Book:Ephraim J. Borowski/Dictionary of Mathematics/Errata

Errata for 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics

Babbage's Analytical Engine

analytical engine or difference engine

a mechanical precursor of the modern digital computer, including a punched-card reader and a memory storage device, of which the principle was described by Charles Babbage in $1834$, but which was never completed.

Sum of Squares of Sine and Cosine

cosine

$\cosh^2 z + \sinh^2 z = 1$

Equilateral Polygon is Equiangular

equiangular

Any equilateral plane figure is also equiangular, and so is regular ...

Fields Medal

Field's medal

Sum of Infinite Geometric Sequence

geometric series

The sum of the finite initial segments of the series is:

$\dfrac {a \paren {r^n - 1} } {r - 1}$,

whence, if the infinite series converges, its sum is $a / \paren {r - 1}$.

Difference of Squares of Hyperbolic Cosine and Sine

hyperbolic function

The hyperbolic functions satisfy the identity:

$\sinh^2 \alpha - \cosh^2 \alpha = 1$

Lucas Numbers

Lucas numbers

the sequence of integers

$2, 1, 3, 4, 7, 11, 18, 29, \dotsc$

derived from the same difference equation as the fibonacci numbers, but using different initial values. (Named after the English mathematician Henry Lucas (died 1663).)

Mersenne Primes

Mersenne numbers or Mersenne primes

... the largest known is $2^{11,213} - 1$.

Mertens' Convergence Theorem

Merten's theorem

Octal

octal

... for example, $371.24_8$ represents the number

$\paren {3 \times 8^2} + \paren {7 \times 8^1} + \paren {1 \times 8^0} + \paren {2 \times 8^{-1} } + \paren {4 \times 8^{-2} } = 249.25_{10}$.

Pentagonal Number

pentagonal number

a figurate number of the form $n \paren {3 n \pm 1}$.

Prime Number

prime, adj. 1 a. (of an integer) having no factors except itself and unity.

Primitive of $\sec x$: Secant plus Tangent Form

Appendix $2$: Table of derivatives and integrals of common functions: Trigonometric functions

$\ds \int \sec x \rd x = \map \ln {\sec x + \tan x} + C$

Primitive of $\csc x$: Cosecant minus Cotangent Form

Appendix $2$: Table of derivatives and integrals of common functions: Trigonometric functions

$\ds \int \csc x \rd x = \map \ln {\csc x - \cot x} + C$