How To Fold It:
The Mathematics of
Linkages, Origami, and Polyhedra

by Joseph O'Rourke

Errata

Last Update:

I would like to thank Ryuhei Uehara at JAIST, who made many corrections as he translated the book to Japanese.

Substantive Errors

Chap
Page
Location
Old
New
Explanation
Corrector
Date
Preface
ix
Lines +1, +5, +6
64 straight scissors cuts ... 16 stright snips of the scissors rather than 64 70 straight scissors cuts ... 18 straight snips of the scissors rather than 70 The exact count depends a bit on what it means to "cut out" the dolls, and whether or not you take some shortcuts, e.g., but cutting the bottom of their feet separately or as a unit. There are 70 straight segments (18+17+17+18), so cutting each separately uses that many cuts. After folding, 18 suffice to cut out the pattern, which is just a bit over 1/4.
Peter Landweber; JOR
24 Aug 2011
1
18
Exer. 1.6, Line-2
    My answer is incorrect. See below.
Charles W. Wampler
21 Aug 2011
Answers to Exer
152
Ans. to Exer. 1.6, Line-3
All the points on the circle of radius 2=1+2=3 can only be reached by forming a zig-zag with the 2nd link opposing the 1st and 3rd. [The claim in that sentence is false and should be removed.] The only points reached uniquely by an n-link robot arm are those on the outer and inner boundary of the reachability annulus—in this case, the circle of radius 5. The points on the circle of radius 3 can be reached by a continuum of configurations of the three links.
Charles W. Wampler
21 Aug 2011

Minor Errors: Typos, etc.

Chap
Page
Location
Old
New
Explanation
Corrector
Date
1
6
Line-3
n > 1 n > 2 Better, as n=2 has already been checked..
Ryuhei Uehara
20 Jan 2012
1
9
Box 1.3, last sentence of 1st para.
The length of these vectors is exactly the link length which they "span," The lengths of these vectors are exactly the link lengths which they "span," Singular→plural
Ryuhei Uehara
24 Dec 2011
1
13
Last para.
    Should be indented because it is part of Case 2.
Ryuhei Uehara
24 Dec 2011
1
20
Line-7
(Ruler Folding) Ruler Folding Remove parentheses.
Ryuhei Uehara
24 Dec 2011
2
36
Line+4
any any Italicsunderline (for typographical consistency)
Ryuhei Uehara
24 Dec 2011
2
37
Line+2 of bottom "Open Subproblem" box
Are there a planar linkages Are there planar linkages Typo.
Peter Landweber
24 Aug 2011
3
41
Line+5 of middle para.
the purely geometric motion of the purely geometric notion of Typo.
Peter Landweber
24 Aug 2011
3
41
Line-4
3 x 36 = 108 links 3 x 36 - 1 = 107 links Mental typo.
Ryuhei Uehara
20 Jan 2012
3
46
Line-14
established for n=1,2,...,n-1 established for 1,2,...,n-1 Clearer.
Ryuhei Uehara
24 Dec 2011
3
47
Line-14
induction hypothesis covers all n up to n-1 induction hypothesis covers all values up to n−1 Clearer.
Ryuhei Uehara
24 Dec 2011
3
54
Fig. 3.16(b)
label v0 on red portion of linkage Label should be instead v5 Typo.
Peter Landweber
24 Aug 2011
4
57
Line-3
(Memory aide: red sunset (Memory aid: red sunset Typo.
Peter Landweber
24 Aug 2011
4
64
Line-6 & -2 of (blue) Box 4.2
V · 360° = (M + V) 180°
2 V = M + V or M - V = 0
V · 360° = (M + V - 2) 180°
2 V = M + V - 2 or M - V = 2
Mental typos.
William Lee
22 Jun 2011
4
66
θ Equation
θ2 + ... θn = 360° θ2 + ... + θn = 360° Add + before θn
Ryuhei Uehara
24 Dec 2011
4
69
Line+6 of Sec.4.6.2
(NP-complete or worse) (NP-complete) It cannot be worse, because there is a polynomial-length witness for an instance of map folding.
Ryuhei Uehara
20 Jan 2012
5
76
Exer. 5.2
for the rectangle for the rectangle. Period missing at end of sentence.
Ryuhei Uehara
24 Dec 2011
5
76
Line-2
see Figure 5.7(a) see Figure 5.7(a). Period missing at end of sentence.
Ryuhei Uehara
24 Dec 2011
5
80
Fig. 5.11(c)
One red crease should be green.
A fixed
~Typo.
MathFest 2011 Minicourse participants
5 Aug 2011
5
82
Fig.5.13 caption
Fold and-One-Cut Fold and One-Cut Remove extra hyphen.
Ryuhei Uehara
24 Dec 2011
5
91
Line-2 of Sec. 6.2.1
Figure 6.7(b) Figure 6.8(b) Typo.
Ryuhei Uehara
24 Dec 2011
6
94
Fig.6.13 caption
0 < θ < 180° 0° < θ < 180° Add ° for consistency.
Ryuhei Uehara
24 Dec 2011
7
101
Line-9
truncated icosahedron truncated icosahedron Italicize.
Ryuhei Uehara
24 Dec 2011
7
106
Line+1
Exercise 6.3[a] Exercise 6.3(a) Typo.
Ryuhei Uehara
24 Dec 2011
7
110
Exer. 7.3
(Understanding) (Understanding) Boldface for consistency.
Ryuhei Uehara
20 Jan 2012
7
113
Line+4
all but one edge of A is cut all but one edge of A are cut Singular→plural
Ryuhei Uehara
24 Dec 2011
7
115
Exer. 7.6
Shortest Paths on Cube. Shortest Paths on Cube. Boldfaceitalics (for typographical consistency)
Ryuhei Uehara
20 Jan 2012
9
135
Line+4
Another Alexandrov folding Another Alexandrov gluing For consistency.
Ryuhei Uehara
4 Feb 2012
9
135
Line-9
convex polygon (Recall... convex polygon. (Recall... Period missing.
Ryuhei Uehara
4 Feb 2012
9
135
Line-5
Take any convex polygon Take any convex polygon P Better to name it P.
Ryuhei Uehara
4 Feb 2012
Answers to Exer
158
Ans. to Exer. 3.5, Line+1
the middle three links the middle two links Typo.
Ryuhei Uehara
8 May 20121
Answers to Exer
159
Ans. to Exer. 4.2, Line-2
leads one of the leads to one of the Typo.
Peter Landweber
24 Aug 2011
Answers to Exer
160
Fig.Ans.15
Row 1, Columns 3 & 4 images
Stamp

3412: Arrows for 1 and 2 were reversed.

4123: The fold connection between 2 and 3 was missing.

Ryuhei Uehara
4 Feb 2012
Answers to Exer
161
Fig.Ans.16
(a) Green line x to AC
EquiTriFC
Green line should be from x to C.
Ryuhei Uehara
8 May 2012
Answers to Exer
162
Line+3
will cut out two squares will cut out a square and a rectangle In general, the second hole is a rectangle.
Ryuhei Uehara
4 Feb 2012
Answers to Exer
166
Line-2
every tree of n vertices has n edges every tree of n vertices has n-1 edges Mental typo!
Ryuhei Uehara
4 Feb 2012