Page 19 - The 'X' Chronicles Newspaper - March 2012

We’ve Got Your Number We’ve Got Your Number Real or Irrational, complex or imaginary, numbers count for something. by Newspaper Staff What’s in a number? Well, depending on which number it is, quite a lot. On a day-to-day basis, most of us only deal with a certain subset of numbers. A few integers here and there, maybe some fractions if we’re trying to slice a cake, or some negative numbers if it’s January and it’s really cold. But outside the confines of daily life, some really odd numbers are lurking. Irrational numbers. Imaginary numbers. Even transcendental numbers. How would you know a transcendental number from an irrational number? We are glad you asked. Forthwith, we provide a list of number categories. Don’t worry, they may seem daunting at first, but really, they’re as easy as pi. 1. NATURAL NUMBERS : Let’s start off with an easy set of numbers. “Natural” numbers are all the positive numbers: 1, 2, 3, 4, and so on all the way up. See, that wasn’t so hard. Only 1/3, for example, which is .33333333333333... us). You probably won’t be using imaginary slightly more complex are the whole numbers, as far as you want to carry it out. See? Nothing numbers for anything anytime soon, but as it which consist of all the natural numbers plus 0. to get freaked out about. happens, engineers find them useful in Well, big deal, you say, but just determining reactance in electronics. remember that the concept of “zero” is 5. IRRATIONAL NUMBERS: Now things are relatively new to Western thought - Europe had starting to get a little more weird. Irrational 8. COMPLEX NUMBERS: So you have your to get along without zero well into the 13th numbers can’t be expressed as integers, nor do real numbers and you have your imaginary century. The Indians, Arabs, and Mayans had ti they present themselves as repeating fractions. numbers, and what fun would it be if they never long before then. So don’t get smug (unless The fractions go on forever, but they never actually got together? Why, no fun at all, which you’re Indian, Arabic, or Mayan, in which case, repeat their sequence. The most famous is why there are complex numbers, which can go right ahead). Moving on from whole irrational number is pi, which is the ratio of the be expressed as x + iy, where x is a real number, numbers, we arrive at: circumference of a circle to its diameter: and iy is an imaginary number. Once again, a 3.14159265 is how it starts, and it keeps on practical application for these numbers comes 2. PRIME NUMBERS: A subset of natural going, irrationally, forever. from engineering. Complex numbers help to numbers. A prime number is greater than 1, and Which is not to say that people have describe electrical impedance. Those crazy is only cleanly divisible (that is, no fractions) by tried to impose rationality on it. In 1897 a bill engineers. What will they think of next! []. itself and 1. Early on, we get a lot of these - 2, was proposed in the Indiana legislature to give 3, 5, 7, 11, 13 - but the further you go down the pi a specific, finite value. It passed unanimously From The ‘X’ Zone line, the more these prime numbers space in the Indiana House of Representative but was themselves out (because, of course, the larger killed in the Senate after Indiana was roundly Book of FACT*oids number get, the more likely they are to be mocked by everyone else in the world for its divisible by lessor numbers). For all that, primes poor math skills. - Every day your kidneys filter about 200 quarts continue to pop up, even among tremendously Incidentally, pi is also a member of a of fluid. large numbers. The largest prime yet discovered particular subset of irrational numbers known as - The shells of cashew nuts contain caustic oil (at this writing anyway) is 4,053,946 digits transcendental numbers, whose definition is as that can blister the skin. long. That’s a mighty big number. follows: a real number that is not the solution of - The number one cause of daytime fatigue is a any single-variable polynomial equation whose lack of water. 3. INTEGERS: All natural numbers, plus zero, coefficients are all integers. - A butterfly’s life span ranges from a week to and then all the negative values of natural ten days. numbers: -1, -2, -3, -4, and so on. Sure, negative 6. REAL NUMBERS: Real Numbers are all - Male cats that are colored both orange and numbers are a little weird - it’s strange to think the numbers we’ve discussed so far: whole, black are sterile. of something as being less than zero - but since rational, and irrational. Well, duh, you say. If - Dogs can make around 10 vocal sounds; cats negative integers pop up in everything from numbers aren’t real, what would you call them? can make over 100. thermometers to simple charts, we’re used to We’re glad you asked! You call them: - Doges see objects in this order: by movement, them. by brightness, and then shape. 7. IMAGINARY NUMBERS: Bo, these aren’t - In the last century Americans’ time spent 4. RATIONAL NUMBERS: Uh-oh, here come the imaginary friends of mathematicians sleeping has decreased 20%. the fractions. But as far as fractions go, rational who’ve inhaled too many marker fumes. - Frogs croak more before a rainstorm. numbers are pretty harmless, since they’re Imaginary numbers are defined as any real - As you age, your thymus gets smaller in size. defined as all numbers that can be expressed as number multiplied by a little something called - Lettuce is part of the sunflower family. x/y, where both x and y are integers. So, the “imaginary unit,” or “i” in shorthand. The - Eating celery burns more calories than the numbers like 1/2, 1/4, 1/8, and so on. Integers imaginary unit is understood to be the positive celery contains. are rational numbers since they can be square root of -1 (in engineering, i is also known - The first humanoid fossil found was a skull expressed as themselves over 1: 3/1, for as “j” or the “j operator,” apparently because fragment unearthed in Germany in 1856. example, is 3. Rational numbers also include engineers like being different from the rest of - A baby panda is smaller than a stick of butter. fractions that endlessly repeat in decimal form: