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

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158 gram This noun is derived from the Greek nouns tÕ gr£mma, a letter, and ¹ gramm», a stroke in writing, a line. It is an invention of the French National Assembly. graph From the Greek verb gr£fw, to write or draw, came the noun graf», a drawing. gravitation See the entry gravity below. From the verb gravo, gravare there was formed the late frequentative verb gravito, gravitare, gravitavi, gravitatus with the meaning to weigh down constantly, and from its fourth principal part was formed the noun gravitatio, gravitationis in the usual manner. gravity The Latin adjective gravis, grave means heavy, and is related to the Greek adjective barÚj with the same meaning. From the adjective there was formed the verb gravo, gravare, gravavi, gravatus with the meaning to load, weigh down, and from this verb was formed the noun gravitas, heaviness, whence came the English noun. gyration The Greek noun gàroj means a ring or circle. The Latin ending -atio, -ationis was then added to the stem to form this macaronic noun. It is therefore a low word. H harmonic The Greek verb ¡rmÒzw means to fit together, to join, especially of carpenter’s work. From it was formed the noun¡rmon…a meaning fitting together, joining, agreement, musical concord. The addition of the adjectival suffix -ikÒj produced the adjective¡rmonikÒj with the meaning skilled in music; the Greeks used this word in its mathematical sense, for example, they spoke of the harmonic mean. If O is an open subset of Rn , a real valued function f 159 defined on O is harmonic if  f/x1 2 + …+  f/xn 2 = 0 everywhere on O. haversine This is an absurd word of the nineteenth century meaning half the versed sine, that is, (1 – cos θ)/2. The formation of words in this way is buffoonery. A similarly contemptible word is coversine, which means the complemental versed sine, and is supposed to mean 1 – sin θ; the authors of it were clumsy butchers and did not bother to take the complete first syllable of the first word. The associated abbreviations hav θ and covers θ are ludicrous. -hedron The Greek verb ›zomai means to sit, and from it is derived the noun ›dra, which means seat, base. The adjective polÚedroj, polÚedron means having many faces, tetr£edroj, tetr£edron means having four faces, ˜x£edroj, ˜x£edron means having six faces, Ñkt£edroj, Ñkt£edron means having eight faces, dwdek£edroj, dwdek£edron means having twelve faces, and e„kos£edroj, e„kos£edron means having twenty faces. The second or neuter form of each adjective was then used alone with the noun scÁma, figure, understood, and we obtained the technical terms polyhedron, tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. helicoid This is a modern word compounded of ›lix, ›likoj, a coil, and the syllable -oid from eŁdoj, shape. The word is used by Konrad Knopp in his discussion of the Riemann surface of the function w = z1/2 (Theory of Functions, Part II, Dover Publications, Inc., New York, 1947, p. 102). helix This word is the Greek ›lix, which means a coil. It comes from the verb ˜l…ttw, to turn around. The Greek plural, which is mandatory, is helices. To write helixes is very low since it has never been used by the best authors. Helical columns were employed in the ancient Middle East, as one can see on the cover of the February 1984 issue of the Yale Alumni Magazine and Journal. The most famous example of these are those of the baldacchino of St. Peter’s Basilica by Bernini; he used six such columns at the Val de Grâce in Paris. Sir Christopher Wren intended the same for St. Paul’s in London, and 160 his plan was consummated after the Second World War. Double helical columns are to be found in the cloisters of St. Paul’s outside the Walls in Rome. The Columns of Trajan and Marcus Aurelius in Rome are inscribed with engravings climbing up as a helix. Columns engraved with helices may be found in Durham Cathedral. The Canopy over the High Altar of St. Mary Major’s in Rome is supported by four columns on which strands of laurel climb as a helix. Bramante constructed a helical staircase in the Apostolic Palace of the Vatican. In the following century, Bernini constructed a similar staircase...