The memoir class - The UK TeX Archive

E. LATEX AND TEX\advance\@tempdima -\textwidth % minus the textwidth\advance\@tempdima -\spinemargin % minus the spinemargin\ifdim\@tempdima < \@tempdimb % should be close to zero%% error % otherwise a problem\fiChanging the subject, on the offchance that you might want to see how the Fibonaccisequence progresses, the first thirty numbers in the sequence are: 1, 1, 2, 3, 5, 8, 13, 21,34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368,75025, 121393, 196418, 317811, 514229 and 832040. I got LaTeX to calculate those numbersfor me, and it could have calculated many more. They were produced by just saying\fibseries{30}. The French mathematician Édouard Lucas (1842–1891) studied sequenceslike this and was the one to give it the name Fibonacci. Lucas also invented thegame called the Tower of Hanoi with Henri de Parville (1838–1909), supplying the accompanyingfable [dP84, RBC74]:In the great temple at Benares beneath the dome that marks the center ofthe world, rests a brass plate in which are fixed three diamond needles, eacha cubit high and as thick as the body of a bee. On one of these needles, at thecreation, God placed sixty-four discs of pure gold, the largest disc resting on thebrass plate, and the others getting smaller and smaller up to the top one. This isthe tower of Bramah. Day and night unceasingly the priests transfer the discsfrom one diamond needle to another according to the fixed and immutablelaws of Bramah, which require that the priest on duty must not move morethan one disc at a time and that he must place this disc on a needle so thatthere is no smaller disc below. When the sixty-four discs shall have been thustransferred from the needle which at creation God placed them, to one of theother needles, tower, temple, and Brahmins alike will crumble into dust andwith a thunderclap the world will vanish.The number of separate transfers of single discs is 2 64 − 1 or just under eighteen anda half million million moves, give or take a few, to move the pile. At the rate of one discper second, with no mistakes, it would take more than 58 million million years before wewould have to start being concerned.In his turn, Lucas has a number sequence named after him. There are many relationshipsbetween the Fibonacci numbers F n and the Lucas numbers L n , the simplest, perhaps,beingL n = F n−1 + F n+1 (E.1)5F n = L n−1 + L n+1 (E.2)The first 15 numbers in the Lucas sequence are: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199,322, 521 and 843. These were produced by saying \gfibseries{2}{1}{15}. The Lucasnumbers are produced in the same manner as the Fibonacci numbers, it’s just the startingpairs that differ.However, it is the definition of the \fibseries and \gfibseries macros that mightbe more interesting in this context.First, create four new counts. \fibtogo is the number of terms to be calculated, \fibis the current term, and \fibprev and \fibprevprev are the two prior terms.442