## Maths 1001: Errata

Below is a list of errata for my book Maths 1001. (This is the complete list of errata from the original version of the book. In subsequent printings, some/all of these should have been put right.)

If you have noticed an error not on this list, I would be very grateful if you could email me at r [DOT] elwes [AT] gmail [DOT] com, or leave a comment here.

Page 13 Logarithms, line 5. “You can take logarithms to any base number, as long as it is positive and not equal to 1”
(9/2011, thanks to Mark R)

Page 32 Highest common factor. This is also known as the “greatest common divisor”, not “denominator”.
(9/2011, thanks to Mark R)

Page 33 Lowest common multiple. This is not also known as the “lowest common denominator”, though the two ideas are closely related!
(9/2011)

Page 41 Knuth’s arrows, second paragraph, second line “…the tower is 4444 storeys high.”
(12/2010, thanks to John P)

Page 53 last line of page, “Pierre Wantzel”
(12/2010, thanks to John P)

Page 58 The graph should show a curve rather than a straight line.
(4/2014, thanks to Mark B)

Page 90 Trigonometric values, “cos π = -1”
(30/1/2011, thanks to Bogumił F)

Page 96 Intersecting chords theorem. Last word should be “circle”.
(28/3/2011, thanks to Bogumił F)

Page 103 The caption for the second diagram should read “octahedron”
(4/2014, thanks to Mark B)

Page 109 penultimate line. “transitionally” should read “translationally”
(4/2014, thanks to Mark B)

Page 115 Quadratic curves, first line. “Principal”
(1/2/2013, thanks to John W)

Page 118 third line from bottom: “…roofing in modern architecture. The archetypal…”
(19/1/2011, thanks to Tommy M)

Page 120 Surfaces of Higher Degree, line 9, in the formula for a superellipse the term y/a should be y/b.
(7/2014, thanks to neozhonghao)

Page 120 The coordinates for point D should be ((2, frac{5pi}{4}))
(4/2014, thanks to Mark B)

Page 122 Top picture. The right label should read e2 π instead of e20 π

Page 127 What the bees don’t know, two lines after the diagrams, “three rhombuses”.
(4/2014, thanks to Mark B)

Page 134 Line 2. “…arrow heads…”
(11/2011, thanks to Walter M)

Page 140 The Perko pair
The second illustrated knot is incorrect! See here.

Also, Perko’s discovery was made in 1973, not 1974.

(7/2013, thanks to Kenneth Perko himself.)

Page 153 Rational solutions of elliptic curves, line 8, “…Bryan Birch and Peter Swinnerton-Dyer…”
(12/2011)

Page 160 The binomial theorem. The fourth displayed formula should read:

(x+y)4 = y4 + 4y3x + 6y2x2 + 4yx3 + x4

Page 164 The Cubic Formula. In the second displayed equation, the second “±” (plus-minus) symbol should be “∓” (minus-plus).

Page 169 The angle between two vectors, line 7, (||v||=sqrt{2^2} = 2).
(4/2014, thanks to Mark B)

Page 170 line 2 (Cauchy-Schwarz inequality) “…as |cos(θ)| must be between 0 and 1.”
(9/2011, thanks to Mark R)

Page 174 Rotation matrices. The final matrix of this entry is incorrect. Reading left to right, top line first, the entries should read √3/2 -1/2 1/2 √3/2
(19/1/2011, thanks to Tommy M)

Page 198 Planar graphs line 4. The first word should be “vertices” not “edges”.
(4/2014, thanks to Mark B)

Page 198 Planar graphs. Penultimate line, the italicized text should read “Kuratowski’s theorem”.
(26/4/2011, thanks to .Mau.)

Page 207 Converging and diverging sequences line 6. The final expression should be (n to infty)
(4/2014, thanks to Mark B)

Page 233 Summing Powers. First displayed sum should run from r=0, not r=1.
(9/2011 Thanks to James A)

Page 242 Cantor Dust. The bottom line of the top diagram is wrong. (Exercise!)

Page 252 The caption to the second diagram should read (y=sin t +ldots) not (y=sin y +ldots)
(4/2014 Thanks to Mark B)

Page 268 Axioms of Peano arithmetic, last line of the page   “∀x,y   x × S(y) = (x × y) + x”
(12/2010, thanks to John P)

Page 281 Algorithms, line 6. The first word should be “word” not “work”.

(4/2012, thanks to anon)

Page 283 Proof theory, line 6, the word “stronger” is not correct and should be deleted. (Gentzen’s system is primitive recursive arithmetic plus quantifier-free induction up to ε0. This is neither stronger nor weaker overall than Peano arithmetic.)
(11/2011, thanks to John B)

Page 299 Fuzzy Sets line 7/8 & Fuzzy Logic line 3. “…Lotfi Zadeh…”
(12/2010, thanks to Mike R)

Page 311 Distributed mathematics projects last two lines. “…RSA factoring challenge…”
(5/2011, thanks to .Mau.)

Page 326 The first digit phenomenon. Correction: Simon Newcomb was indeed a 19th century scholar, but Frank Benford was a 20th century man.
(5/2011, thanks to .Mau.)

Page 331 False positives, second para, last line. 0.99×0.0003+0.05×0.9997=0.050282
The following displayed equation should end 0.99×0.0003/0.050282=0.00591
Two lines later, “a little under 0.6%”.
(10/2012, thanks to Anon.)

Page 334 The law of truly large numbers, line 2. “…Persi Diaconis…”
(5/2011, thanks to .Mau.)

Page 346, top table. The average number of occurrences of the digraph “st” should read “20” not “8.5”.
(5/2011, thanks to .Mau. Updated 2/2012)

Page 388, Electroweak theory, line 6, last word “very”.
(5/2011, thanks to .Mau.)

Page 410 The 1089 Theorem, line 4. “Such numbers are of the form d9e, where d+e=9.”