 测量温室的地表面积，再除以5。

First calculated by Euclid, this ratio was popularized by Italian mathematician Luca Pacioli, who wrote a book in 1509 extravagantly extolling its aesthetic properties. Supposedly, Leonardo da Vinci, who drew 60 drawings for this book, incorporated it into the dimensions of Mona Lisa's features, a choice some claim is responsible for her beauty.

这一比例最早由欧几里得（Euclid）计算出来，后来由意大利数学家卢卡·帕西奥利（Luca Pacioli）推广开来。帕西奥利在1509年写了一本书，对其美学特性大加赞美。据说，为这本书画了60幅画的达芬奇，在蒙娜丽莎的面部尺寸中引入了这一比例，有人认为这是蒙娜丽莎之美就在于此。

popularize/polularise 表示“宣传，推广；使大众化”，英文解释为“to make something become popular”举个🌰：

It was Pavarotti in the 1980s who really popularized opera. 帕瓦罗蒂在20世纪80年代真正推动了歌剧的大众化。

extravagantly /ɪkˈstræv.ə.ɡənt.li/ 1）表示“奢侈地，铺张地；浪费地”，英文解释为“in a way that causes you to spend too much money or use too much of something”举个🌰：

It is an extravagantly priced car. 这是一辆价格昂贵的汽车。

2）表示“过度地；不切实际地”，英文解释为“in an extreme way that may be unreasonable or too much”举个🌰：

My English teacher extravagantly praised a poem I had written. 我的英语老师对我写的一首诗赞不绝口。

extol /ɪkˈstəʊl/ 表示“赞扬；赞颂；赞美”，英文解释为“to praise something or someone very much”举个🌰：

She is forever extolling the virtues of her children. 她总在夸耀自己家孩子的优点。

aesthetic /iːsˈθetɪk；esˈθetɪk/ 表示“审美的；有审美观点的；美学的”，英文解释为“concerned with beauty and art and the understanding of beautiful things”，如：an aesthetic appreciation of the landscape 用审美的眼光欣赏风景。

表示“据信；据传；据说；想象上；大概；恐怕”，英文解释为“according to what is generally thought or believed but not known for certain”

1）表示“包含；将…包括在内”，英文解释为“If one thing incorporates another thing, it includes the other thing.”举个🌰：

The new cars will incorporate a number of major improvements. 

这种新型汽车将包含许多重大的改进。

2）表示“使并入”，英文解释为“If someone or something is incorporated into a large group, system, or area, they become a part of it.”

🎬电影《草叶》（Leaves of Grass）中的台词提到：We've been wanting to incorporate more philosophy into the curriculum. 我们一直很想在课程中增加更多的哲学课程。

The first inkling that phi occurs in nature came from another Italian, Fibonacci, while studying how rabbits multiply. A common reproductive assumption was that each pair of rabbits begets another pair every month.

另一位意大利人斐波纳契（Fibonacci）在研究兔子繁殖方式时，首次发现黄金比例在自然界中出现。一个常见的繁殖假设是，每对兔子每个月都会生出另一对兔子。

表示“略知；模糊的印象”，英文解释为“a feeling that something is true or likely to happen, although you are not certain”举个🌰：

I didn't have the slightest inkling that she was unhappy. 我根本不知道她不高兴。

multiply /ˈmʌl.tɪ.plaɪ/ 表示“大幅增加；乘，使相乘”，英文解释为“to increase very much in number, or (in mathematics) to add a number to itself a particular number of times”举个🌰：

In warm weather these germs multiply rapidly. 在温暖的天气里这些细菌会迅速繁殖。

表示“生殖；生育；繁殖”，英文解释为“relating to the process of reproduction”。

beget /bɪˈɡet/ 1）表示“成为…的父亲”，英文解释为“to be the father of”举个🌰：

In the Bible it says that Adam begat Cain and Abel. 《圣经》中说亚当生了该隐和亚伯。

2）表示“引起，导致”，英文解释为“to cause”举个🌰：

Poverty begets hunger, and hunger begets crime. 贫穷导致饥饿，而饥饿则导致犯罪。

Start with a single rabbit pair, and successive populations will then follow the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on – that is, get multiplied by a monthly "growth ratio" of 2.

从一对兔子开始，接下来的数量将遵循以下序列：1、2、4、8、16、32、64、128、256……，也就是乘以每月的“增长率”2。

表示“接连地，连续地”，英文解释为“happening one after the other without any break”举个🌰：

It was the team's fourth successive defeat. 那是球队接连第4次失利。

population /ˌpɒp.jəˈleɪ.ʃən/ 还可以表示“（统称）（一定范围内的）人口，动物总数”，英文解释为“all the people or animals of a particular type or group who live in one country, area, or place”

What Fibonacci observed, though, was that rabbits spent the first cycle reaching sexual maturity and only began reproducing after that. A single pair now gives the new, slower progression 1, 1, 2, 3, 5, 8, 13, 21, 34… instead.

然而，斐波那契观察到的是，兔子在第一个周期达到性成熟后才开始繁殖。从一对兔子开始，如今新的、较慢的增长序列是：1、1、2、3、5、8、13、21、34……

maturity /məˈtʃʊə.rə.ti/ 1）表示“发育成熟，长成”，英文解释为“the state of being completely grown physically”举个🌰：

How long does it take for the chicks to grow to maturity? 小鸡多长时间才能长大？

2）表示“（心智）成熟；成熟阶段；完善的状态”，英文解释为“the quality of behaving mentally and emotionally like an adult；a very advanced or developed form or state”

3）表示“（保险合同或投资）到期，开始有回报”，英文解释为“the time when an insurance agreement or investment becomes ready to be paid”举个🌰：

The investment reaches maturity after ten years. 这项投资10年后开始获得回报。

This is the famous sequence named after Fibonacci; notice that each population turns out to be the sum of its two predecessors.

这就是以斐波那契命名的著名数列，注意到每个数都是它前面两个数之和。

表示“用…的名字给…命名”，英文解释为“to give someone or something the same name as another person or thing”举个🌰：

He was named after his grandfather. 他的名字跟他的爷爷一样。

predecessor表示“前任，前辈；原有事物，前身”，英文解释为“someone who had a job or a position before someone else, or something that comes before another thing in time or in a series”。

📍successor表示“继任者，接替者；继承人；接替的事物”，英文解释为“someone or something that comes after another person or thing”举个🌰：

This range of computers is very fast, but their successors will be even faster. 这个系列的电脑速度很快，但它的换代产品速度会更快。

The constant 'e' 常数e

February offers another blockbuster constant, Euler's number e, which has the value 2.718…. So mark next February 7 for the shindig.

二月有另一个重磅常数，欧拉数e，其值为2.718……所以下一个2月7日来纪念它吧。

表示“轰动；巨型炸弹；一鸣惊人的事物；轰动一时的书籍/电影”，英文解释为“a book or film that is very good or successful informal”，如：the latest Hollywood blockbuster 好莱坞最新大片。此前在《流浪地球》（The Wandering Earth）一文中的标题就为：The Wandering Earth is China's biggest sci-fi blockbuster.

🎬电影《创：战纪》（Tron: Legacy）中的台词提到：I would like you to meet, our next blockbuster. 我很乐意向大家呈现我们的巨作。

shindig /ˈʃɪn.dɪɡ/ 表示“喧闹的事件（或情形）；（尤指）狂欢会，盛大庆祝会”，英文解释为“a noisy event or situation, especially a large, energetic party, celebration, etc.”举个🌰：

They're going to their neighbours' for a shindig. 他们去邻居家里狂欢。

To understand e, consider "doubling" growth again, but now in terms of the "population" of dollars in your bank account. By some miracle, your money in this example is earning you 100 percent interest, compounded each year. Each $1 invested becomes $2 at year's end.

要理解常数e，请再次回顾下“翻倍”增长，但现在要考虑你银行账户中美元的“总量”。在这个例子中，凭借某种神奇力量，你的钱每年会为你赚取100%的利息，每年复利一次。每投资1美元，到年底就变成了2美元。

interest /ˈɪn.trəst/ 表示“（存款的）利息”，英文解释为“money that you earn from keeping your money in an account in a bank or other financial organization”举个🌰：

You should put the money in a savings account where it will earn interest. 你应该把钱存在有利息的储蓄户头上。

2）表示“（围起来的）场地，楼群，院落”，英文解释为“an area surrounded by fences or walls that contains a group of buildings”举个🌰：

They marched into the compound. 他们进入大院。

作动词，表示“使加重，使加剧，使恶化”，英文解释为“to make a problem or difficult situation worse”举个🌰：

Her terror was compounded by the feeling that she was being watched. 她有种被人监视的感觉，这加剧了她的恐惧感。

作动词或者形容词，还可以表示“（利息）以复利计算的”，英文解释为“used to refer to a system of paying interest in which interest is paid both on the original amount of money invested (= given to companies hoping to get more back) or borrowed and on the interest that has collected over a period of time”如：compound interest 复利。

Suppose, however, the interest is compounded semi-annually. Then 50 percent of the interest is credited midyear, giving you $1.50. You get the remaining 50 percent interest on this $1.50 at the end of the year, which works out to $0.75, giving you $2.25 ($1.50 + $0.75).

然而，假设利息每半年复利一次。然后，50%的利息在年中入账，变成1.5美元。到年底，你会得到这1.5美元剩余的50%利息，相当于0.75美元，最后变成2.25美元（1.5美元+0.75美元）。

So your investment gets multiplied by 2.25, rather than 2.

那么，你的投资额是被乘以2.25，而不是2。

What if a war broke out between banks, each offering to compound the same 100 percent interest over shorter and more frequent intervals? Would the sky be the limit in terms of your payout?

如果银行之间在竞争，每家银行都提供同样的100%复利，但复利的间隔时间更短且更频繁，那么你的收益是否会无限制增长呢？

The answer is no. You could raise your growth ratio from 2 to about 2.718 – more precisely, to e – but no higher. Although you get more frequent credits, they have progressively diminishing returns.

答案是否定的。你可以将增长率从2提高到2.718——更准确地说，是常数e，但不能再高了。尽管你会获得更频繁的收益，但它们的回报逐渐递减。

1）表示“减少；（使）减弱，缩减；降低”，英文解释为“to become or to make sth become smaller, weaker, etc.”举个🌰：

His influence has diminished with time. 随着时间的推移，他的影响已不如从前了。

2）表示“贬低；贬损；轻视”，英文解释为“to make sb/sth seem less important than they really are”举个🌰：

I don't wish to diminish the importance of their contribution. 我并不想贬低他们所作贡献的重要性。

In the late 17th century, the discovery of calculus led to a quantum leap in people's ability to grapple with the Universe. Math could now analyze anything that changed – which extended its domain to most phenomena in nature.

17世纪末，微积分的发现使人们探索宇宙的能力有了巨大的飞跃。数学现在可以分析任何变化——这将其领域扩展到自然界的大多数现象。

calculus /ˈkæl.kjə.ləs/ 表示“微积分”，英文解释为“an area of advanced mathematics in which continuously changing values are studied”

The constant e is famous because of its iconic role in calculus: It turns out to be the most natural growth factor to track change. Consequently, it shows up in laws describing many natural processes – from population growth to radioactive decay.

常数e因其在微积分中的标志性作用而闻名：事实证明，它是跟踪变化的最自然的增长因子。因此，它出现在在从人口增长到放射性衰变等许多描述自然过程的定律中。

表示“放射性的”，英文解释为“Something that is radioactive contains a substance that produces energy in the form of powerful and harmful rays. ”举个🌰：

The government has been storing radioactive waste at Fernald for 50 years.

该政府50年来一直在弗纳德储存放射性废物。

decay /dɪˈkeɪ/ 表示“（放射性物质的）衰变”，英文解释为“the process by which a radioactive substance changes to a different form, producing radiation”或者表示“腐蚀；衰败，衰弱”，英文解释为“the process of decaying”如：environmental/industrial/moral/urban decay 环境恶化/工业衰退/道德沦丧/城市衰落。

Next on our calendar of mathematical constants would come pi, of course, for March.

当然，在我们的数学常数日历上，接下来就是3月份的π。

My nominee for April is Feigenbaum's constant delta, which equals 4.669… and measures how quickly growth processes spin off into chaos.

四月份，我的提名是费根鲍姆（Feigenbaum）常数delta，等于4.669…衡量增长过程中陷入混沌状态的速度。

I'll wait for my first batch to achieve official holiday status before going any further – happy to consider any candidates you want to nominate.

我准备等我的第一批提名纪念日获批后再继续提名——很乐意考虑你想提名的任何常数。

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