CATEGORIES:
Teaching Mathematics
Numerical Methods and Grid Generation, $k$-Fibonacci numbers
TO APPEAR:
2024
137. An Interesting Geometric Series. Mathematics Magazine, 97 (3), (2024) 328.
2023
136. Similarity Classes in the Eight-Tetrahedron Longest-Edge Partition of a Regular Tetrahedron. Mathematics, 11 (21), (2023) Art. no. 4456. (With Miguel A. Padrón, and José Pablo Suárez).
135. Similarity Classes of the Longest-Edge Trisection of Triangles. Axioms, 12 (10), (2023) Art. no. 913. (With F. Perdomo).
134. Una identidad tangente-cotangente y su aplicación, Gaceta de la RSME, 26 (2) (2023) 316.
133. 107.06 Proving inequalities via definite integration: a visual approach. The Mathematical Gazette, Volume 107 (568) March (2023) 136-140. (With N. Haque).
2022
132. Iterated Partial Sums of the $k$-Fibonacci Sequences. Axioms, 11 (10) (2022) Art. no. 542. (With F. Falcón).
131. The Shortest-Edge Duplication of Triangles. Mathematics, 10 (19), (2022) Art. no. 3643. (With M.A. Padrón, F. Perdomo, J.P. Suárez).
130. Suma de una serie geométrica mediante sumas telescópicas. Revista Mixba'al, 13 (1) (2022)
129. Proof Without Words: A Riemann Sum. The Mathematical Gazette, 106 (566) (2022) 331.
128. Similarity classes generated by the 8T-LE partition applied to trirectangular tetrahedra. Journal of Computational and Applied Mathematics, 409 (2022) Art. no. 114150. (With M.A. Padrón).
127. Sum of an Alternating Geometric Series Via Self-Similarity, The American Mathematical Monthly, 129 (4) (2022) 380.
126. A function-based proof of the harmonic mean geometric mean -- arithmetic mean inequalities, The Mathematical Gazette, 106 (565) (2022) 130-131.
2021
125. A Mechanically-Based Proof of the Arithmetic Mean Harmonic Mean Inequality, Int. J. of Mathematical Education in Science and Technology, 52 (8) (2021) 1250-1252. (With M.A. Padrón).
124. Proof Without Words: HM-LM-AM inequalities, Mathematics Magazine 94 (2) (2021) 148.
123. $\displaystyle \sum_{n=2}^{\infty} \frac{1}{n H_{n-1}}$ diverges while $\displaystyle \sum_{n=2}^{\infty} \frac{1}{n H_{n}^{1+\varepsilon}}$ converges, The Mathematical Gazette, 105 (562) (2021) 161-162. (With J. Marshall Ash).
122. Exponential inequalities, The American Mathematical Monthly 128 (2) (2021) 162.
2020
121. Proof Without Words: Half Row Sums in Pascal's Triangle, Mathematics Magazine 93 (4) (2020) 308.
120. 104.22 Proof without Words: Minimum perimeter of an inscribed quadrangle to a square, The Mathematical Gazette 104 (560) (2020) pp. 338-339.
119. 104.14 More on zero-over-zero limits of special type, The Mathematical Gazette 104 (560) (2020) 310-313.
118. The 8T-LE partition applied to the obtuse triangulations of the 3D-cube. Mathematics and Computers in Simulation 176 (1) (2020) 254-265. (With M.A. Padrón).
117. No existe una serie convergente que sea la mayor, Gaceta de la RSME, 23 (2) (2020) 262. (With J. Marshall Ash).
116. No existe una serie divergente que sea la menor, Gaceta de la RSME, 23 (2) (2020) 242. (With J. Marshall Ash).
115. Harmonic, Logarithmic, and Arithmetic Means and Corollaries, The American Mathematical Monthly, 127 (5) (2020) 427.
2019
114. $k$th Power of a Partial Sum, The American Mathematical Monthly, 126 (5) (2019) 467.
113. Proof Without Words: The Square of a Sum, Mathematics Magazine 99 (2) (2019) 17.
112. Hamiltonian Triangulations and Space Filling Curves. Journal of Computational and Applied Mathematics 346 (1) (2019) 18--25. (With A. Márquez, J.P. Suárez).
2018
111. Proof Without Words: Tangent plus Cotangent is greater or equal than 2, Mathematics Magazine 91 (5) (2018) 363-363.
110. Identidades de tipo Machin con π y dos arcotangentes. Gaceta de la RSME, 21 (2) (2018) 608.
109. 102.42 Proof without Words: An alternating geometrical series, The Mathematical Gazette 102 (555) (2018) 504-505.
108. The Generalized Harmonic Series Diverges by the AM-GM Inequality, Mathematics Magazine 91 (3) (2018) 217.
107. Proof Without Words: An Alternating Geometric Series, The College Mathematics Journal 49 (3) (2018) 200.
106. The Harmonic Series Diverges, The American Mathematical Monthly 125 (3) (2018) 222.
105. Proof Without Words: Three Arctangent Identities, Mathematics Magazine 91 (1) (2018) 51.
2017
104. Bone modeling using the morton space-filling curve. Int. J. of Recent Advances in Multidisciplinary Research, 04 (12) (2017) 3154-3159 (With J.P. Suárez, D.R. Hernández, P. Abad)
103. Proof Without Words: A Pascal-like Triangle with Pell Row Sums, The College Mathematics Journal 48 (5) (2017) 346.
102. Relación entre la k-ésima media metálica y arc tan(2/k), La Gaceta de la RSME Vol. 20 (2017), Num. 2, 268.
101. Proof without words: Arctangent of Two and the Golden Ratio, Mathematics Magazine 90 (3) (2017) 179.
100. Proof without words: Sum of a Row in Pascal's Triangle, The College Mathematics Journal 48 (3) 188.
99. ¿Comprenden los alumnos los enunciados de los problemas?, Boletín de la Sociedad «Puig Adam» de Profesores de Matemáticas 103 (2017) 72-89. (With S. Falcón y P. Medina)
98. Proof without words: Partial Column Sums in Pascal’s Triangle, Mathematics Magazine 90 (2) (2017) 117-118.
97. Proof without words: Triangle with Maximum Area for Given Base and Perimeter, The College Mathematics Journal 48 (1) (2017) 51.
2016
96. An olympiad mathematical problem, proof without words and generalization, The Mathematical Gazette 100 (549) 524-525. (With L. Ma Li)
95. Proof without words: sum of a numerical series by telescoping, The Mathematical Gazette 100 (549) 523.
94. Proof Without Words: Alternating Row Sums in Pascal's Triangle, Mathematics Magazine 89 (4) (2016) 281.
93. Proof Without Words: The Parallelogram With Maximum Perimeter for Given Diagonals Is the Rhombus, Mathematics Magazine 89 (4) (2016) 251.
92. Proof Without Words: Arithmetic Mean of two Means, The College Mathematics Journal 47 (2) (2016) 125.
91. Proof Without Words: Limit of a Recursive Arithmetic Mean, Mathematics Magazine 89 (3) (2016) 189.
90. Proof Without Words: Limit of a Recursive Root Mean Square, Mathematics Magazine 89 (3) (2016) 177-178.
89. Proof Without Words: Sum of Triangular Numbers, Mathematics Magazine 89 (1) (2016) 36-37.
88. Visual proof of the limit of f-mean recurrence sequences, The Mathematical Gazette, 100 (576) (2016) 139-141.
87. Longest-edge n-section algorithms: Properties and open problems. Journal of Computational and Applied Mathematics, 293 (2016) 139-146. (With S. Korotov and J.P. Suárez)
2015
86. The Parallelogram with Maximum Perimeter for given Diagonals is the Rhombus -- A Proof Without Words and a Corollary, Mathematics Magazine, 88 (5) (2015) 369-361.
85. Corrigendum to “A new proof of the degeneracy property of the longest-edge n-section refinement scheme for triangular meshes” [Applied Mathematics and Computation 219 (4) (2012) 2342-2344], Applied Mathematics and Computation, 260 (2015) 412-413. (With F. Perdomo)
84. On the maximum angle condition for the conforming longest-edge n-section algorithm for large values of n, Computer Aided Geometric Design, 32(1) (2015) 69-73. (With S. Korotov y J.P. Suárez)
2014
83. Proof Without Words: Limit of a Recursive Arithmetic Mean, The College Mathematics Journal, 45(5) (2014) 364.
82. A mathematical proof of how fast the diameters of a triangle mesh tend to zero after repeated trisection, Mathematics and Computers in Simulation, 106 (2014) 95-108. (With F. Perdomo, E. Quevedo y J.P. Suárez)
81. There are simple and robust refinements (almost) as good as Delaunay, Mathematics and Computers in Simulation, 106 (2014) 84-94. (With A. Márquez, A. Moreno-González y J.P. Suárez)
80. Properties of triangulations obtained by the longest-edge bisection, Central European Journal of Mathematics, 12 (12) (2014) 1796-1810. (With F. Perdomo)
2013
79. Two-sided estimation of diameters reduction rate for the longest edge n-section of triangles with n >= 4, Applied Mathematics and Computation, 224 (1) (2013) 492-500. (With J.P. Suárez, T. Moreno y P. Abad)
78. Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metric, Applied Mathematics and Computation, 221 (15) (2013) 424-432. (With F. Perdomo)
77. Proof without words: Fibonacci Triangles and Trapezoids. Mathematics Magazine, 86 (1) (2013) 55. (With H. R. Walser)
2012
76. A Local refinement algorithm for the longest-edge trisection of triangle meshes, Mathematics and Computers in Simulation, 82 (12) (2012) 2971-2981. (With S. Falcón, J.P. Suárez y P. Abad)
75. A new proof of the degeneracy property of the longest-edge n-section refinement scheme for triangular meshes, Applied Mathematics and Computation, 219 (4) (2012) 2342-2344. (With F. Perdomo)
74. Properties of the Longest-Edge n-section Refinement Scheme for Triangular Meshes, Applied Mathematics Letters, 25 (12) (2012) 2037-2039. (With J.P. Suárez, T. Moreno y P. Abad)
73. Dos resultados del valor medio, Boletín de la Sociedad Puig Adam, 90 (2012) 84-89. (With S. Falcón)
2011
72. Short proofs of combinatorial identities for n! Ars Combinatoria, Volume C, July, (2011) 337-339. (With S. Falcón)
71. A note on ''Some inequalities in inner product spaces related to the generalized triangle inequality'' by S.S. Dragomir et al., Appl. Math. & Comput., 217 (2011) 9497–9498 (With K. Sadarangani)
2010
70. Proof without words: Two inequalities proved by convexity. Math. Gazette, July 2010, 32-33. (With S. Falcón)
69. Proof without words: Mengoli's Series. Mathematics Magazine, 83 (2) 140.
68. On the non-degeneracy property of the longest-edge trisection of triangles. Applied Mathematics and Computation. Vol. 216 (3) (2010) 862-869. (With S. Falcón and J.P. Suárez)
2009
67. Binomial Transforms of the k-Fibonacci sequences. Int. J. Nonlinear Sciences and Numerical Simulation. Vol. 10 (11/12) (2009) 1527-1538. (With S. Falcón)
66. K-Fibonacci sequences modulo m. Chaos, Solitons and Fractals, 41 (1) (2009) 497-504. (With S. Falcón)
65. The metallic ratios as limits of complex valued transformations. Chaos, Solitons and Fractals, 41 (1) (2009) 1-13. (With S. Falcón)
64. A novel proof that
. Mathematics and Computer Education Journal, 43 (2) (Spring 2009), 181-182.
63. On k-Fibonacci sequences and polynomials and their derivatives. Chaos, Solitons and Fractals, 39 (3) (2009) 1005-1019. (With S. Falcón)
62. Local refinement based on the 7-triangle longest-edge partition. Mathematics and Computers in Simulation, 79 (8) (2009) 2444-2457. (With A. Márquez, A. Moreno-González, y J.P. Suárez)
61. Diagrama geométrico y subdivisión híbrida de triángulos. Rev. Int. de Métodos Numéricos en Cálculo y Diseño en la Ingeniería, 25 (1) 61-78. (With J.P. Suárez, y G.F. Carey)
60. A mean value property for pairs of integrals. Acta Mathematica Universitatis Comenianae, 78 (1) (2009) 65-70. (With A. Mingarelli, y J.M. Pacheco)
59. Four-triangles adaptive algorithms for RTIN terrain meshes. Mathematical and Computer Modelling, 49 (5) (2009) 1012-1020. (With J.P. Suárez)
58. On k-Fibonacci numbers of arithmetic indexes. Applied Mathematics and Computation, 208 (1) (2009) 180-185. (With S. Falcón)
57. Proof Without Words: Bernoulli's Inequality. Mathematics Magazine, 82 (1) 62.
2008
56. A recurrence relation for Fibonacci sums: a combinatorial approach. Math. Gazette, 92 (525) (2008) 480-482. (With S. Falcón)
55. Proof Without Words: Exponential Inequalities. Mathematics Magazine, 81 (5) (2008) 374.
54. Combinatorial proofs of Honsberger type identities. Int. J. of Mathematical Education in Science & Technology, 39 (6) 785-792. (Con S. Falcón)
53. The 7-triangle longest-side partition of triangles and mesh quality improvement. Finite Elements in Analysis and Design, 44 (12-13) 748-758. (With A. Márquez, A. Moreno-González, and J.P. Suárez)
52. Propagation of longest-edge mesh patterns in local adaptive refinement. Communications in Numerical Methods in Engineering, 24 (7) (2008) 543-553. (With J.P. Suárez, and G.F. Carey)
51. On the 3-dimensional k-Fibonacci spirals. Chaos, Solitons and Fractals,38 (4) (2008) 993-1003. (With S. Falcón)
50. Razones metálicas en un circuito eléctrico ilimitado. Boletín de la Sociedad Puig Adam, 79 (2008) 26-31. (With A. Martín, y S. Falcón)
49. Identities for generalized Fibonacci numbers: a combinatorial approach. Int. J. of Mathematical Education in Science & Technology, 39, 4 (2008) 563-566. (With S. Falcón)
48. The k-Fibonacci hyperbolic functions. Chaos, Solitons and Fractals 38 (2) (2008) 409-420. (With S. Falcón)
47. A triangle inequality and its elementary proof. Math Horizons, 15, 4 (2008) 30. (With J.V. Martín)
2007
46. Refinement based on longest-edge and self-similar four-triangle partitions. Mathematics and Computers in Simulation, 75 (5-6) (2007) 251-262. (With M.A. Padrón, J.P. Suárez)
45. Proof without words: Every triangle can be subdivided into six isosceles triangles. Mathematics Magazine, 80 (3), June 2007, 195.
44. The eight-tetrahedra longest-edge partition and Kuhn triangulations. Computers and Mathematics with Applications, 54 (3) (2007) 427-433.
43. Proof without words: Alternating sum of an even number of triangular numbers. Mathematics Magazine, 80 (1), February 2007, 76.
42. The k-Fibonacci Sequence and the Pascal 2-triangle. Chaos, Solitons and Fractals, 33 (1) (2007) 38-49. (With S. Falcón)
41. On the Fibonacci k-numbers. Chaos, Solitons and Fractals, 32 (2) (2007) 1615-1624. (With S. Falcón)
40. Proof without words: Alternating Sums of Squares of Odd Numbers. Mathematics Magazine, 80 (1), February 2007, 74-75.
39. A geometric diagram and hybrid scheme for triangle subdivision. Computer Aided Geometric Design. 24 (1) (2007) 19–27. (With J.P. Suárez, and G.F. Carey)
2006
38. Proof without words: Knopp series for pi. Teaching Mathematics and Computer Science,4, 2 (2006) 451-452.
37. Block-balanced meshes in iterative uniform refinement. Computer Aided Geometric Design. 23 (9) (2006) 684–697. (With J.P. Suárez)
36. Las sucesiones de Fibonacci, Lucas y Pell como casos particulares de la sucesión generalizada de Fibonacci. Boletín de la Sociedad Puig Adam, 74 (2006) 62-67. (With S. Falcón)
35. Proof without words: Sum of a geometric series via equal base angles in isosceles triangles. Mathematics Magazine, October 2006, Vol. 79, No. 4, p. 250.
34. Proof with a few words: sine and cosine of the half angle. Mathematics and Computer Education Journal, Winter 2006, Vol. 40, Number 1, p. 57.
33. El problema de propagación del refinamiento en cuatro triángulos por la arista mayor. Rev. Int. de Métodos Numéricos en Cálculo y Diseño en la Ingeniería, 22 (1) (2006) 3-17. (With J.P. Suárez, M.A. Padrón)
2005
32. Computational aspects of the refinement of 3D tetrahedral meshes. Journal of Computational Methods in Sciences and Engineering 5, 4 (2005) 215-224. (With J.P. Suárez, P. Abad, and M.A. Padrón)
31. Proof without words: Four circles. Teaching Mathematics and Computer Science, 3, 2 (2005) 307-309.
30. The propagation problem in longest-edge refinement. Finite Elements in Analysis and Design 42, 2 (2005) 130-151. (With J.P. Suárez, and G.F. Carey)
29. Proof without words: Limit of a recursive sequence. Teaching Mathematics and Computer Science 3, 1 (2005) 121-122. (With P. Abreu E.Guerra)
28. Average adjacencies for tetrahedral skeleton-regular partitions. Journal of Computational and Applied Mathematics, 177 (2005) 141–158. (With M.-C. Rivara)
27. A comparative study between some bisection based partitions in 3D. Applied Numerical Mathematics 55, 3, November (2005) 357-367. (With M.A. Padrón, J.P. Suárez)
26. Fractality of refined triangular grids and space-filling curves. Engineering with computers 20 (2005) 323–332. (With M.A. Padrón, J.P. Suárez)
25. Non-degeneracy study of the 8-tetrahedra longest-edge partition. Applied Numerical Mathematics, 55, 4, December (2005) 458-472. (With M.A. Padrón, J.P. Suárez)
24. Volumen de la n-esfera. Boletín de la Sociedad Puig Adam, 69 (2005) 82-90. (With S. Falcón and J.P. Suárez)
2004
23. Proof without words: Partial sum and sum of a geometric series. Teaching Mathematics and Computer Science 2, 2 (2004) 423.
22. Proof without words. Teaching Mathematics and Computer Science 2, 1 (2004) 207.
21. The 8-tetrahedra longest-edge partition of right-type tetrahedra. Finite Elements in Analysis and Design 41 (2004) 253–265. (With M.A. Padrón, J.P. Suárez, and S. Falcón)
20. Mesh quality improvement and other properties in the four-triangles longest-edge partition. Computer Aided Geometric Design 21 (4) (2004) 353–369. (With J.P. Suárez, M.A. Padrón, S. Falcón, and D. Amieiro)
19. Adaptive techniques for unstructured nested meshes. Applied Numerical Mathematics 51 (2004) 565–579. (With M.A. Padrón and J.P. Suárez)
18. Non-equivalent partitions of d-triangles with Steiner points. Applied Numerical Mathematics 49, 3-4 (2004) 415–430. (With J.P. Suárez, and M.A. Padrón)
2003
17. Algoritmos eficientes para la generacion de niveles de detalle en modelos digitales del terreno. Anales de Ingeniería Gráfica Vol. 16 (2003) 60-68. (With J.P. Suárez)
16. Refinement and hierarchical coarsening schemes for triangulated surfaces. Journal of WSCG 11, No.3 (2003) 440-447. (With J.P. Suárez)
15. Estructuras de datos geométricas para algoritmos de refinamiento basados en el esqueleto. Rev. Int. de Métodos Numéricos en Cálculo y Diseño en la Ingeniería 19, 1 (2003) 89-109. (With J.P. Suárez and G.F. Carey)
2002
14. On the adjacencies of triangular meshes based on skeleton-regular partitions. Journal of Computational and Applied Mathematics 140 (2002) 673–693. (With María-Cecilia Rivara)
13. Conditional convergence of numerical series. Int. J. of Mathematical Education in Science & Technology, 33, 2 (2002) 267-272. (With E. Gómez)
12. Explicación geométrica de una medida de forma de símplices n-dimensional.Rev. Int. de Métodos Numéricos en Cálculo y Diseño en la Ingeniería.Vol. 18, 4 (2002) 475-480. (With G.F. Carey)
2001
11. Graph-based data structures for skeleton-based refinement algorithms. Communications in Numerical Methods in Engineering, 17 (2001) 903–910. (With J.P. Suárez and G. F. Carey)
2000
10. Local refinement of simplicial grids based on the skeleton. Applied Numerical Mathematics 32 (2000) 195–218. (With G.F. Carey)
9. A 3D refinement/derefinement algorithm for solving evolution problems. Applied Numerical Mathematics 32 (2000) 401–418. (With M.A. Padrón and G.F. Carey)
1999
8. Un algoritmo de desrefinamiento para mallas de tetraedros basado en el esqueleto. Rev. Int. de Métodos Numéricos en Cálculo y Diseño en la Ingeniería. Vol. 15 (1999) 471-483. (Con M.A.Padrón)
7. Two approximations to Pi. Int. J. of Mathematical Education in Science & Technology, 30, 5 (1999) 782-787. (With J.L. Bonet and M.A.Padrón)
1998
6. Fractals, mesh generation and adaptivity. Fractalia, Vol. 24 (1998) 8-15.
1997
5. Application of a nonlinear evolution model to fire propagation. Nonlinear Anlaysis, Theory, Methods & Applications, Vol. 30, N. 5 (1997) 2873-2882. (With R. Montenegro, L. Ferragut, and M.I. Asensio)
1996
4. The fractal behavior of triangular refined/derefined meshes. Communications in Numerical Methods in Engineering, 12 (1996) 295–302.
3. An improved derefinement algorithm of nested meshes. Advances in Engineering Software, 27 (1996) 51–57. (With R. Montenegro, and L. Ferragut)
1994
2. Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems. Communications in Numerical Methods in Engineering, 10, 5 (1994) 403–412. (With R. Montenegro, and L. Ferragut)
1992
1. Derefinement algorithm of nested meshes. IFIP Transactions A, IFIP Transactions A: Computer Science and Technology, A-12, 1 (1992) 409–415. (With L. Ferragut and R. Montenegro)
