Book:David Nelson/The Penguin Dictionary of Mathematics/Second Edition/Errata

Errata for 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.)

Directed Angle

angle

Often an angle is regarded as the measure of the rotation involved in moving from one initial axis to another final axis (termed a direction angle).

Frequency of Beats

beats

The frequency at which the amplitude fluctuates is the beat frequency, which is equal to the difference in frequency of the combining waves, $\size {f_1 - f_2}$.

Eugenio Beltrami

Beltrami, Eugenio (1835-99)

Paradoxien des Unendlichen

Bolzano, Bernhard Placidus (1781-1848)

He also published an influential work, Paradoxes of the Infinite (1850), in which he anticipated some of the later results of *Cantor.

William Brouncker

Brouncker, William, Viscount (1620-85)

Edward Cocker

Cocker, Edward (1631-75)

Jan de Witt

conic (conic section)

The treatment of conic sections by coordinate geometry was begun in the $17$th century, notably by Jan de Witt $\text {1629}$ – $\text {1672}$ ...

Eccentric Angle

eccentric angle

The angle that a radius of the *auxiliary circle makes with the positive $x$-axis, used in forming the parametric equations of an *ellipse or *hyperbola.

Eisenstein's Conjecture

Eisenstein, Ferdinand Gotthold Max (1823-52)

German mathematician who proposed the still unproved conjecture that numbers of the form $2^2 + 1, 2^{2^2} + 1, 2^{2^{2^2} } + 1, \ldots$ are prime.

Historical Note on Elliptic Functions

elliptic functions

Functions first derived from *elliptic integrals by Abel in $1826$.

Daniel Gabriel Fahrenheit

Fahrenheit degree

[After G.D. Fahrenheit (1686-1736)]

Farey Sequence

Farey sequence (of order $n$)

Farey sequence (of order $n$) (C. Haros, 1802; J. Farey; 1816)

Ad Locos Planos et Solidos Isagoge

Fermat, Pierre de (1601-65)

Further work in his Isagoge ad locus planos et solidos (1679, On the Plane and Solid Locus) foreshadowed the later analytic geometry of Descartes ...

Floating-Point Representation: $105.7$

floating-point representation

For example, $105.7 = 0.1057 \times 10^{-3}$.

Period of Rotation of Plane of Oscillation of Foucault's Pendulum

Foucault's pendulum

To an observer on earth the plane of oscillation [of Foucault's pendulum] makes one rotation every $24$ hours (approximately).

Historical Note on Fuzzy Logic

fuzzy logic

A system of logic proposed in $1965$ by Lofti Zadeh, an Iranian electrical engineer, ...

Gauss-Seidel Method

Gauss-Seidel method

Now, writing $\mathbf x_n$ for the column vector of values of $x_1, x_2, x_3$ after the $n$th iteration, and

$\mathbf L = \begin {pmatrix} a_{1 1} & 0 & 0 \\ a_{2 1} & a_{2 3} & 0 \\ a_{3 1} & a_{3 2} & a_{3 3} \end {pmatrix}, \mathbf U = \begin {pmatrix} 0 & a_{1 2} & a_{1 3} \\ 0 & 0 & a_{2 3} \\ 0 & 0 & 0 \end {pmatrix}$

the iterative relationship is

$\mathbf x_{n + 1} = \mathbf L^{-1} \paren {\mathbf b - \mathbf U \mathbf x_n}$

Jørgen Pedersen Gram

Gram-Schmidt method

It is named after Jorgen Pederson Gram (1850-1916) and Erhard Schmidt (1876-1959).

Determinant of Order $3$ Hilbert Matrix

Hilbert matrix

For $n = 3$,

$H_3 = \begin {pmatrix} 1 & \tfrac 1 2 & \tfrac 1 3 \\ \tfrac 1 2 & \tfrac 1 3 & \tfrac 1 4 \\ \tfrac 1 3 & \tfrac 1 4 & \tfrac 1 5 \\ \end {pmatrix}$

and $\map \det {H_3} = 1 / 12 \, 160$.

Inverse of Curve under Inversive Transformation

inversion 1.

A curve $\map f {x, y} = 0$ has an inverse $\map f {x', y'} = 0$, where

$x' = \dfrac {r^2 x} {x^2 + y^2} \qquad y' = \dfrac {r^2 y} {x^2 + y^2}$

Maurice Henry Quenouille

jack-knife (M.L. Quenouille, 1949)

Nikolai Ivanovich Lobachevsky

Lobachevsky, Nikolai Ivanovich (1793-1856)

Congruence Transformation

matrix (plural matrices)

$(2)$ Congruent transformation in which $X$ is the ${}^*$transpose of $Y$; ...

Pietro Mengoli

Mengoli, Pietro (1626-82)

Emmy Noether

Noether, Amalie (Emmy) (1883-1935)

William Oughtred

Oughtred, William (1575-1660)

Reducible Polynomial

reducible polynomial

A *polynomial is reducible over a *field $F$ if it can be factored into two polynomials having coefficients in $F$.

Rhombohedron

rhombohedron

A hexagonal prism.

Willebrord van Royen Snell

Snell, Willebrord van Royen (1580-1626)

Alfred Tarski

Tarski, Alfred (1902-85)

Wronskian

Wronskian

It is named after the Polish mathematician Józef Maria Hoene-Wroński (1776-1853).

Primitive of $\sqrt {x^2 - a^2}$

$\ds \int \sqrt {x^2 - a^2} \rd x = \frac 1 2 a^2 \cosh^{-1} \frac x a + \frac 1 2 {x \sqrt {x^2 - a^2} } + C$