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!


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…”


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.”