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Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s——Part I. Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci Goniometry
(Articles)
Alexey Stakhov
,
Samuil Aranson
Applied Mathematics
Vol.2 No.1
,January 30, 2011
DOI:
10.4236/am.2011.21009
6,363
Downloads
12,405
Views
Citations
Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part II. A New Geometric Theory of Phyllotaxis (Bodnar’s Geometry)
(Articles)
Alexey Stakhov
,
Samuil Aranson
Applied Mathematics
Vol.2 No.2
,February 25, 2011
DOI:
10.4236/am.2011.22020
6,096
Downloads
11,937
Views
Citations
Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part III. An Original Solution of Hilbert’s Fourth Problem
(Articles)
Alexey Stakhov
,
Samuil Aranson
Applied Mathematics
Vol.2 No.3
,March 24, 2011
DOI:
10.4236/am.2011.23033
6,355
Downloads
12,402
Views
Citations
Hilbert’s Fourth Problem: Searching for Harmonic Hyperbolic Worlds of Nature
(Articles)
A. P. Stakhov
Journal of Applied Mathematics and Physics
Vol.1 No.3
,September 24, 2013
DOI:
10.4236/jamp.2013.13010
6,852
Downloads
9,598
Views
Citations
The Mathematics of Harmony, Hilbert’s Fourth Problem and Lobachevski’s New Geometries for Physical World
(Articles)
Alexey Stakhov
,
Samuil Aranson
Journal of Applied Mathematics and Physics
Vol.2 No.7
,June 13, 2014
DOI:
10.4236/jamp.2014.27056
3,874
Downloads
5,244
Views
Citations
Chebyshev Polynomials with Applications to Two-Dimensional Operators
(Articles)
Alfred Wünsche
Advances in Pure Mathematics
Vol.9 No.12
,December 24, 2019
DOI:
10.4236/apm.2019.912050
563
Downloads
2,369
Views
Citations
A History, the Main Mathematical Results and Applications for the Mathematics of Harmony
(Articles)
A. P. Stakhov
Applied Mathematics
Vol.5 No.3
,February 11, 2014
DOI:
10.4236/am.2014.53039
8,355
Downloads
11,670
Views
Citations
Multi Parameters Golden Ratio and Some Applications
(Articles)
Seyed Moghtada Hashemiparast
,
Omid Hashemiparast
Applied Mathematics
Vol.2 No.7
,July 5, 2011
DOI:
10.4236/am.2011.27108
5,830
Downloads
12,072
Views
Citations
On the k–Lucas Numbers of Arithmetic Indexes
(Articles)
Sergio Falcon
Applied Mathematics
Vol.3 No.10
,October 11, 2012
DOI:
10.4236/am.2012.310175
6,736
Downloads
9,943
Views
Citations
Sums of Squares of Fibonacci Numbers with Prime Indices
(Articles)
A. Gnanam
,
B. Anitha
Journal of Applied Mathematics and Physics
Vol.3 No.12
,December 18, 2015
DOI:
10.4236/jamp.2015.312186
3,467
Downloads
4,966
Views
Citations
Relationships between Some
k
-Fibonacci Sequences
(Articles)
Sergio Falcon
Applied Mathematics
Vol.5 No.15
,August 8, 2014
DOI:
10.4236/am.2014.515216
6,413
Downloads
8,487
Views
Citations
The Power Integrations of Trigonometric and Hyperbolic Functions
(Articles)
Ahmed M. Ali
,
Omar M. Abd-Alkanee
Open Access Library Journal
Vol.6 No.8
,August 29, 2019
DOI:
10.4236/oalib.1105618
576
Downloads
1,781
Views
Citations
Non Degeneration of Fibonacci Series, Pascal’s Elements and Hex Series
(Articles)
Balasubramani Prema Rangasamy
Advances in Pure Mathematics
Vol.10 No.7
,July 21, 2020
DOI:
10.4236/apm.2020.107024
563
Downloads
1,447
Views
Citations
Squares from
D
(–4) and
D
(20) Triples
(Articles)
Zvonko Čerin
Advances in Pure Mathematics
Vol.1 No.5
,September 21, 2011
DOI:
10.4236/apm.2011.15052
3,309
Downloads
6,954
Views
Citations
On the Norms of
r
-Toeplitz Matrices Involving Fibonacci and Lucas Numbers
(Articles)
Hasan Gökbaş
,
Ramazan Türkmen
Advances in Linear Algebra & Matrix Theory
Vol.6 No.2
,June 2, 2016
DOI:
10.4236/alamt.2016.62005
2,123
Downloads
3,014
Views
Citations
On the Norms of
r
-Hankel Matrices Involving Fibonacci and Lucas Numbers
(Articles)
Hasan Gökbaş
,
Hasan Köse
Journal of Applied Mathematics and Physics
Vol.6 No.7
,July 10, 2018
DOI:
10.4236/jamp.2018.67117
805
Downloads
1,836
Views
Citations
Lucas Symbolic Formulae and Generating Functions for Chebyshev Polynomials
(Articles)
Do Tan Si
Journal of High Energy Physics, Gravitation and Cosmology
Vol.7 No.3
,June 25, 2021
DOI:
10.4236/jhepgc.2021.73052
156
Downloads
599
Views
Citations
The Summation of One Class of Infinite Series
(Articles)
Jonathan D. Weiss
Applied Mathematics
Vol.5 No.17
,October 28, 2014
DOI:
10.4236/am.2014.517269
6,080
Downloads
7,651
Views
Citations
Frobenius Series Solutions of the Schrodinger Equation with Various Types of Symmetric Hyperbolic Potentials in One Dimension
(Articles)
Hippolyte Nyengeri
,
René Simbizi
,
Audace Girukwishaka
,
Rénovat Nizigiyimana
,
Eugène Ndenzako
Open Access Library Journal
Vol.5 No.7
,July 26, 2018
DOI:
10.4236/oalib.1104728
595
Downloads
2,013
Views
Citations
Application of the Frobenius Method to the Schrodinger Equation for a Spherically Symmetric Hyperbolic Potential
(Articles)
Hippolyte Nyengeri
,
Rénovat Nizigiyima
,
Eugène Ndenzako
,
Félix Bigirimana
,
Dieudonné Niyonkuru
,
Audace Girukwishaka
Open Access Library Journal
Vol.5 No.10
,October 29, 2018
DOI:
10.4236/oalib.1104950
631
Downloads
2,520
Views
Citations
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