Math in Everyday LifeDate: 10/17/2002 at 18:58:21 From: Chelsea Wolfert Subject: How do you use math in your everyday life? How do you use math in your everyday life? Date: 10/18/2002 at 19:06:37 From: Doctor Achilles Subject: Re: How do you use math in your everyday life? Hi Chelsea, Thanks for writing to Dr. Math. I can think of two possible ways to interpret your question. The first is that you want to know what it is I do for a living and how math relates to that on a daily basis. The second is that you want to know how I use math in my non-career life. I'll attempt to answer each of these questions. Regarding the first (what I do for a living and how I use math in my job): I am a biomedical researcher, and math is essential to what I do. I study how cells work; I'm particularly interested in how calcium molecules are used as a way for cells to communicate with each other. There are molecules inside cells which, when they come into contact with calcium, change their shape and then go on to cause other changes inside the cell. You might think at first that if you double the concentration of calcium inside the cell, you will double the amount of signaling. This is a good first guess. Let's think for a second about what that would mean. Let's use the variable "y" to stand for the amount of signaling and the variable "x" to stand for the concentration of calcium. We can write the equation: y = mx So if we double x, then y will also double. m is the slope of this relation, which you can find by doing experiments. But it turns out to be much more complicated than that. There is some debate exactly what the relation is between calcium concentration and signaling, but it seems that doubling the concentration of calcium will increase signaling by about sixteen times (at low calcium concentrations) and can have drastically different effects at higher concentrations. The relation between concentration of calcium and amount of signaling actually is a complicated equation containing logarithms, all sorts of exponents, and other complicated mathematical operations. There are dozens of other ways I use math in my career, but this is just one example. Regarding the second question: how I use math outside my career. Again, there are many ways I can think of. First, I like to play card games. In order to be good at them, I need to calculate probabilities quickly and accurately. For example, if 6 spades have been played, that means there are 7 spades that have not been played. If I have 3 spades, that leaves 4 unaccounted for. So what is the probability that each of the other three players has spades in his or her hand? I also buy groceries and make other purchases. If one box of napkins has 200 for $3.12 and another box has 250 for $3.99, which is the better deal? If my car goes 260 miles on 9.15 gallons of gasoline, how many miles am I getting per gallon? If on the next tank, it goes 200 miles on 8.45 gallons, then is it starting to get bad mileage and do I need to take it to a mechanic, or is it okay? If I'm travelling, and there is a room which I can split with 3 other people for x dollars/ night, and another room which I can split with one other person for y dollars/night, which is the better deal? How can I tell? How much money do I have in my bank account? How much do I owe on my credit card? What will the interest on my credit card cost me if I don't pay the entire bill this month? I like to cook as well. If the recipe calls for one pound of beef and 1/3 cup oil, but I want to make half as much, how much beef should I use? How much oil? What if I want to make one and half times as much? How much should I make for a given number of people? It's 4:03 now, if the recipe cooks for 75 minutes, what time will it be done? I also play video games that have puzzles to solve. This requires math and logic as well. These are just the ways in which I've used math in the last week or so. The list goes on and on. Hope this helps. If you have other questions about this, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/ Date: 10/19/2002 at 08:36:49 From: Doctor Jeremiah Subject: Re: How do you use math in your everyday life? Hi Chelsea, I (like everyone else) use math both in my career and in my non-career life. I write computer software and math is a very big part of that. You probably know that computers don't understand English. In fact, they don't even understand real numbers. All they know about is whether the electricity at that transistor is on or off. So numbers (and everything else) in a computer are based on a bunch of electrical signals. It turns out that if you get these on/off signals organized you can make numbers in binary. With decimal based numbers there are ten different symbols that can be used to make numbers: 0 1 2 3 4 5 6 7 8 9 . But in binary there are only two: 0 (off) 1 (on). So when you count in decimal you use the digits from 0 up to 9. But what is the next number after 9? There are no more symbols left, so you go back to 0 and add another column. So the next value after 9 is 10. It's the same in binary. You start at 0 and count until you run out of digits, and then you start back at 0 with another column. So counting in binary goes: 0 1 10 11 100 101 ... So a binary number like 101101001 is really 361 in decimal. How do you convert between binary and decimal? Well, there are exponents and remainders from division involved. That's just one example, but changing number bases is very important in careers that involve computers. When I am not writing software or answering math questions at Dr. Math I sometimes shoot off model rockets. It's a fun hobby! But I want to know how high my rockets go. Without having a huge ruler how would you do this? I don't know if you have heard of trigonometry, but it is mathematics about angles. If I stand a known distance from the rocket's launchpad and I shoot the rocket off, when the rocket is at its absolute top if I measure the angle between the ground and the rocket I can calculate the height. This works for the height of anything, by the way, not just rockets. It's not the only way to measure the height of a rocket. If you don't have a protractor with you to measure the angle, you can do it with a watch. All you need to do is measure the length of time from when the rocket gets to the top until it gets back to the ground. Then you can calculate the height because you know that the accelaration of gravity is constant. Even baking requires math, and I love to bake (and eat) cookies. I have a recipe for cookies that is really good, but I wanted to take some cookies to work to share. I wanted enough for my whole team. The recipe makes about 3 1/2 dozen cookies, but I figured I would need about 200 cookies if I took them to share with my work mates. I don't remember the exact numbers right now so I am going to guess. I am going to use U.S. measurements, so if you aren't from the United States, please forgive me. If the recipe called for 2 2/3 cups of flour and I wanted enough batter for 200 cookies, how much flour would I use? Worse yet, if the recipe called for 1 1/2 teaspoons of vanilla, how much would I need for 200 cookies? I wouldn't want to do it with teaspoons (it would take forever) so how many tablespoons would that be? Or would cups be better? Here is another example. Say you are at the store and you want to buy something like flour for all those cookies. They have two sizes: one is 3 1/2 times the size of the other. The small one costs $3.79 and the large one costs $11.99. Which one is the better deal? And what if there is more than one brand to choose from? Then it would get really complicated! Did you know that music is actually math in disguise? I won't go into it, but there is a lot of stuff in the archives about that. You can search for answers in the archives using the Dr. Math searcher: http://mathforum.org/library/drmath/mathgrepform.html - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ |
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