274 Index close-together method: <strong>of</strong> cubing, 77, 78 in multiplying three-by-three numbers, 183–88; exercises, 192–93; answers, 265–68 Colburn, Zerah, 49, 53, 109 cold fusion debacle, 228–29 columns <strong>of</strong> numbers, adding (on paper), 132–33; exercises, 149; answers, 256 complements, 25–28 confirmation bias, 224, 225, 229 conspiracy theories, 224 creationism, 229 criss-cross method <strong>of</strong> multiplication on paper, 138–45; exercises, 150; answers, 257 cube roots, quick, 209–11 cubing: close-together method, 77, 78 two-digit numbers, 76–79; exercises, 79; answers, 248 data filters, 225–26 day <strong>of</strong> the week, 8–10, 214–21 day codes, 214–15 exercises, 221; answers, 270 Julian vs. Gregorian calendar, 220 leap years, 220 month codes, 215 year codes, 216–18 death premonitions, 223, 224 decimalization, 93–98; exercises, 98; answers, 250 Demon-Haunted World, The (Sagan), 227 Devi, Shakuntala, 146 digital roots, checking solutions via, 133 digits (fingers), xii distributive law, 50–51 divisibility, testing for, 98–102 by 2, 99; exercises, 101; answers, 250 by 3, 99; exercises, 101; answers, 250 by 4, 99; exercises, 101; answers, 250 by 5, 100; exercises, 101; answers, 251 by 6, 100; exercises, 101; answers, 250 by 7, 100; exercises, 102; answers, 251 by 8, 99; exercises, 101; answers, 250 by 9, 99; exercises, 101; answers, 250–51 by 11, 100; exercises, 102; answers, 251 any odd number not ending in 5, 100–101; exercises (by 17), 102; answers, 251 division, 80–107 decimalization, 93–98; exercises, 98; answers, 250 fractions, 103; exercises, 103; answers, 252 guesstimation, 112–14; exercises, 129; answers, 254–55 left to right, 80 numbers ending in 25 or 75, 97 one-digit numbers, 81–84; exercises, 84; answers, 249 quotient in, 87 rule <strong>of</strong> “thumb” in, 84–86 as simplification process, 82 simplifying problems <strong>of</strong>, 90–93, 98 square root estimation, 117–21; exercises, 130; answers, 255 square roots with pencil and paper, 135–38; exercises, 150; answers, 257 two-digit number into four-digit number, 89–90 two-digit numbers, 87–93; exercises, 93; answers, 249 when divisor ends in 5, 97 dreams, frequency <strong>of</strong>, 223 estimations, 12; see also guesstimation evolution, theory <strong>of</strong>, 229
Index 275 factoring a number: in three-by-three multiplication, 181–83; exercises, 192–93; answers, 265–68 in three-by-two multiplication, 169–72; exercises, 175–76; answers, 259–62 in two-digit multiplication, 63–68; exercises, 68; answers, 243 Fibonacci numbers, xi Fleischman, Martin, 228–29 fractions, 102–7 adding with equal denominators, 104–5; exercises, 105; answers, 252 adding with unequal denominators, 105–6; exercises, 106; answers, 252 dividing, 103; exercises, 103; answers, 252 multiplying, 102; exercises, 102; answers, 252 one-digit, 93–96 simplifying, 96–97, 103–4; exercises, 104; answers, 252 subtracting, 106–7; exercises, 107; answers, 252–53 friendly products, 66–68 Fuller, Thomas, 168 Gardner, Martin, 53–54 Gauss, Carl Friedrich, 20 Glois, Évariste, 121 Gold, Thomas, 228 Great Mental Calculators, The (Smith), xxi group theory, 121 guesstimation, 108–30 addition, 108–11; at the supermarket, 111; exercises, 128; answers, 253 division, 112–14; exercises, 129; answers, 254–55 multiplication, 114–17; exercises, 129; answers, 254–55 sign for “approximately,” 109 square roots, 117–21; exercises, 130; answers, 255 subtraction, 111–12; exercises, 129; answers, 254 hearing numbers, 16 HIV-AIDS skeptics, 230 instant multiplication, 1–4 interest: calculating, 125–28; exercises, 130; answers, 256 repaying a loan, 126–27 Rule <strong>of</strong> 70, 125–26 Rule <strong>of</strong> 110, 126 introspection illusion, 227 Kevles, Daniel, 227–28 Law <strong>of</strong> Large Numbers, 223 laws <strong>of</strong> probability, 224 leapfrog addition, 203–6 leap years, day <strong>of</strong> the week, 10, 220 left-to-right computations: addition, 6–8, 11–21 division, 80 multiplication, 30–31, 33 subtraction, 6–7, 21–28 loan, repaying with interest, 126–27; exercises, 130; answers, 256 logarithmic spirals, xi magic squares, 206–9 how to construct, 207–8 why this trick works, 208–9 magic 1089, 200–202 <strong>math</strong>: creative thinking in, xxiv figuring out loud, xiv as language <strong>of</strong> science, xi useful language <strong>of</strong>, xvii Mathemagics, xiii, xix, xxiii “amazing” sum (Randi), 212–14 leapfrog addition, 203–6 magic squares, 206–9 magic 1089, 200–202
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