The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse
Page 27
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.