Book:Christopher Clapham/The Concise Oxford Dictionary of Mathematics/Errata
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Errata for The Concise Oxford Dictionary of Mathematics
Fifth Edition
Accurate to $n$ Decimal Places
- accurate (correct) to $n$ decimal places
- $\sqrt {86.56} = 9.30076...$ is $9.30$ correct to two decimal places.
Acre
- acre
Normal Subgroup of Symmetric Group on More than $4$ Letters is Alternating Group
- alternating group
- For $n > 4$, it is the only proper, *normal subgroup of $S_n$, apart from the *empty set.
Uniform Antiprism is Semiregular Polyhedron
- antiprism
- If the end faces are regular and the triangular faces are equilateral, the antiprism is a semi-regular polygon.
Uniform Prism is Semiregular Polyhedron
- Archimedean solid
- Right-regular *prisms with square side faces ... are semi-regular [polyhedra].
Uniform Antiprism is Semiregular Polyhedron
- Archimedean solid
- ... (right-regular) *antiprisms whose side faces are equilateral triangles are semi-regular [polyhedra].
Expansion Theorem for Determinants
- cofactor
- (i) The expression $a_{i1} A_{i1} + a_{i2} + \cdots + a_{in} A_{in}$ has the same value for any $i$, and is the definition of $\det \mathbf A$, the determinant of $\mathbf A$.
Cosine of Sum
- compound angle formulae (in trigonometry)
- $\map \cos {a \pm b} = \cos a \cos b \pm \sin a \sin b$
Equiangular Spiral
- equiangular spiral
- The equation can be written $r = k \theta + b$
Uniform Prism is Semiregular Polyhedron
- prism
- A right-regular prism in which the rectangular faces are square is semi-regular (see Archimedean solid).
Transversable Graph
- transversable graph
Norbert Wiener
- Wiener, Norbert (1899-1969)
Edward Witten
- Witten, Edward (1957- )
Primitive of $\dfrac 1 {\sqrt {a^2 + x^2} }$
- Appendix $7$: Integrals
- $\ds \int \frac {\d x} {\sqrt {a^2 + x^2} } = \dfrac 1 a \tan^{-1} {\frac x a}$
Primitive of $\sqrt {a^2 - x^2}$
- Appendix $7$: Integrals
- $\ds \int \sqrt {x^2 + x^2} \rd x = \frac 1 2 x \sqrt {x^2 + x^2} + \frac 1 2 a^2 \sin^{-1} \frac x a$
Sixth Edition
Accurate to $n$ Decimal Places
- accurate (correct) to $n$ decimal places
- $\sqrt {86.56} = 9.30076...$ is $9.30$ correct to two decimal places.
Solution Space of Nonhomogeneous Linear Equation forms Affine Space
- affine space
- For example, the solutions to the ODE $y' ' - y = 1$ has a solution set $S$ ...
Intersection Distributes over Union
- algebra of sets
- $A \cap \paren {B \cup C} = \paren {A \cap B} \cup \paren {A \cap \mathop \cap C}$
Uniform Antiprism is Semiregular Polyhedron
- antiprism
- If the end faces are regular and the triangular faces are equilateral, the antiprism is a semi-regular polyhedron.
Uniform Prism is Semiregular Polyhedron
- Archimedean solid
- Right-regular *prisms with square side faces ... are semi-regular [polyhedra].
Uniform Antiprism is Semiregular Polyhedron
- Archimedean solid
- ... (right-regular) *antiprisms whose side faces are equilateral triangles are semi-regular [polyhedra].
Uniform Prism is Semiregular Polyhedron
- prism
- A right-regular prism in which the rectangular faces are square is semi-regular (see Archimedean solid).
Reduction Formula for $\ds \int \sin^n x \rd x$
- Appendix $8$: Integrals: Reduction Formulae
- For $I_n = \int \sin^n x \rd x$, where $n \ge 2$, then
- $I_n = -\dfrac {\sin^n x \cos x} n + \dfrac {n - 1} n I_{n - 2}$.
Reduction Formula for $\ds \int \sin^n x \rd x$
- Appendix $8$: Integrals: Reduction Formulae
- For $I_n = \int \cos^n x \rd x$, where $n \ge 2$, then
- $I_n = \dfrac {\cos^n x \sin x} n + \dfrac {n - 1} n I_{n - 2}$.