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数学英语 32 How to Use Math to Make Estimates

时间:2010-11-19 03:50来源:互联网 提供网友:fi1171   字体: [ ]
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by Jason Marshall

In the first “secret-agent math” article, “How to Use Math to Send Encrypted Messages,” we learned how to decrypt messages secured with absolutely unbreakable encryption using nothing more than simple integer arithmetic. It was all great fun, but by the end of the article you, the character in our story had been kidnapped! Today, the plot continues—read on to find out what happens.
But first, the podcast edition of this article was sponsored by Go to Meeting. With this meeting service, you can hold your meetings over the Internet and give presentations, product demos and training sessions right from your PC. For a free, 45 day trial, visit GoToMeeting.com/podcast.
 
How Long Can You Survive in a Sealed Room?
At the end of the last “secret-agent math” article, you’d been whisked away from a coffee shop by a group of kidnappers1. Now, several hours later after a long and bumpy2 car ride you hear the engine shut off. You’re pulled from the trunk, led down a long hallway, and then tossed into a small dimly-lit room. Your captors tell you that the room has been tightly sealed, that it has no ventilation, and that you’d better hope your employers meet their ransom3 demands before you run out of breathable air. Needless to say, you’re a bit troubled by all this. But you’re also a secret agent—so instead of sulking you decide to start working on getting yourself out.
What to do first? Well, you realize you first need to figure out how much time you have to escape before you run out of air so that you know just how quickly you need to work. And for the first time in our story, you—the secret agent you, that is—are stumped4. You realize that while you learned all sorts of things in school and in your spy training, nobody ever taught you how to calculate this sort of thing. Your breathing picks up as you get nervous. Realizing that your reaction is wasting air, you take a moment, steady your breath, and think. You resolve to start from the beginning, take things step-by-step, and figure it out.
How Can You Calculate the Volume of a Room?
You reason that if you figure out how big the room is and how big each of your breaths are, then you should be able to figure out how many breaths of air the room contains. So, how big is the room? Walking from one side to the other you find that it’s about three steps across. You know that one of your steps is a little more than three feet, so you figure the room is about ten feet wide (3 x 3 = 9, plus a little more because your steps are more than 3 feet is about 10). The room looks pretty square so you figure it must also be about ten feet long. And the height of the ceiling seems a little higher than the heights of your ceilings at home, which you can just touch if you jump and know are eight feet high. You jump in your cell and find that you can reach to within about one foot of the ceiling, so you figure the ceiling must be about nine feet high. So, you’re stuck in a room that’s 10 feet wide, 10 feet deep, and 9 feet high—and that means you have 10 feet x 10 feet x 9 feet = 900 cubic feet of air! In other words, if you had a box that’s one foot long on each side, you’d have 900 of those boxes full of air. Though that’s not terrible, it’s not the best news either.
What is the Volume of a Single Breath?
But what’s the volume of one of your breaths? When you’re faced with a question like this, the quick and dirty tip is to try and use everyday references to help you make educated guesses (just as you used your ceilings at home as a reference to figure out the height of the ceiling in your cell). At one point or another most of us have exhaled5 into and filled up a plastic sandwich bag just before popping it. The volume of air in one of your breaths must, therefore, be about the same as the volume of air in an inflated6 sandwich bag. But how much air is that? Well, an inflated bag has an odd shape, so it’s hard to say exactly; but a sandwich bag is very roughly the same size as an orange. And an orange is very roughly the same size as a box about three inches on a side. So, the volume of one of your breaths must be about 3 inches x 3 inches x 3 inches = 27 cubic inches. Or, since three inches is the same as one-quarter foot, one of your breaths has a volume of 1/4 foot x 1/4 foot x 1/4 foot = 1/64 cubic feet.
How Many Breaths of Air are in the Room?
At this point you mutter to yourself: “If the volume of air in a single breath would fit into a cube three inches on a side, then all I have to do is figure out how many of those cubes of air will fit inside this room—that’s the number of breaths I have left before….” Your mind races as you worry that you may have already used up most of these cubes of air. But, again, you calm down and go on to reason that since you know the volume of air in the room, and the volume of air in one of your breaths, the number of breaths in the room is just the volume of the room divided by the volume of a single breath. Or, since each breath has a volume of 1/64 cubic feet, that means that each cubic foot of air must contain 64 breaths. But you also know that you have 900 total cubic feet of air in the room, which means that the room contains 64 x 900 = 57,600 breaths. What a relief—that’s a lot of breaths! Isn’t it?
How Much Time Do You Have to Escape?
Well, just how long does that actually give you to escape? You realize that you need one last piece of information: How often do you breathe? So, you count the number of breaths you take in a minute. On average, most people breathe 15 to 20 times a minute. Since you’re under a fair bit of stress, it’s no surprise that you’re breathing about 20 times per minute. That comes out to 28,800—or approximately 30,000—breaths per day (that’s 20 breaths per minute, times 60 minutes per hour, times 24 hours per day). Dividing the 57,600—or roughly 60,000—total breaths in the room by the 30,000 breaths you take per day, you find that you have about a two-day supply of air. Now that really is a relief! Feeling calm and confident that your capable colleagues will rescue you within this two day time-frame, you decide to stop worrying and instead pull out your phone to post a funny picture of you sitting in your cell to Facebook. And then, you take a nap.
Don’t Be Afraid to Think!
So, what’s really the point of all this? Well, as our secret agent has learned, math isn’t about solving a bunch of problems within a fixed7 time-limit (unless you’re taking the SAT). It’s about facing situations that you’re not familiar with and drawing upon the knowledge you’ve accumulated to devise solutions. So here’s the quick and dirty tip: Think! Think your way through problems. If it seems too hard, try anyway. The more you try to make estimates and figure things out using math, the more frequently you’ll be successful.
Wrap Up
Okay, that’s all the math we have time for today. Thanks again to our sponsor this week, Go to Meeting. Visit GoToMeeting.com/podcast and sign up for a free 45 day trial of their online conferencing service.
Please email your math questions and comments to................You can get updates about the Math Dude podcast, the “Video Extra!” episodes on YouTube, and all my other musings about math, science, and life in general by following me on Twitter. And don’t forget to join our great community of social networking math fans by becoming a fan of the Math Dude on Facebook.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

 


点击收听单词发音收听单词发音  

1 kidnappers cce17449190af84dbf37efcfeaf5f600     
n.拐子,绑匪( kidnapper的名词复数 )
参考例句:
  • They were freed yesterday by their kidnappers unharmed. 他们昨天被绑架者释放了,没有受到伤害。 来自《简明英汉词典》
  • The kidnappers had threatened to behead all four unless their jailed comrades were released. 帮匪们曾经威胁说如果印度方面不释放他们的同伙,他们就要将这四名人质全部斩首。 来自《简明英汉词典》
2 bumpy 2sIz7     
adj.颠簸不平的,崎岖的
参考例句:
  • I think we've a bumpy road ahead of us.我觉得我们将要面临一段困难时期。
  • The wide paved road degenerated into a narrow bumpy track.铺好的宽阔道路渐渐变窄,成了一条崎岖不平的小径。
3 ransom tTYx9     
n.赎金,赎身;v.赎回,解救
参考例句:
  • We'd better arrange the ransom right away.我们最好马上把索取赎金的事安排好。
  • The kidnappers exacted a ransom of 10000 from the family.绑架者向这家人家勒索10000英镑的赎金。
4 stumped bf2a34ab92a06b6878a74288580b8031     
僵直地行走,跺步行走( stump的过去式和过去分词 ); 把(某人)难住; 使为难; (选举前)在某一地区作政治性巡回演说
参考例句:
  • Jack huffed himself up and stumped out of the room. 杰克气喘吁吁地干完活,然后很艰难地走出房间。
  • He was stumped by the questions and remained tongue-tied for a good while. 他被问得张口结舌,半天说不出话来。
5 exhaled 8e9b6351819daaa316dd7ab045d3176d     
v.呼出,发散出( exhale的过去式和过去分词 );吐出(肺中的空气、烟等),呼气
参考例句:
  • He sat back and exhaled deeply. 他仰坐着深深地呼气。
  • He stamped his feet and exhaled a long, white breath. 跺了跺脚,他吐了口长气,很长很白。 来自汉英文学 - 骆驼祥子
6 inflated Mqwz2K     
adj.(价格)飞涨的;(通货)膨胀的;言过其实的;充了气的v.使充气(于轮胎、气球等)( inflate的过去式和过去分词 );(使)膨胀;(使)通货膨胀;物价上涨
参考例句:
  • He has an inflated sense of his own importance. 他自视过高。
  • They all seem to take an inflated view of their collective identity. 他们对自己的集体身份似乎都持有一种夸大的看法。 来自《简明英汉词典》
7 fixed JsKzzj     
adj.固定的,不变的,准备好的;(计算机)固定的
参考例句:
  • Have you two fixed on a date for the wedding yet?你们俩选定婚期了吗?
  • Once the aim is fixed,we should not change it arbitrarily.目标一旦确定,我们就不应该随意改变。
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