scholarly journals A SHORT NOTE ON FIBONACCI NUMBERS IN A GENERALIZED PYTHAGOREAN TRIPLES

2021 ◽  
Vol 4 (1) ◽  
pp. 90-95
Author(s):  
Emily L Casinillo ◽  
Leomarich F Casinillo
Keyword(s):  
Fibonacci Numbers ◽  
Short Note ◽  
Pythagorean Triples ◽  
New Formula

This paper aims to construct a new formula that generates a Fibonacci numbers in a generalized Pythagorean triples. In addition, the paper formulates some Fibonacci identities and discuss some important findings.

Palindromic Closures and Thue-Morse Substitution for Markoff Numbers

2017 ◽  
Vol 12 (2) ◽  
pp. 25-35 ◽  
Author(s):  
Christophe Reutenauer ◽  
Laurent Vuillon
Keyword(s):  
Fibonacci Numbers ◽  
Recursive Construction ◽  
Pell Numbers ◽  
New Formula ◽  
Markoff Numbers

Abstract We state a new formula to compute the Markoff numbers using iterated palindromic closure and the Thue-Morse substitution. The main theorem shows that for each Markoff number m, there exists a word v ∈ {a, b}∗ such that m − 2 is equal to the length of the iterated palindromic closure of the iterated antipalindromic closure of the word av. This construction gives a new recursive construction of the Markoff numbers by the lengths of the words involved in the palindromic closure. This construction interpolates between the Fibonacci numbers and the Pell numbers.

Pythagorean Triples from Harmonic Sequences

2001 ◽  
Vol 94 (3) ◽  
pp. 218-222
Author(s):  
Angelo S. DiDomenico ◽  
Randy J. Tanner
Keyword(s):  
Mathematics Teacher ◽  
Fibonacci Numbers ◽  
Whole Numbers ◽  
Multiplication Tables ◽  
Pythagorean Triples ◽  
Mathematical Experience ◽  
Ancient Times

Pythagorean triples have intrigued generations of mathematics explorers, including students, since ancient times. One of their most charming features is their connection with various other areas of mathematics. In the Mathematics Teacher, for example, authors have shown that Pythagorean triples can be generated from the Fibonacci numbers (Bertucci 1991), from geometric sequences (Carbeau 1993), and from both the addition and multiplication tables of whole numbers (DiDomenico 1993, 1995). These findings are indeed fascinating; when shared with students, they spark interest and curiosity and lead to a truly enriching mathematical experience. Students, in fact, independently found that Pythagorean triples could be generated from Fibonacci numbers and geometric sequences. This article reveals another surprising connection that shows how all primitive Pythagorean triples can be generated from harmonic sequences.

scholarly journals Some Results on a Generalized Version of Congruent Numbers

2021 ◽  
Vol 3 (1) ◽  
pp. 1-6
Author(s):  
Leomarich F. Casinillo ◽  
Emily L. Casinillo
Keyword(s):  
Elliptic Curve ◽  
Subject Classification ◽  
Pythagorean Triples ◽  
Congruent Number ◽  
Pythagorean Triple ◽  
New Formula ◽  
Curve Equation

AbstractThis paper aims to construct a new formula that generates a generalized version of congruent numbers based on a generalized version of Pythagorean triples. Here, an elliptic curve equation is constructed from the derived generalized version of Pythagorean triples and congruent numbers and gives some new results.Keywords: Pythagorean triple, congruent number, elliptic curve equation. AbstrakArtikel ini bertujuan untuk mengkonstruksi formula baru yang membangun versi yang lebih umum dari bilangan-bilangan kongruen berdasarkan versi triple Pythagoras yang diperumum. Di sini, akan dikonstruksi suatu persamaan kurva eliptik dari triple Pythagoras dan bilangan-bilangan kongruen dalam versi yang diperumum untuk menghasilkan hasil-hasil yang baru.Kata kunci: triple Phytagoras, bilangan kongruen, persamaan kurva eliptik.2010 Mathematics subject classification: 11A07, 11A41, 11D45, 11G07.

A group structure on the golden triples

2021 ◽  
Vol 105 (562) ◽  
pp. 87-97
Author(s):  
Howard Sporn
Keyword(s):  
Mathematics Teachers ◽  
Group Structure ◽  
Golden Ratio ◽  
Fibonacci Numbers ◽  
Mathematics Students ◽  
Pythagorean Triples ◽  
And Mathematics

Some favourite topics of both mathematics teachers and mathematics students are the golden ratio, Fibonacci numbers, groups, and Pythagorean triples. The material of this paper involves the first three, and there are some analogies with the fourth.

A new formula for using the audiogram to predict hearing loss for speech. (Rep. No. 273).

1956 ◽  
Author(s):  
J. Donald Harris ◽  
Henry L. Haines ◽  
Cecil K. Myers
Keyword(s):  
Hearing Loss ◽  
New Formula

Macrosomia – a new formula for optimized fetal weight estimation

2008 ◽  
Vol 68 (S 01) ◽  
Author(s):  
NC Hart ◽  
J Siemer ◽  
B Meurer ◽  
TW Goecke ◽  
RL Schild
Keyword(s):  
Fetal Weight ◽  
Weight Estimation ◽  
Fetal Weight Estimation ◽  
New Formula

Introduction

2018 ◽  
Author(s):  
Peter Hopkins
Keyword(s):  
Final Section ◽  
Short Note ◽  
Current Situation ◽  
Research Projects ◽  
Everyday Lives ◽  
Early Settlement ◽  
The Everyday ◽  
Initial Research

The chapters in this collection explore the everyday lives, experiences, practices and attitudes of Muslims in Scotland. In order to set the context for these chapters, in this introduction I explore the early settlement of Muslims in Scotland and discuss some of the initial research projects that charted the settlement of Asians and Pakistanis in Scotland’s main cities. I then discuss the current situation for Muslims in Scotland through data from the 2011 Scottish Census. Following a short note about the significance of the Scottish context, in the final section, the main themes and issues that have been explored in research about Muslims in Scotland.

Short Note: A Record of Twin Fetuses in a Harbor Porpoise (Phocoena phocoena) Stranded on the Dutch Coast

2014 ◽  
Vol 40 (4) ◽  
pp. 394-397 ◽  
Author(s):  
Lonneke L. IJsseldijk ◽  
Andrea Gröne ◽  
Sjoukje Hiemstra ◽  
Jeroen Hoekendijk ◽  
Lineke Begeman
Keyword(s):  
Short Note ◽  
Phocoena Phocoena ◽  
Harbor Porpoise ◽  
Dutch Coast
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