Showing papers on "Fibonacci number published in 1978"
20 citations
TL;DR: It is proved, as an application of the Principle of Optimal Design, that the cost (the entropy) of normal asymmetric phyllotaxis (characterized by the Fibonacci sequence) is minimal among all other types of phyllotsaxis.
17 citations
TL;DR: It is shown that the modified contact pressure model, if based on the concept of mechanical pressures between primordia in contact, cannot account for the divergence angles found in low phyllotaxis systems, but this deficiency can be overcome if the contact pressure effect is regarded as a chemical phenomenon.
13 citations
TL;DR: In this paper, the Reidemeister-Schreier algorithm is used to show that two closely related classes X(n) and Y(n), of two generator two relation groups, are finite and not metabelian and the orders of these groups are determined and shown to be divisible by powers of Fibonacci numbers or powers of Lucas numbers.
Abstract: Two closely related classes X(n) and Y(n) of two generator two relation groups are studied. The group presentations arise from an investigation of a Fibonacci type group of order 1512. The Reidemeister-Schreier algorithm is used to show that the groups X(n) are finite and not metabelian. The orders of these groups are determined and shown to be divisible by powers of Fibonacci numbers or by powers of Lucas numbers. In addition these groups add to the relatively few examples of non-metabelian two generator two relation groups whose orders are known precisely.
11 citations
01 Jan 1978
TL;DR: In this article, a Verfahren zur Behandlung gewisser exponentialler Gleichungen und diophantischer Gleichingsungen is presented.
Abstract: GENERALIZED TWO-PILE FIBONACCI NSM 459 8. T. Skolem, "Ein Verfahren zur Behandlung gewisser exponentialler Gleich-ungen und diophantischer Gleichungen," 8de Skand.
6 citations
TL;DR: In this article, the Fibonacci Numbers and Pineapple Phyllotaxy were studied in a two-year college mathematics journal, Vol. 9, No. 3, pp. 132-136.
Abstract: (1978). Fibonacci Numbers and Pineapple Phyllotaxy. The Two-Year College Mathematics Journal: Vol. 9, No. 3, pp. 132-136.
4 citations
Patent•
20 Sep 1978
TL;DR: In this paper, a digital-analog converter comprises a reference value adder having its multi-igit input coupled to a multidigit output of a switch unit and a Fibonacci p-code convolution unit.
Abstract: A digital-analog converter comprises a reference value adder having its multidigit input coupled to a multidigit output of a switch unit and a Fibonacci p-code convolution unit. The fibonacci p-code convolution unit has its multidigit output coupled to a multidigit input of the switch unit. The Fibonacci p-code convolution unit comprises n stages, each of which, related to a certain bit position in a range from one to n-2, comprises an AND gate and an OR gate. Each of the stages corresponding to bit positions from zero to n-1 comprises a flip-flop, an OR gate and an AND gate. The set and reset inputs of the flip-flop of each stage are coupled, respectively, to the output of the AND gate and to the output of the OR gate. The set input of the flip-flop of the stage of the zero bit position is a counting input of the digital-analog converter. First and second inputs of the OR gate of the stage of the ith bit position are coupled, respectively, to the outputs of the AND gates of the (i+l)th and (i+p+l)th states. First, second and third inputs of the AND gate of the ith stage, beginning with the (p+l)th stage, are coupled, respectively, to the reset output of the flip-flop of the same stage, to the set output of the flip-flop of the (i-l)th stage and to the set output of the flip-flop of the (i-p-l)th stage. The remaining inputs of all the AND gates are joined together to constitute a clock input of the digital-analog converter, where n is the length of the Fibonacci p-code and i=0,1,2, . . . , n-l.
3 citations
Journal Article•
TL;DR: Finkelstein and Whitley as mentioned in this paper considered the problem of finding the expected number of tosses of a p-coin until k consecutive heads appeared and showed that the problem is NP-hard.
Abstract: FIBONACCI NUMBERS IN COIN TOSSING SEQUENCES 0. Struve, The Universe (Cambridge, Mass.: MIT Press, 1962). Brian Marsden, letter to the author dated 1976. B. A. Read, The Fibonacci Quarterly, Vol. 8 (1970), pp. 428-438. F.X.Byrne, Bull. Amer. Astron. Soc., Vol. 6 (1974), pp. 426-427. L. H. Wasserman, et al. , Bull. Amer. Astron. Soc, Vol. 9 (1977), p. 498. FIBONACCI NUMBERS IN COIN TOSSING SEQUENCES MARK FINKELSTEIN and ROBERT WHITLEY University of California at Irvine, Irvine, CA 92717 The Fibonacci numbers and their generating function appear in a natural way in the problem of computing the expected number [2] of tosses of a fair coin until two consecutive heads appear. The problem of finding the expected number of tosses of a p-coin until k consecutive heads appear leads to clas- sical generalizations of the Fibonacci numbers. First consider tossing a fair coin and waiting for two consecutive heads. Let 0 n be the set of all sequences of H and T of length n which terminate in BE and have no other occurrence of two consecutive heads. Let S n be the num- ber of sequences in 0 n . Any sequence in 0 n either begins with T, followed by a sequence in 0 n -i, or begins with ET followed by a sequence in C n _ 2 . Thus, S n = S n -1 + Sn-2, Si = 0, S 2 Consequently, S n -i = F ny the nth Fibonacci number. termination in n trials is S n /2 n . Letting The probability of Z 2 n^ n > and using the generating function (1 - x - x 2 ) ~ l for the Fibonacci numbers, yields g{x) = x 2 /(1 - x - x 2 ). Hence, the expected number of trials is J2nS n /2 n n = l We generalize this result to the following Tk
3 citations
TL;DR: In this article, it was shown that a certain class of Fibonacci groups can not be right ordered, and the question remaining is: are the torsion-free members of this class unique products groups?
Abstract: We show that a certain class of Fibonacci groups can not be right ordered. A question remaining is: Are the torsion-free members of this class unique products groups?
TL;DR: The number of n-bit words with a given longest run of 1's is computed and a relation between these numbers and the Fibonacci numbers is outlined and investigated.
Abstract: The number of n-bit words with a given longest run of 1's is computed. A relation between these numbers and the Fibonacci numbers is outlined and investigated.