Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots

G

151 G g g Gamma is the third letter of the Greek alphabet. The area of the plane region Hn bounded by the x-axis, the hyperbola with equation y = 1/x, and the vertical lines x = n and x = n + 1 is ln[(n + 1)/n]. The area of the rectangle Rn with vertices (n,0), (n + 1,0), (n,1/n), (n + 1,1/n) is 1/n, and the rectangle Rn contains the region Hn. If we let gn be the area of the region inside Rn but outside of Hn, then the series g1 + g2 + g3 + g4 + g5 +… may be shown to converge by the limit comparison test with 1/n3/2 , and the sum is called g, the Eulerian gamma constant. We then have, for large n, the following approximation for the partial sum of the harmonic series: 1 + 1/2 + 1/3 + …+ 1/n ≈ ln (n + 1) + g . The small case Greek gamma was used by Euler (1707–1783) to denote the limiting value of (1 + 1/2 + 1/3 + …+ 1/n) – ln (n + 1). It is unknown whether Euler’s constant is rational or irrational. I have seen the symbol C used for this constant, for example, by Konrad Knopp. The value of g is .57721566 to eight decimal places; there is a mnemonic device to remember this, but it requires knowledge of papal history. The year 772 was the year of the election of Adrian I, and 1566 was the year of the accession of Pius V to the supreme pontificate. Englishmen and Americans must learn to pronounce the name Euler Oi-ler, not You-ler. gamma This is the third letter of the Greek alphabet, used in mathematics to denote a function of Euler and a probability distribution. In the mid-thirteenth century, the diagrams in mathematical manuscripts started to be labeled A, B, C,… in accordance with the Latin order of the letters, instead of A, B, G,…, the Greek order, as previously. The capital gamma Γ is the symbol for the gamma function, which generalizes the factorial function to the set of positive real numbers. 152 gematria This is the Hebrew \UXPJ, the transliteration of, and therefore the Hebrew word for, geometry. It eventually acquired the specialized meaning of the superstitious use of mathematics, especially the deriving of meaning from the numerical value of the letters that compose words. The most famous case of this is Revelation XIII 18: Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.. The earliest occurrence of the word is in the Talmud (Pirke Aboth III, 23): Rabbi Eleazar Hisma said: Offerings of birds and purifications of women, these, yea these, are the essential precepts. Astronomy and geometry are but fringes to wisdom. (R. Travers Herford, The Ethics of the Talmud: Sayings of the Fathers, Schocken Books, New York, 1966, p. 93) Actually, the word in this Talmudic text is in the plural number WY \UXPJand so cannot mean geometry, as Herford translates, but must instead mean mathematical calculations. gender One of the articles mentioned on the cover of the January 2012 issue of the Notices of the American Mathematical Society is “Debunking Myths about Gender and Mathematics Performance.” The noun gender comes from the Latin genus, which means type, kind. The d crept in because of mispronunciation in Old French. Nouns in Latin, Greek, Russian, and German are divided into three types or kinds, masculine, feminine, and neuter. Nouns in Arabic, Hebrew, French, and Italian are of two types, masculine and feminine. English nouns have no such classes. Thus, gender is a technical term in certain languages conveying the information as to which class a noun belongs. Sex pertained to living beings and identified them as male or female. The use of gender in place of sex would formerly have been marked wrong, but it has now become commonplace. The noun sex is ever more being restricted to mean physical sexual activity. The topic is a hornets’ nest. 153 The occasional use of humankind as an alternative to mankind is sanctioned by Gibbon and is unobjectionable. generalization The Latin adjective generalis means belonging to the genus, that is to say, to the specific class or kind in question. It acquired the meaning of relating to all as opposed to...