Book:Christopher Clapham/The Concise Oxford Dictionary of Mathematics/Sixth Edition/Errata

Errata for 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.)

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

$I_n = \dfrac {\cos^n x \sin x} n + \dfrac {n - 1} n I_{n - 2}$.

Also see

• Errata for Fifth Edition