Geometric Folding Algorithms:

by Erik D. Demaine and Joseph O'Rourke 
Chap 
Page 
Location 
Old 
New 
Explanation  Corrector 
Date 

5 
66 
Eq. 5.2 
l_{3} <= (l_{1}l_{2}) + (l_{4}+...+l_{n}) ... But Eq. (5.2) is just a rearrangment of Eq. (5.1), ... 
l_{3} <= (l_{1}l_{2}) + (l_{4}+...+l_{n})
or (l_{1}+l_{2}) <= l_{3}+...+l_{n}... But Eq. (5.2) is just a rearrangment of Eq. (5.1), and Eq. (5.3) follows easily from Eq. (5.1) ... 
Missed a case, which easily follows.  Ryuhei Uehara 
5Jul08 
8 
135,136 
Table of coords; Fig.8.7 
v_{4}: ( 0, 0, (3/2)ε )  v_{4}: ( 1/2, 0, (3/2)ε )  Mental typo: v_{3}v_{4} must be longer to force overlap.  Andrew Winslow 
30Nov10 
8 
143 
Line+12 of Sec. 8.2.1 
Define such a chain to be convex if all of its vertices lie on the convex hull  Define such a chain to be convex if all of its edges lie on the convex hull  A zigzag chain could have all its vertices on the hull be not be convex in the sense we intended.  Sebsatien Collette 
6 Feb 08 
11 
190 
Line+1 
2. ..., say α, is not acute ...  2. ..., say α, is not acute, and ac ≤ ab ... 3. If α is not acute but ac > ab, [click here for completion of new case]. 
Case 2 only covers a subcase; Case 3 completes the argument (due to Ryuhei Uehara).  Ryuhei Uehara 
23Feb08 
22 
326 
Sec. 22.5.2 Domes, Line+5 
and at most one can have adjacent faces diverge (because divergence implies an angle greater than π, and there is only 2π total angle to G). 
and at most one can have adjacent faces diverge (because divergence implies a turn angle greater than π, and there is only 2π total angle to G). The one exception, when G is a trapezoid and two turn angles are =π, is easily seen to unfold without overlap. 
With G a trapezoid, P is a wedge of just four faces, and nonoverlap is straightforward. 
JOR 
9Aug07 
We are greatly indebted to Ryuhei Uehara, our Japanese translator, for his meticulously reading of the text.
Chap 
Page 
Location 
Old 
New 
Explanation  Corrector 
Date 

Contents 
viii; 165 
Part II line 
Part II: Paper  Part II: Origami  Part name changed  JOR 
6Nov07 
1 
9 
Line 10 
when a linkage is rigid, that is, can move at all.  when a linkage is rigid, that is, cannot move at all.  Typo  Ryuhei Uehara 
17Aug07 
1 
11 
Line 3 
It is sometime useful  It is sometimes useful  Typo  Ryuhei Uehara 
17Aug07 
2 
18; 19 
Line 7; Line 3 
let us say that k=2n ... specifying the coordinates for point reduces this to k=2n2. ... O( n^{4n2} ... )  let us say that k=2n+2 ... specifying the coordinates for one point reduces this to k=2n. ... O( n^{4n+2} ... )  n links means n+1 vertices  Ryuhei Uehara 
17Aug07 
2 
18 
Line +9 
(Abrams and Shrist 2002)  (Abrams and Ghrist 2002)  Typo  Julian Wilson 
15Jan10 
2 
19 
Box 2.1, Line +4 
For a univariate polynomials  For univariate polynomials  Typo  Ryuhei Uehara 
1Jun08 
2 
19 
Box 2.2, Line 4 
is in PSPACE (1988).  is in PSPACE.  ~Typo  Ryuhei Uehara 
17Aug07 
2 
21 
Line 8 
32^{7} > 10^{10}  50^{14} > 10^{23}  ~Typo  Ryuhei Uehara 
17Aug07 
2 
22 
Line 1 
Plantingua  Plantinga  Typo  Julian Wilson 
18Jan10 
2 
23 
Sec. 2.2.2, Line +3 
Mis  M is  Printer error on spacing  Ryuhei Uehara 
8Nov07 
2 
24 
Fig. 2.3 caption, Line +3 
Each ... fan ... represent  Each ... fan ... represents  Typo  Ryuhei Uehara 
8Nov07 
2 
26 
Line +2 
must both lie at 1 if all is to fit 
must both lie at s if all is to fit 
Typo 
Joe Malkevitch 
2Oct07 
3 
32 
Figure 3.3 
Edge connecting the α angle to the β angle 
Should be labeled “a” 
The length of this edge is referred to as a in the text 
Gregory Price 
10Sep07 
3 
32 
Figure 3.3 
Origin  Origin should be labeled “O”  Described as O in the text.  Ryuhei Uehara 
28Nov07 
3 
33 
Figure 3.5 
Angle α at y, angle β at b 
Angle β at y, angle α at b 
Opposite contraparallelogram angles are equal 
Andrea Hawksley & Howard Samuels 
18Sep07 
3 
37 
Fig. 3.10 
[(a) of Fig. 3.10 ]  [horizontal edge should be labeled e]  e is used in the proof.  Ryuhei Uehara 
5Jul08 
3 
37 
Line+1 of 3.2.2.1 
...locate a joint in the interior of a bar.  ...locate a joint in the interior of a bar (as in Figure 3.5).  Used in Fig. 3.5 before its use in Fig. 3.10.  Ryuhei Uehara 
30Nov07 
2 
41 
Box 3.2, Line +4 
constancy of ab . bd  constancy of ac . bd  Typo  Ryuhei Uehara 
1Jun08 
4 
45 
Figure 4.3 caption 
graphy 
graph 
Typo 
Gregory Price 
20Sep07 
4 
48 
Lines8,6 
(Badoiu et al. to appear)  (Badoiu et al. 2006)  Editor error  Ryuhei Uehara 
13Jan08 
4 
48 
Theorem 4.3.2 
A graph is generically rigid if some subgraph is minimally generically rigid  A graph is generically rigid only if some subgraph is minimally generically rigid  ~Typo  Ryuhei Uehara 
1Jun08 
4 
48 
Line2 
Connelly (to appear)  Connelly (2005)  Editor error  Ryuhei Uehara 
13Jan08 
4 
48 
Line2 
in any dimension with vertex (d+1)connectivity  in any dimension d with vertex (d+1)connectivity  Typo  Ryuhei Uehara 
13Jan08 
4 
51 
Box 4.1, last two equations 
v_{3}^{x} = v_{4}^{x} v_{3}^{x} = v_{4}^{x} = 0 
v_{3}^{x} = v_{4}^{x} , 
Typo: punctuation  Ryuhei Uehara 
13Jan08 
4 
52 
Line+3 
infinitesimally rigid  infinitesimally rigid  Typo: should be italicized because being defined  Ryuhei Uehara 
13Jan08 
4 
49 
Section 4.4.1, first display equation 
(L − x_{i} + x_{j})^{2} + (y_{i} + y_{j})^{2} 
(L − x_{i} + x_{j})^{2} + (−y_{i} + y_{j})^{2} 
Signs of y's should be opposite, like x's 
Edwin Chen 
18Sep07 
5 
60 
Lemma 5.1.1 statement 
of an arm A of n links  of an arm C of n links  Proof uses C for arm.  Greg Clark 
6Jun08 
5 
60 
Lemma 5.1.1 Proof eqn 
{p + S(l_{n})  p ∈ R_{n1}}  ∪_{p ∈ R_{n1}} p + S(l_{n})  Intended union of circles, but specified a set of circles.  Greg Clark 
6Jun08 
5 
61 
End of statement of Thm.5.1.2 
; else, r_{i} = l_{m}  s  ; else, r_{i} = l_{M}  s  Typo  Ryuhei Uehara 
5Jul08 
5 
62 
Line+7 of 2nd para. of Sec. 5.1.1.3 
(i.e, α_{i}=0 for all internal joints)  (i.e, α_{i}=π for all internal joints)  ~Typo  Ryuhei Uehara 
23Feb08 
5 
63 
Caption to Fig. 5.5 
(l_{M}=6)<(s=15)  (l_{M}=6)<(s=11)  Typo  Ryuhei Uehara 
23Feb08 
5 
63 
Line+4 of Sec.5.1.1.4 
l_{1} and l_{3} respectively  l_{1} and l_{2} respectively  Typo  Ryuhei Uehara 
23Feb08 
5 
66 
Line2 
in R^{3}  in R^{3}  R should be \mathbb{R}.  Ryuhei Uehara 
23Feb08 
5 
71 
Line+5 of 2nd para. of Box. 5.1 
Figure 5.17(b)  Figure 5.17(a)  Typo  Ryuhei Uehara 
23Feb08 
5 
73 
Last line of proof of Lemma 5.3.2 
, which requires v_{1} and v_{3} to reach π.  , which requires v_{1} and v_{3} to reach π, respectively.  Did not mean to imply that the two triangles must collapse at the same time.  Ryuhei Uehara 
23Feb08 
5 
77 
Line+2 of Step 3 
where ε _{i} = min {...} ^{}  where ε _{i} = min_{k} {...}  Clarification that min is over k.  Ryuhei Uehara 
23Feb08 
5 
78 
Last 2 paras. of proof. 
Let ... [2 paragraphs]^{}  [add indenting]  Should be indented to be part of Step 5.  Ryuhei Uehara 
23Feb08 
5 
79 
Line+2 
on the lengths a,b,c,d of its edges:  on the lengths of its edges:  a,b,c,d are vertex labels, not edge lengths.  Ryuhei Uehara 
23Feb08 
5 
79 
Lines9 to 6 
The initial polygon P_{0} Figure 5.27(a) ...  The initial polygon P_{0} (Figure 5.27(a)) ...  Citations of the four parts of this figure should be in parentheses.  Ryuhei Uehara 
23Feb08 
5 
82 
Fig. 5.30 
[circle]  [C]  Circle in the figure should be labeled C.  Ryuhei Uehara 
23Feb08 
5 
84 
Caption to Fig. 5.33 
are shown shaded.  are shown red.  ~Typo.  Ryuhei Uehara 
23Feb08 
5 
84 
Caption to Fig. 5.34 
A 3D polygon  A 3D open chain  ~Typo.  Ryuhei Uehara 
23Feb08 
6 
87 
Table 6.1 column heading 
Can trees trees lock?  Can trees lock?  Typo.  Ryuhei Uehara 
6Apr08 
6 
89 
Line3 of proof of Theorem 6.3.1 
Unfolding of P.  Unfolding of K.  Typo.  Ryuhei Uehara 
6Apr08 
6 
93 
Line+8 
the set all positions  the set of all positions  Typo.  Ryuhei Uehara 
6Apr08 
6 
95 
Figure 6.9 caption 
Biedl et al. 1998a, Tech. Rep.  Biedl et al. 1998a.  ~Typo.  Ryuhei Uehara 
6Apr08 
6 
95 
Section 6.5, para. 3 
the tree in Figure 6.9 is locked 
the tree in Figure 6.9(a) is locked 
Figure 6.9 contains several trees; this sentence refers to the first 
Gregory Price 
20Sep07 
6 
105 
Line+6 of Sec. 6.7.1 
because each of the components are  because each of the components is  Typo  Ryuhei Uehara 
6Apr08 
6 
111 
Line+8 
(p. 100 and  (p. 100) and  Typo  Ryuhei Uehara 
6Apr08 
6 
115 
Line+1 of Sec. 6.8.5 
(all chains can be straightened)  (all chains can be straightened/convexified)  ~Typo  Ryuhei Uehara 
6Apr08 
7 
124 
Table 7.1, 2f row 
“? ?” 
“– –” 
This follows from Theorem 5 of Demaine et al (2002b), as described in the last sentence on p.125. 
Stefan Langerman 
21May07 
7 
124 
Line4 
The columns of the table cover .... out to k=4.  The columns of the table cover .... out to k=45.  ~Typo  Ryuhei Uehara 
1May08 
7 
127 
Fig. 7.4, 7.5 captions 
... can lock.  ... can interlock.  More precise terminology.  Ryuhei Uehara 
1May08 
7 
127 
Line+4 
if e_{1} and e_{2} are long enough  if e_{1} and e_{3} are long enough  Typo  Ryuhei Uehara 
1May08 
7 
127 
Theorem 7.3.1 
A triangle can interlock with a closed, flexible 4chain 
A triangle can interlock with an open, flexible 4chain 
See Figure 7.5. 
Stefan Langerman 
21May07 
8 
136 
Line+9 
composed of eight links  composed of nine links  ~Typo  Ryuhei Uehara 
5Jul08 
8 
138141 
Sections 
8.1.5 8.1.6 8.1.7 
8.1.4.1 8.1.4.2 8.1.4.3 
Section numbering error.  Ryuhei Uehara 
5May08 
8 
143 
Lemma 8.2.1 
i.e., angle α'_{i} is replaced with α_{i} ≤ α'_{i} ≤π  angle α'_{i} is replaced with α_{i} ≤ α'_{i} ≤π  Drop i.e., because there is not exact equivalence: at least one angle is strictly opened, i.e., cannot have α_{i}= α'_{i} for all i.  Ryuhei Uehara 
5May08 
8 
146 
Line6 
Instead of proving the lemma, we describe instead the fourth  Instead of proving the lemma, we describe the fourth  Drop 2nd instead.  Ryuhei Uehara 
5May08 
9 
148 
Central Eq. 
...C... 
...C'... 
Typo. Replace C by C' throughout the equation.  Ryuhei Uehara 
16May08 
9 
149150 
Figs. 9.2 & 9.3 
Fig. 9.3 ... Fig. 9.2 
Fig. 9.2 ... Fig. 9.3 
Interchange ordering of figures, and renumber according to citation ordering.  Ryuhei Uehara 
16May08 
9 
149150 
Figure captions 
Demaine et al. 2006 
Demaine et al. 2006c 
Publisher error.  Ryuhei Uehara 
16May08 
9 
153 
Line+9 
there is a positive probability 
there is a positive probability ρ 
Clarification.  Ryuhei Uehara 
16May08 
9 
153 
Line+10 
> ρ 
≥ ρ 
More precise.  Ryuhei Uehara 
16May08 
9 
153 
Line+4 
There is, 
There is such a chain, 
Clarification.  Ryuhei Uehara 
16May08 
9 
155 
Line+2 
(He and A.Scheraga 1998) 
(He and Scheraga 1998) 
Remove "A." Publisher error.  Ryuhei Uehara 
16May08 
9 
160 
Line+12 
(When two P nodes are not adjacent, 
(When two P nodes are adjacent, 
Drop "not"! ~Typo.  Ryuhei Uehara 
16May08 
10 
170 
Figure 10.1 caption 
crane crease pattern  crane mountainvalley pattern  More precise description  Ryuhei Uehara 
28Nov07 
11 
173 
Line2 
on the folded state f.  on the folded state f(P).  Typo  Ryuhei Uehara 
5Jul08 
11 
175 
Sec. 11.1.3 
OneDimensional Paper  1D Paper  For consistency  Ryuhei Uehara 
5Jul08 
11 
175 
Line6 of Sec. 11.1.3 
\ {c}  \ {c_{i}}  Missing subscript i.  Ryuhei Uehara 
5Jul08 
11 
177 
Sec. 11.1.3 
the asymmetry condition  the asymmetry condition  Italicize because definition.  Ryuhei Uehara 
5Jul08 
11 
181 
Line1 of Case 2 
the noncrossing constraint imposes no additional conditions  the noncrossing condition imposes no additional constraints  Typo  Ryuhei Uehara 
5Jul08 
11 
182 
Lines 14 
, or if [...to end of Case 4]  ,or if λ(p±,q+) are defined, as in Figure 11.8(d), then we require that these λ values are equal. However, if λ(p+,q±) are defined, as in Figure 11.8(e), then we require that λ(q+,p+)=−λ(q−,p+).  Superscripts do not match (d) and (e) of Fig.11.8.  Ryuhei Uehara 
5Jul08 
11 
186 
Fn.9 
the resulting curve on P  the resulting curve on f(P)  Typo  Ryuhei Uehara 
5Jul08 
11 
187 
Line9 before Sec. 11.5 
the subpiece of paper B_{q}  the subpiece of paper B_{p}  Typo  Ryuhei Uehara 
5Jul08 
11 
188 
Line7 
(p,x)=  (p,q)=  Typo  Ryuhei Uehara 
5Jul08 
11 
188 
Line+14 
winding number  winding number (cf. p. 200)  Used before defined.  Ryuhei Uehara 
25Aug08 
12 
195 
Line+20 
mingling, if, for every maximal sequence ... of (at least two) consecutive creases  mingling, if, for every maximal sequence ... of consecutive creases  At the bottom of the page we permit j=i, so mingling works for one crease as well.  Ryuhei Uehara 
25Aug08 
12 
195 
Line5 
let ... be consecutive creases  let ... be maximally consecutive creases  Implied, but clearer to be explicit.  Ryuhei Uehara 
25Aug08 
12 
196 
Line+4 
2. ... and (c_{i1},c_{j}) the innermost  2. ... and (c_{i1},c_{i}) the innermost  Typo  Ryuhei Uehara 
25Aug08 
12 
198 
Line+4 
its crimp pattern  its mountainvalley pattern  More precise language.  Ryuhei Uehara 
25Aug08 
12 
198 
Figure 12.7 
[Left / Right indices]  Left: i+1→i+2; i→i+1; []→i. Right: i+1→i+2; []→i+1.  Indices in figure incorrect.  Ryuhei Uehara 
25Aug08 
12 
198 
Line1 of Proof of Thm. 12.1.6 
if the list ever becomes empty,  if the list ever becomes empty before reaching a complete folded state,  Ryuhei Uehara 
25Aug08 

12 
202 
Line+2 
Figure 12.9(c) (right to middle) shows a simple example of this process. Figures 12.10 and 12.11 illustrate ... a more complex example.  Figures 12.10 and 12.11 illustrate ... a complex example.  The reference to 12.9(c) is incorrect.  Ryuhei Uehara 
25Aug08 
12 
206 
Fig. 12.13 
θ_{i1}+θ_{i+k}θ_{i1}  θ_{i1}+θ_{i+k}θ_{i}  Typo  Ryuhei Uehara 
25Aug08 
12 
206 
L+4 
the smallest extreme angle  the smaller extreme angle  More elegant language.  Ryuhei Uehara 
25Aug08 
12 
206 
L8 
By Theorem 12.2.3,  By Theorem 12.2.4,  Typo  Ryuhei Uehara 
25Aug08 
12 
208 
L+2 of Proof 
Corollary 12.2.9  Theorem 12.2.9  Typo  Ryuhei Uehara 
25Aug08 
12 
209 
L+2 of Proof 
n1 mountains and n+1 valleys  n/21 mountains and n/2+1 valleys  Typo (they sum to n)  Ryuhei Uehara 
25Aug08 
12 
209 
L10 
Figures 12.8(c) and 12.9  Figures 12.8(c) and 12.9(c)  Typo  Ryuhei Uehara 
25Aug08 
12 
211 
L+12 
xyplane plane  xyplane  Typo  Ryuhei Uehara 
25Aug08 
12 
211 
Middle 
R_{yz}(θ_{i}) =  R_{yz}(φ_{i}) =  Typo  Ryuhei Uehara 
25Aug08 
13 
214 
Figure 13.6(b), top right 
Vertical mountain/valley lines  Vertical valley/mountain lines  Typo  ED 
2Jan16 
13 
215 
Line+5 of Proof 
Thus, θ_{i1} and θ_{i} remain  Thus, θ_{i1} and θ_{i+1} remain  Typo  Ryuhei Uehara 
27Oct08 
13 
215 
L2 
Figure 13.1  Figure 13.1(b)  Typo  Ryuhei Uehara 
27Oct08 
13 
230 
Fig. 14.6 
v_{0},v_{1}  Vertical creases at v_{0},v_{1} missing in figure.  ~Typo  Ryuhei Uehara 
27Oct08 
13 
219 
Fig. 13.5 
[Rightmost figure, top, above upward arrow]  [label false missing]  Typo  Ryuhei Uehara 
30Nov07 
13 
222 
Line+8 
Each of these three ... per input produce  Each of these three ... per input produces  Typo  Ryuhei Uehara 
30Nov07 
15 
232 
Line+13 
and that too only  and then only  More elegant language.  Ryuhei Uehara 
18Nov08 
15 
234 
Caption of Fig. 15.2 
(> 180°) ... (> 270°)  (> 90°) ... (> 135°)  Typos.  Ryuhei Uehara 
18Nov08 
16 
241 
Fig. 16.2(f) 
[some crease lines incorrect]  [Part (f) fixed (PDF)]  ~Typo.  Ryuhei Uehara 
29Nov08 
16 
244 
Fig. 16.5 label 
Forele g  Foreleg  Typo.  Ryuhei Uehara 
29Nov08 
17 
266 
Lines+9,+11 
1. the first offset amount ... 2. the first offset amount ... 
1. the smallest offset amount ... 2. the smallest offset amount ... 
Inaccurate word choice.  Ryuhei Uehara 
27Dec08 
17 
268 
Lines+7 
Figure 17.19(c)  Figure 17.19(c)  Typo  Ryuhei Uehara 
27Dec08 
17 
258 
Fig. 17.8 (turtle) 
[Two vertical creases]  One M crease should be a V; one V crease missing. Corrected turtle.color.pdf here. 
Typos  JOR 
23Jan08 
17 
278 
Line 2 
See Section 26.2 (p.437)  See Section 26.2 (p.438)  Typo  ED 
6Jul08 
18 
283 
Line 1 
the skeletal subdivision  the straightskeleton subdivision  Clearer  Ryuhei Uehara 
12 Jan09 
19 
287 
Footnote 
"petals of conics"  "pedals of conics"  Typo  Ryuhei Uehara 
12 Jan09 
20 
292 
Line 2 
0 nor 180^{o} ... 0 or 180^{o}  0^{o} nor 180^{o} ... 0^{o} or 180^{o}  Clearer  Ryuhei Uehara 
12 Jan09 
20 
293 
Sec. 20.2, Line+2 
Ukranian^{}  Ukrainian  Typo  Ryuhei Uehara 
12 Jan09 
20 
293 
Footnote 2 
[URL]^{}  http://www.ronresch.com/  Stale URL  Ryuhei Uehara 
12 Jan09 
21 
299 
Section 21.1, paragraph 2, sentence 1 
unfoldings, are now called “nets” 
unfoldings, what are now called “nets” 
Grammatical error caused by typesetter 
Edwin Chen 
17Oct07 
21 
303 
Lines+13 
the locus of points of S at a distance r of p  the locus of points of S at most a distance r of p  disk, not circle  Ryuhei Uehara 
22Jan09 
21 
303 
Lines1 
(108°)  (108°).  period missing at end of sentence  Ryuhei Uehara 
22Jan09 
21 
304 
Section 21.2, last paragraph 
notation of curvature 
notion of curvature 
Typo 
Edwin Chen 
17Oct07 
22 
308 
Line+12 
to a bound of 2/3(F2) pieces.  to a bound of (2/3)(F2) pieces.  ~Typo  Ryuhei Uehara 
11Mar09 
22 
308 
Line+17 
(and polyhedral duals are ... (p.339)  (and polyhedral duals are ... (p.339))  Typo  Ryuhei Uehara 
11Mar09 
22 
319 
Line+2 
If α is even larger, satisyfing α > 2 β + γ / 2,  If α is even larger, satisyfing α > 2 β + γ,  ~Typo  Ryuhei Uehara 
11Mar09 
22 
322 
Line+1 
We conclude this section on special classes with a proof sketch (...) that "dome" polyhedra can be edgeunfolded without overlap.  After sketching a proof that "dome" polyhedra can be edgeunfolded without overlap, we look at convex unfoldings, orthogonal polyhedra, and conclude with open problems in Section 22.5.5.  Sentence reflected earlier sectioning.  Ryuhei Uehara 
11Mar09 
22 
333 
Last line before Sec. 22.6 
(p. 361)  (p. 362)  ~Typo  JOR 
8Jun09 
22 
333 
Fig. 22.38 caption 
unfolding of a cuboctahedron  unfolding of a great rhombicuboctahedron  ~Typo  Ryuhei Uehara 
11Mar09 
22 
322 
Line+1 of Section 22.5.1 
A prismoid is ... equiangular convex polygons 
A prismoid is ... angularly similar convex polygons  ~Typo 
Don Hatch 
31Jul08 
23 
339 
Line+2 of Steinitz's Theorem 
The graph of edges and vertices of a convex polyhedron forms ...  The edges and vertices of a convex polyhedron form ...  ~Typo  Ryuhei Uehara 
9Apr09 
23 
342 
Line+13 
different, isolated, incongruent convex shapes  isolated, incongruent convex shapes  Redundant description  Ryuhei Uehara 
9Apr09 
23 
346 
Line7 
two dashed diagonals  two red diagonals  Figure changed  Ryuhei Uehara 
9Apr09 
23 
351 
Line+11 
Then all vertices have curvature ≥ π  Then at least four vertices have curvature ≥ π  ~Typo  Ryuhei Uehara 
9Apr09 
23 
355 
Line+2 
vector of squared edge lengths l  vector l of squared edge lengths  Clearer  Ryuhei Uehara 
9Apr09 
23 
355 
Line19 
attaching simplices ... at their faces  attaching simplices ... at their facets  More precise  Ryuhei Uehara 
9Apr09 
24 
362 
Line2 
continuuous Dijkstra  continuous Dijkstra  Typo  C.E.E. Zonneveld 
8 Oct 09 
24 
366 
Line6 Line3 
\triangle ( x_{i}, v_{j}, v_{k} )  \triangle x_{i}, v_{j}, v_{k}  Notational consistency  Ryuhei Uehara 
17Apr09 
24 
366 
Footnote 6 
Aleksandrov  Alexandrov  Spelling consistency  Ryuhei Uehara 
17Apr09 
24 
369 
Line+3 
cutting edges a'a and ax'  cutting edges a'a and ax  x, not x'  Ryuhei Uehara 
17Apr09 
24 
370 
Line9 
at the v_{i}  at the v_{j}  Notational consistency  Ryuhei Uehara 
17Apr09 
24 
375 
Section 21.4.0.1 numbering 
24.4.0.1 
24.4.1  Typo 
ED 
1Dec07 
24 
376 
Line+4 
the corners of C  the corners of curve C  ~Typo  Ryuhei Uehara 
17Apr09 
24 
377 
Line3 
(see Figure 24.23.  (see Figure 24.23).  Typo  Ryuhei Uehara 
17Apr09 
24 
378 
Caption to FIg. 24.23 
∂Q.  ∂Q, the boundary of Q.  First use of ∂.  Ryuhei Uehara 
17Apr09 
25 
382 
Line before Thm. 25.1.3 
[at end of sentence]  , where x,y=y,x  Clearer to spell out implication  Ryuhei Uehara 
10May09 
25 
383 
Line11 
xv_{i} < r  _{ } xv_{i } < r  Typo.  Ryuhei Uehara 
3May09 
25 
389 
2nd boxed table 
(6,0): 108  (6,0): 98  Typo.  Kensuke Yoshida & Takashi Horiyama  14Jun10 
25 
389 
4th boxed table 
(6,4): 168  (6,0): 158  Typo.  Kensuke Yoshida & Takashi Horiyama  14Jun10 
25 
390 
Item 3., Line+2 
v_{1}, v_{5} and v_{6}, v_{0}  { v_{1}, v_{5} } and { v_{6}, v_{0} }  Notational consistency  Ryuhei Uehara 
3May09 
25 
390 
Sec. 25.2.3 Line+1 
Figure 24.22(b)  Figure 25.6(b)  Typo  Ryuhei Uehara 
3May09 
25 
393 
Line11 
Figure 25.11(c)  Figure 25.11(c)  Typo  Ryuhei Uehara 
3May09 
25 
394 
Line 
≤ 1  ≤ π  Units of π later  Ryuhei Uehara 
3May09 
25 
397 
Proof, Line+3 
...an even number m...  (The choice of even m is for illustration convenience; the proof is no different for odd m.)  To cover all even n=2m+2  Ryuhei Uehara 
3May09 
25 
399 
Sec. 25.5, Line+3 
Koishi Hirata  Koichi Hirata  Typo  Ryuhei Uehara 
3May09 
25 
399 
Line12 
vertices v_{i} and e_{i}  vertices v_{i} and edges e_{i}  Clearer  Ryuhei Uehara 
3May09 
25 
401,2 
Figs. 25.20, 25.22 
[ μ ]  [ μ is the supplement of the angle illustrated]  ~Typo  Ryuhei Uehara 
10May09 
25 
401 
Line16 
interior of e_{j}  interior of e_{j1}  Typo  Ryuhei Uehara 
3May09 
25 
401 
Line10 
between v_{i} and v_{k}  between v_{i} and v_{j}  Typo  Ryuhei Uehara 
3May09 
25 
410 
Line6,5 
e_{0}, e_{3}, e_{6}, e_{9} ... e_{3}  e_{0}, e_{4}, e_{7}, e_{10} ... e_{4}  Indices off by 1  Ryuhei Uehara 
3May09 
25 
412 
Line+1 after Proof 
this lemma  this corollary  ~Typo  Ryuhei Uehara 
3May09 
25 
422 
Table 25.1 
Comb. Type Y, 2nd Geom. Type Y  Comb. Type Y, 2nd Geom. Type T  Typo  Ryuhei Uehara 
10May09 
25 
423 
Line+2 
dissection ... is a partition of each into a finite number of pieces so that the pieces of A can be rearranged to form B  dissection ... is a partition of each into a finite number of congruent pieces, so that the pieces of A can be rearranged to form B and vice versa  Clearer  Ryuhei Uehara 
3May09 
25 
425 
Fig. 25.53(b) 
[interior bold line]  [should be dashed]  Typo  Ryuhei Uehara 
3May09 
25 
427 
Line+6 
the the  the  Typo  Ryuhei Uehara 
3May09 
25 
428 
Line1 of Proof 
claimed by the lemma.  claimed by the theorem.  ~Typo  Ryuhei Uehara 
3May09 
25 
434 
Fig. 25.62 
[topmost pink rectangle]  [should be blue]  ~Typo  Ryuhei Uehara 
10May09 
26 
437 
Sec. 26.2, Line+2 
definitions ... has been  definitions ... have been  Plural.  Ryuhei Uehara 
4May09 
26 
438 
Line 3 before Sec. 26.3 
mentioned in Part II (p.273)  mentioned in Part II (p.278)  Typo  ED 
6Jul08 
Biblio 
443 
3rd entry 
Aaron Abrams and Robert Shrist  Aaron Abrams and Robert Ghrist  Typo  Julian Wilson 
15Jan10 
Biblio 
445 
5th entry, bellcastro and Hull 2002b 
348: 1290  348: 273282  Typo in page numbers  Ryuhei Uehara 
25Aug08 
Biblio 
452 
15th entry 
Graver, Servatius, Servatius,
Combinatorial Rigidity

Move to become 6th entry
on the page 
Bibliographical item out of sorted order. 
Joe Malkevitch 
1Oct07 
Index 
468 
Open Problem, 9.1 
9.1: Locked Length Ratio, 154 9.2: Locked FixedAngle Chains, 154 
9.2: Locked Length Ratio, 154 9.3: Locked FixedAngle Chains, 154 
Two open problems are accidentally labeled 9.1 
ED 
10Sep07 