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The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse

Page 27

by Jennifer Ouellette


  sines

  Pestalozzi, Johann

  Peters, Lulu Hunt

  Philip, King

  physics

  π

  Pines Calyx

  Pirates of Penzance, The (Gilbert and Sullivan)

  plague

  Plane Loci (Apollonius of Perga)

  Plato

  Plutarch

  pneumonic plague

  Poetics (Aristotle)

  population

  position

  determining, from speed

  determining speed from

  in Devil Dive ride

  in Space Mountain ride

  in surfing

  in Tower of Terror ride

  Pride and Prejudice and Zombies (Grahame-Smith)

  Principia (Newton)

  Principle of Population, The (Malthus)

  probability

  Buffon’s needle and

  sample space in

  Psychological Science

  Pullman, Philip

  pyramid

  rational numbers

  Recorde, Robert

  Rees, Peter

  Reflections on the Motive Power of Fire (Carnot)

  ReRev.com

  Robespierre, Maximilien

  Rogent, Elies

  Romero, George

  Roughing It (Twain)

  roundworms

  Rousseau, Jean-Jacques

  Ruth, Babe

  Saarinen, Eero

  sample space

  Saturn

  Science

  Scripps Institute

  Second Life

  Seife, Charles

  septicemic plague

  Short, Thomas

  sigmoid curve

  Simond, Paul-Louis

  sines

  sinusoids

  six degrees of separation

  Six Flags

  $64,000 Question, The

  Smart Cars and Smart Roads

  Smith, Reginald

  Smith?, Robert

  Smith, William Benjamin

  Snow, John

  social networks

  Soll, Jack

  sound waves

  digital signal processing and

  Southern Fried Science

  Space Mountain

  Spectator

  speed (velocity)

  determining, from position

  determining position from

  in Devil Dive ride

  evaporation rate and

  in Space Mountain ride

  in surfing

  in Tower of Terror ride

  speed limits on highways

  speedometers

  Splash Mountain

  Squaring the Circle: Geometry in Art and Architecture (Calter)

  Standard Mathematical Tables

  Staphylococcus aureus

  Star Wars: Episode III—Revenge of the Sith

  steam engines

  Stefansson, Vilhjalmur

  step reckoner

  stereotype threat

  straight line

  finding slope of

  sunsets

  surfing

  Sustainable Dance Club

  Swyers, Kenneth

  Taft, William Howard

  Taggett, Mike

  tangents

  Tavris, Carol

  Thermodynamics Diet

  “Thoughts About Dice Games” (Galileo)

  Tour of the Calculus, A (Berlinski)

  Tower of Terror

  traffic flow

  tulips

  Twain, Mark

  28 Days Later

  2001: A Space Odyssey

  vampires

  vector calculus

  vectors

  food choices and

  in disease spread

  velocity, see speed

  Verhulst, Pierre

  Virgil

  virtual worlds

  Vitruvius

  vomit comet

  Wansink, Brian

  Watanabe, Terrance

  water waves

  Watkins, Bill

  watts

  wavelength

  waves

  amplitude of

  cosine, see cosines

  Fourier transform and

  frequency of

  sine

  sound

  water

  weight loss

  devices for

  diet pills for

  diets for

  Harris-Benedict equation and

  Wheatstone, Charles

  Whelan, Jim

  Whitehead, Henry

  William the Conqueror

  Witch of Agnesi

  work

  World of Warcraft

  worms

  Yersin, Alexandre

  Zander, Gustav

  Zeno

  Zero: The Biography of a Dangerous Idea (Seife)

  Zombieland

  zombies

  Cordyceps fungi and

  Pride and Prejudice and Zombies

  Smith?’s model of

  Zonaras, John

  1 This account is given by Valerius Maximus, in Memorable Doings and Sayings. Historians differ as to how the soldier slew Archimedes, but a medieval woodcut depicts his head being cleft in two. Several accounts report that Marcellus was much distressed by the mathematician’s death, since he had great respect for the man’s ingenuity—even though that ingenuity had delayed his conquering of Syracuse.

  2 Sophie Germain is best known for inventing the “Germain primes.” If you double a Germain prime number and add 1, you get another prime number. For example, double the prime number 2 is 4, plus 1 is 5—which is also a prime number.

  3 To give you an idea of the depth of my ignorance at the outset, The Complete Idiot’s Guide to Calculus proved to be a bit over my head. Perhaps it should be retitled The Half-Wit’s Guide to Calculus.

  4 Spinach turned out to be the key to unlocking the mystery. Uwe Bergmann, a Stanford physicist at the Synchrotron Radiation Laboratory, heard about the Archimedes palimpsest at a conference in Germany and realized his method for studying photosynthesis in spinach could also be applied to the parchment, without damaging the manuscript. Spinach contains iron; and the ink used on the palimpsest also contained iron, so the same technique could be used.

  5 Abraham Lincoln kept a copy of Euclid in his saddlebag, and studied it late at night by lamplight. “You never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight,” he later wrote.

  6 From an account by John Zonaras, who wrote in the twelfth century A.D.: “At last in an incredible manner he burned up the whole Roman fleet. For by tilting a kind of mirror toward the sun he concentrated the sun’s beam upon it; and owing to the thickness and smoothness of the mirror he ignited the air from this beam and kindled a great flame, the whole of which he directed upon the ships that lay at anchor in the path of the fire, until he consumed them all.”

  7 A Welsh mathematician named Robert Recorde is credited with inventing the equal sign. He used it first in his 1557 treatise The Whetstone of Witte, which introduced algebra to England.

  8 The acceleration is constant once the apple starts falling.

  9 Another of Zeno’s paradoxes involved Achilles in a footrace with a tortoise. Since Achilles is so much faster, the tortoise gets a head start. Each time Achilles closes the distance by half, the tortoise also moves a bit more ahead. The distance between them gets smaller and smaller, but Achilles can never catch up, since the progression goes on forever. Except in real life, it doesn’t, and he can pass the tortoise quite easily.

  10 My former college English professor, Janet, says that her epiphany on the limit came during a lecture on Zeno’s paradox of Achilles and the tortoise, using the number .111 . . .—which is equivalent to 1/9, the point where Achilles catches up with the tortoise (i.e., the limit). Janet didn
’t take the matter on faith. The woman is a rigorous scholar, so she did all those painstaking calculations herself, adding everything up to find that this endless series of repeating decimal places really did converge to 1/9.

  11 According to the many billboards dotted along I-15 advertising the Mad Greek Cafe.

  12 Othello, act III, scene 3, line 365.

  13 You will find a mathematical breakdown of this process in appendix 1.

  14 Physicists are probably freaking out reading this, since they habitually use p to denote momentum, having already assigned m to denote mass in their equations. But it’s the context that gives the variable meaning, so for now, I’m sticking with p.

  15 The eighteenth-century mathematician Johann Bernoulli, whom we will meet in chapter 8, also appreciated the difficulty. “But just as much as it is easy to find the differential (derivative) of a given quantity, so it is difficult to find the integral of a given differential,” he once wrote. “Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.” † The derivative of ax N is anxN-1 (a times n times x times xN-1) for any constants a and n. Likewise the integral of ax N is equal to . Now aren’t you sorry you asked?

  16 Yes, a Prius can get up to those speeds, as we learned in 2007 when former vice president Al Gore’s son was pulled over for going 110 mph in his hybrid. And the car’s sleek aerodynamic shape means it has a lower drag coefficient than, say, the boxy Scion xB.

  17 It may very well be safer to drive more slowly, according to a 2008 study by scientists at the University of Adelaide in Australia. They found that the risk of serious injury or death from a car crash doubles for every 5 km/h above 60 km/h. So if you’re traveling at 65 km/h, you are twice as likely to be involved in a serious or fatal crash; at 70 km/h, that risk is four times as high. This is because drivers need at least 1.5 seconds to respond to a perceived danger, and the faster one travels, the less time there is to react.

  18 “Einstein is gambling as if there were no tomorrow,” an eminent physicist is said to have remarked. His companion replied, “What troubles me is that he may know something!”

  19 According to Dominic, the origin of the term eighty-sixed dates back to the days when the Mafia ran Vegas casinos. Whenever cheaters were caught, the pit boss would instruct his henchmen to “eighty-six that guy”—code for taking the victim eight miles out of town and burying him six feet under.

  20 Crapaud is French for “toad,” you see, and the French are oh-so-fond of eating plump, juicy frog legs sautéed in butter and lots of garlic. An alternative theory is that the name is a corruption of a losing throw in hazard, called crabs, but that explanation lacks the jaunty panache of the crapaud theory.

  21 In May 2009, a middle-aged woman from New Jersey named Patricia Demauro set a new record for the longest craps roll in recorded history: four hours and eighteen minutes. It was only her second time playing craps. She finally lost after 154 rolls of the dice.

  22 Legend has it that the American Physical Society once held its annual meeting in Las Vegas. The assembled physicists shunned all the usual decadent delights: show-girls, hookers, blackjack, roulette, craps, and copious amounts of alcohol, plus they were lousy tippers. There wasn’t a single barroom brawl. The city made so little money, the APS was asked never to come back to Vegas. Now the society holds its major meetings in more sober, straitlaced places like Cincinnati, Indianapolis, and Denver.

  23 Apparently Disney was forced to choose between working water fountains or running toilets, and he wisely chose the latter. That didn’t stop the ungrateful crowds from accusing him of deliberately sabotaging the water fountains to sell more soda (Pepsi had sponsored the park opening).

  24 A group of British adrenalin junkies formed the Oxford University Dangerous Sports Club and leaped from Bristol’s 250-foot Clifton Suspension Bridge in 1979. They were promptly arrested, but undeterred: They went on to jump from the Golden Gate Bridge, mobile cranes, and hot-air balloons.

  25 Check out appendix 1 for the mathematical solution to this problem.

  26 I was relieved to learn her father married three times, since the thought of one woman enduring that many pregnancies boggles the mind.

  27 Scott Carpenter, Gordon Cooper, John Glenn, Wally Schirra, Alan Shepard, and Deke Slayton. Alas, Gus Grissom was one of three astronauts killed ten years earlier in a tragic launch-pad fire.

  28 Which is not to say there isn’t considerable art involved in designing a good roller coaster. “This isn’t rocket science; it may be more complicated than that,” Space Mountain’s ride track engineer Bill Watkins recalled. “Once a rocket leaves the Earth’s atmosphere, there is little drag to contend with . . . [and] they don’t have to worry about getting a Mickey Mouse hat caught in their wheels.”

  29 Many of the animatronic animals are recycled from an older, less popular attraction called “America Sings,” which closed in April 1988, because construction of Splash Mountain was already far over its $75 million budget. Sadly, the animals still sing.

  30 Eureka (Greek heurēka) means “I’ve found (it),” and ever since, surprising scientific insights have been known as eureka moments. Ironically, Archimedes most likely never said that, certainly not while running naked through the streets. Blame the Roman architect Vitruvius, who first recorded the anecdote two hundred years after Archimedes’ death.

  31 There is still considerable debate as to whether tulip mania constituted a true bubble market in modern economic terms. A bubble forms when investors place so much demand on a product that the price soars far beyond what that product could possibly be worth. Wikipedia offers a corollary to that definition: “For tulip mania to have qualified as an economic bubble, the price of tulip bulbs would need to have become unhinged from the intrinsic value of the bulbs.” Did this happen or not? Discuss.

  32 I am cheating a little by assuming a constant rate of change.

  33 This works in reverse on mortgage interest. Not all of your monthly payment goes toward paying off your principal. Most of it goes toward interest in the early years, because interest is always paid on the outstanding balance of the loan, which decreases over time as you pay down the principal.

  34 See appendix 2, “Calculus of the Living Dead,” for a detailed breakdown of this type of calculus problem.

  35 An alternate theory proposes that while Y. pestis is responsible for modern outbreaks of plague—and yes, there are still outbreaks around the world, mostly concentrated in Africa—the Black Death that ravaged Western Europe in the fourteenth century was caused by something like anthrax or an Ebola-like virus. The evidence is sketchy, however. An analysis of the remains of early plague victims in France showed DNA from Y. pestis and none from anthrax, for example.

  36 It was discovered simultaneously by a Japanese scientist named Shibasaburo Kitasato, but the microbe is named after Yersin.

  37 Yes, there really is a question mark at the end of his name. He changed it to distinguish himself from the zillions of other Robert Smiths in the world, including the lead singer of the Cure: “It’s been twenty years now and sadly his career shows no sign of drying up,” the epidemiologist laments.

 

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