• The KIPS Transactions:PartA
• /
• v.14A no.4
• /
• pp.249-254
• /
• 2007

In this paper, we consider the embedding problem of postorder Fibonacci circulant. We show that Fibonacci linear array, Fibonacci mesh, Fibonacci tree, Fibonacci cubes and Hypercube are a subgraph of postorder Fibonacci circulant.

• The KIPS Transactions:PartA
• /
• v.15A no.1
• /
• pp.27-34
• /
• 2008

In this paper, We propose a new parallel computer topology, called the Postorder Fibonacci Circulants and analyze its properties. It is compared with Fibonacci cubes, when its number of nodes is kept the same of comparable one. Its diameter is improved from n-2 to $[\frac{n}{3}]$ and its topology is changed from asymmetric to symmetric. It includes Fibonacci cube as a spanning graph.

• School Mathematics
• /
• v.11 no.2
• /
• pp.243-260
• /
• 2009

In this paper, we have designed a teaching unit for the learning mathematising of secondary pre-service teachers by exploring generalized fibonacci sequences. First, we have found useful formulas for general terms of generalized fibonacci sequences which are expressed as combinatoric notations. Second, by using these formulas and CAS graphing calculator, we can help secondary pre-service teachers to conjecture and discuss the limit of the sequence given by the rations of two adjacent terms of an m-step fibonacci sequence. These processes can remind secondary pre-service teachers of a series of some mathematical principles.

• Journal of KIISE:Computer Systems and Theory
• /
• v.36 no.6
• /
• pp.437-450
• /
• 2009

In this paper, we propose seven edge labeling methods. The methods produce three case of edge labels-sets of Fibonacci numbers {$F_k|k\;{\geq}\;2$}, {$F_{2k}|k\;{\geq}\;1$} and {$F_{3k+2}|k\;{\geq}\;0$}. When a sort of interconnection network, the circulant graph is designed, these edge labels are used for its jump sequence. As a result, the degree is due to the edge labels.

• Journal for History of Mathematics
• /
• v.21 no.4
• /
• pp.87-104
• /
• 2008

In this paper we investigate several properties and characteristics of the generalized Fibonacci sequence $\{g_n\}$={a, b, a+b, a+2b, 2a+3b, 3a+5b,...}. This concept is a generalization of the famous Fibonacci sequence. In particular we find the identities of sums and the nth term $g_n$ in detail. Also we find the generalizations of the Catalan's identity and A. Tagiuri's identity about the Fibonacci sequence, and investigate the relation between $g_n$ and Pascal's triangle, and how fast $g_n$ increases. Furthermore, we show that $g_n$ and $g_{n+1}$ are relatively prime if a b are relatively prime, and that the sequence $\{\frac{g_{n+1}}{g_n}\}$ of the ratios of consecutive terms converges to the golden ratio $\frac{1+\sqrt5}2$.

• The Korean Journal of Applied Statistics
• /
• v.22 no.5
• /
• pp.1103-1113
• /
• 2009

We know that the first digits sequence of fibonacci numbers obey Benford's law. For the sequence in which the first two numbers are the arbitrary integers and the recurrence relation $a_{n+2}=a_{n+1}+a_n$ is satisfied, we can find that the first digits sequence of this sequence obey Benford's law. Also, we can find the stucture of the first digits sequence of this sequence with the exploratory data analysis tools.

• Journal of Educational Research in Mathematics
• /
• v.18 no.3
• /
• pp.373-389
• /
• 2008

In this paper, we designed a teaching unit for the learning mathematization of secondary pre-service teachers through exploring the relationship between partition models and generalized fibonacci sequences. We first suggested some problems which guide pre-service teachers to make phainomenon for organizing nooumenon. Pre-service teachers should find patterns from partitions for various partition models by solving the problems and also form formulas front the patterns. A series of these processes organize nooumenon. Futhermore they should relate the formulas to generalized fibonacci sequences. Finding these relationships is a new mathematical material. Based on developing these mathematical materials, pre-service teachers can be experienced mathematising as real practices.

• School Mathematics
• /
• v.12 no.4
• /
• pp.619-638
• /
• 2010

In this paper, we listed and reviewed some properties on polygonal numbers, pyramidal numbers and Pascal's triangle, and Fibonacci sequence. We discussed that the properties of gnomonic numbers, polygonal numbers and pyramidal numbers are explained integratively by introducing the generalized k-dimensional pyramidal numbers. And we also discussed that the properties of those numbers and relationships among generalized k-dimensional pyramidal numbers, Pascal's triangle and Fibonacci sequence are suitable for teaching and learning of mathematical reasoning and connections.

• Journal for History of Mathematics
• /
• v.28 no.3
• /
• pp.151-164
• /
• 2015

The purpose of this paper is to develop a teaching and learning material integrated two subjects Pythagorean theorem and Fibonacci numbers. Traditionally the former subject belongs to geometry area and the latter is in algebra area. In this work we integrate these two issues and make a discovery method to generate infinitely many Pythagorean numbers by means of Fibonacci numbers. We have used this article as a teaching and learning material for a science high school and found that it is very appropriate for those students in advanced geometry and number theory courses.

• Journal of the Institute of Convergence Signal Processing
• /
• v.19 no.2
• /
• pp.42-46
• /
• 2018

Adaptive signal processing is quite important in various signal and communication environments. In adaptive signal processing methods since the least mean square(LMS) algorithm is simple and robust, it is used everywhere. As the step is varied in the variable step(VS) LMS algorithm, the fast convergence speed and the small excess mean square error can be obtained. Various variable step LMS algorithms are researched for better performances. But in some of variable step LMS algorithms the computational complexity is quite large for better performances. The fixed step LMS algorithm with a low computational complexity merit and the variable step LMS algorithm with a fast convergence merit are combined in the proposed sporadic step algorithm. As the step is sporadically updated, the performances of the variable step LMS algorithm can be maintained in the low update rate using Fibonacci sequence. The performances of the proposed variable step LMS algorithm are proved in the adaptive equalizer.