1. “Proof without words: Another Pythagorean theorem” (with Claudi Alsina), College Mathematics Journal, 53 (2022), p. 38 PDF

2. “Proof without words: Solutions to the Pell Equation x² – Ny² = 1 ,” Mathematics Magazine, 95 (2022), pp. 154-155 PDF

3. “Proof without words: Tangents of multiples of π/24,” College Mathematics Journal, 53 (2022), p. 226 PDF

4. “Proof without words: Consecutive powerful numbers, College Mathematics Journal, 53 (2022), p. 318 PDF

5. “Nesbitt’s inequality,” Mathematics Magazine, 95 (2022), pp. 403-404 PDF

6. “Golden tiles and arctangent identities,” Mathematics Magazine, 95 (2022), pp. 569-570 PDF

1. “Proof without words: n⁴ + 4ⁿ is composite for n ≥ 2,” Mathematics Magazine, 94 (2021), p. 69 PDF

2. “Plato’s approximation of pi,” Mathematics Magazine, 94 (2021), p. 137 PDF

3. “Means, Milne’s inequality, and quadrilateral area” (with Claudi Alsina), Aequationes Mathematicae, 95 (2021), pp. 623-627 https://rdcu.be/cmCkc

4. “Pythagorean triples and π/4,” Mathematics Magazine, 94 (2021), pp. 225-226 PDF

5. “Machin’s formula via a proof without words,” College Mathematics Journal, 52 (2021), p. 355 PDF

6. “Pi is less than twice phi,” Mathematics Magazine, 94 (2021), p. 387 PDF

1. “Titu’s lemma,” Mathematics Magazine, 93 (2020), p. 70 PDF

2. “Squared primes modulo 24,” Mathematics Magazine, 93 (2020), p. 228 PDF

3. “Elementary proofs of the trigonometric inequalities of Huygens, Cusa, and Wilker,” Mathematics Magazine, 93 (2020), pp. 276-283 PDF

4. “Almost Equilateral Heronian Triangles,” Mathematics Magazine, 93 (2020), pp. 378-379 PDF

1. “Proof without words: Pythagorean primes and triangular numbers,” College Mathematics Journal, 50 (2019), p. 378 PDF

1. “Even perfect numbers end in 6 or 28, Mathematics Magazine, 91 (2018), pp. 140-141 PDF

2. “Further integral skinning with applications,” College Mathematics Journal, 49 (2018) pp. 327-332 PDF

3. “Periodic continued fractions via a proof without words,” Mathematics Magazine, 91 (2018), pp. 364-365 PDF

1. “Proof without words: Perfect numbers modulo 7,” College Mathematics Journal, 48 (2017), p. 17 PDF

2. “Proof without words: Diophantus of Alexandria’s sum of squares identity,” Mathematics Magazine, 90 (2017), p. 134 PDF

3. “Computing an expected hitting time for the 3-urn Ehrenfest model via electric networks” (with Y.-P. Chen, I. H. Goldstein, and E. D. Lathrop), Statistics and Probability Letters, 127 (2017), pp. 42-48 PDF

4. “Proof without words: Nested square roots,” College Mathematics Journal, 48 (2017), p. 204 PDF

5. “The Maclaurin inequality and rectangular boxes” (with C. Alsina), Mathematics Magazine, 90 (2017), pp. 228-230 PDF

1. “Independence results for multivariate tail dependence coefficients” (with J. Fernández-Sánchez, J. J. Quesada-Molina, and M. Úbeda-Flores), Fuzzy Sets and Systems, 284 (2016), pp. 129-137 PDF

2. “Proof without words: The pentagon-hexagon-decagon identity,” The College Mathematics Journal, 47 (2016), p. 10 PDF

3. “Proof without words: Perfect numbers and sums of odd cubes,” Mathematics Magazine, 89 (2016), pp. 14-15 PDF

4. “Proof without words: Infinitely many almost-isosceles Pythagorean triples exist,” Mathematics Magazine, 89 (2016), pp. 103-104 PDF

5. “Multi-polygonal numbers,” Mathematics Magazine, 89 (2016), pp. 159-164 PDF

6. “Proof without words: A surprising integer result,” College Mathematics Journal, 47 (2016), p. 94 PDF

7. “Proof without words: The golden ratio,” College Mathematics Journal, 47 (2016), p. 108 PDF

8. “The structure of the class of maximum Tsallis-Havrda-Chavát entropy copulas” (with J. E. García and V. A. González-López), Entropy, 18 (2016), p. 264 PDF

9. “On being an MAA author” (with J. Jensen-Vallin), MAA Focus, August/September 2016, pp. 12-13, 15 PDF

10. “Proof without words: Perfect numbers and triangular numbers,” College Mathematics Journal, 47 (2016), p. 171 PDF

11. “Proof without words: Square triangular numbers and almost isosceles Pythagorean triples,” College Mathematics Journal, 47 (2016), p. 179 PDF

12. “Proof without words: Nearly cubic Pythagorean boxes,” College Mathematics Journal, 47 (2016), p. 190 PDF

13. “Proof without words: A right triangle identity,” College Mathematics Journal, 47 (2016), p. 355 PDF

1. “Proof without words: The area of a regular dodecagon,” The College Mathematics Journal, 46 (2015), p. 10 PDF

2. “Proof without words: A trigonometric proof of the arithmetic mean-geometric mean inequality,” The College Mathematics Journal, 46 (2015), p. 42 PDF

3. “Proof without words: President Garfield and the Cauchy-Schwarz inequality” (with C. Alsina), Mathematics Magazine, 88 (2015), pp. 144-145 PDF

4. “Proof without words: A trigonometric identity for secx + tanx,” Mathematics Magazine, 88 (2015), p. 151 PDF

5. “Proof without words: Sums of every third triangular number,” The College Mathematics Journal, 46 (2015), p. 98 PDF

6. “Proof without words: Each but two triangular numbers is a sum of three triangular numbers,” College Mathematics Journal, 46 (2015), p. 172 PDF

7. “Proof without words: Sums of odd and even squares,” Mathematics Magazine, 88 (2015), pp. 278-279 PDF

8. “Proof without words: Centered triangular numbers,” The College Mathematics Journal, 46 (2015), p. 335 PDF

1. “Proof without words: Alternating sums of consecutive squares,” The College Mathematics Journal, 45 (2014), p. 16 PDF

2. “Proof without words: The difference of consecutive integer cubes is congruent to 1 modulo 6” (with C. Alsina and H. Unal), The College Mathematics Journal, 45 (2014), p. 135 PDF

3. "Proof without words: Pythagorean quadruples,” The College Mathematics Journal, 45 (2014), p. 179 PDF

4. “Best-possible bounds on the set of copulas with given degree of non-exchangeability” (with G. Beliakov, B. DeBaets, H. DeMeyer, and M. Úbeda-Flores), Journal of Mathematical Analysis and Applications, 417 (2014), pp. 451-468 PDF

5. “Pairwise and global dependence in trivariate copula models” (with F. Durante, J. J. Quesada-Molina, and M. Úbeda-Flores), In A. Laurent, O. Strauss, B. Bouchon-Meunier, and R. R. Yager, eds, Information Processing and Management of Uncertainty in Knowledge-Based Systems, v. 444 (2014) of Communications in Computer and Information Science, pp. 243-251. PDF

6. “Proof without words: Ptolemy’s inequality” (with C. Alsina), Mathematics Magazine, 87 (2014), p. 291 PDF

7. “Proof without words: Summing squares by counting triangles,” The College Mathematics Journal, 45 (2014), p. 349 PDF

8. “Proof without words: A sine identity for triangles,” The College Mathematics Journal, 45 (2014), p. 376 PDF

1. "A new index to measure positive dependence in trivariate distributions" (with J. E. García and V. A. González-López), Journal of Multivariate Analysis, 115 (2013), pp. 481-495. PDF

2. “Proof without words: Squares modulo 3,” The College Mathematics Journal, 44 (2013), p. 283 PDF

3. “Proof without words: The formulas of Hutton and Strassnitzky,” Mathematics Magazine, 86 (2013), p. 350. PDF

1. "Directional dependence in multivariate distributions" (with M. Úbeda Flores), Annals of the Institute of Statistical Mathematics, 64 (2012), pp. 677-685. PDF

2. "Proof without words: The triple angle sine and cosine formulas" (with C. Alsina), Mathematics Magazine, 85 (2012), p. 43. PDF

3. "Proof without words: The Pythagorean theorem with equilateral triangles" (with C. Alsina), The College Mathematics Journal, 43 (2012), p. 226. PDF

4. "How close are pairwise and mutual independence?" (with M. Úbeda Flores), Statistics and Probability Letters, 82 (2012), pp. 1823-1828. PDF

5. "Proof without words: An alternating series," The College Mathematics Journal, 43 (2012), p. 370. PDF

6. "Proof without words: Runs of triangular numbers" (with H. Unal), Mathematics Magazine, 85 (2012), p. 373. PDF

1. "Proof without words: Inequalities for two numbers whose sum is one" (with C. Alsina), Mathematics Magazine, 84 (2011), p. 228. PDF

2. "Multivariate copulas, quasi-copulas and lattices" (with J. Fernández Sánchez and M. Úbeda Flores), Statistics and Probability Letters, 81 (2011), pp. 1365-1369. PDF

1. "An invitation to proofs without words" (with C. Alsina), European Journal of Pure and Applied Mathematics, 3 (2010), pp. 118-127. PDF

2. "Teaching Tip: The limit of (sin t)/t" (with C. Alsina), The College Mathematics Journal, 41 (2010), p. 192 PDF

3. "Quasi-copulas and signed measures" (with with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Fuzzy Sets and Systems, 161 (2010), pp. 2328-2336. PDF

4. "Proof without words: New Pythagorean-like theorems" (with C. Alsina), The College Mathematics Journal, 41 (2010), p. 370. PDF

1. "Kendall distribution functions and associative copulas" (with with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Fuzzy Sets and Systems, 160 (2009), pp. 52-57. PDF

2. "Letter to the editor: Isosceles dissections", Mathematics Magazine, 82 (2009), p. 77. PDF

3. "Worst VaR scenarios with given marginals and measures of association" (with R. Kaas and R. J. A. Laeven), Insurance; Mathematics and Economics, 44 (2009), pp. 146-158. PDF

4. "Proof without words: Steiner's problem on the number e", Mathematics Magazine, 82 (2009), p. 102. PDF

5. "Teaching tip: Partial sums of geometric series", The College Mathematics Journal, 40 (2009), p. 278. PDF

6. "Proof without words: Squares in Circles and Semicircles," Mathematics Magazine, 82 (2009), p. 359. PDF

7. "Proof without words: A reciprocal Pythagorean theorem," Mathematics Magazine, 82 (2009), p. 370.PDF

1. "Euler's triangle inequality via proofs without words," Mathematics Magazine, 81 (2008), pp. 58-61. PDF

2. "On the construction of copulas and quasi-copulas with given diagonal sections" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Insurance: Mathematics and Economics, 42 (2008) pp. 473-483. PDF

3. "A sampler of visual proofs in first-year calculus," available at the AP Central website (http://apcentral.collegeboard.com).

4. "Visual gems of number theory." Math Horizons, February 2008, pp. 7-9, 31. PDF

5. "Geometric proofs of the Weitzenböck and Hadwiger-Finsler inequalities" (with C. Alsina), Mathematics Magazine, 81 (2008), pp. 216-219. PDF

6. "Proof without words: Carnot's theorem for acute triangles" (with C. Alsina), The College Mathematics Journal, 39 (2008), p. 111. PDF

7. "Symmetries of random discrete copulas" (with A. Erdely and J. M. González-Barrios), Kybernetika, 44 (2008), pp. 846-863. PDF

1. "Extremes of nonexchangeability," Statistical Papers, 48 (2007) pp. 329-336. PDF

2. "Proof without words: The area of a right triangle," Mathematics Magazine, 80 (2007), p. 45. PDF

3. "On the relationship between Spearman's rho and Kendall's tau for pairs of continuous random variables" (with G. A. Fredricks), Journal of Statistical Planning and Inference, 137 (2007), pp. 2143-2150. PDF

4. "A visual proof of the Erdös-Mordell inequality" (with C. Alsina), Forum Geometricorum, 7 (2007), pp. 99-102. PDF

5. "On Candido's identity" (with C. Alsina), Mathematics Magazine, 80 (2007), pp. 226-228. PDF

6. "On the diagonals of a cyclic quadrilateral" (with C. Alsina), Forum Geometricorum, 7 (2007) pp. 147-149. PDF

7. "Robust fits for copula models" (with B. V. M. Mendes and E. F. L. de Melo), Communication in Statistics--Simulation and Computation, 36 (2007), pp. 997-1017. Website

1. "Proof without words: Every fourth power greater than one is sum of two nonconsecutive triangular numbers," Mathematics Magazine, 79 (2006) p. 44. PDF

2. "Proof without words: Padoa's inequality," Mathematics Magazine, 79 (2006) p. 53. PDF

3. "Proof without words: Right triangles and geometric series," Mathematics Magazine, 79 (2006) p. 60. PDF

4. "Proof without words: Inclusion-exclusion for triangular numbers," Mathematics Magazine, 79 (2006) p. 65. PDF

5. "Proof without words: A weighted sum of triangular numbers," Mathematics Magazine, 79 (2006) p. 317. PDF

1. "Proof without words: Candido's identity," Mathematics Magazine, 78 (2005), p. 131. PDF

2. "Proof without words: Sums of triangular numbers," Mathematics Magazine, 78 (2005), p. 231. PDF

3. "Dependence modeling with Archimedean copulas," Proceedings of the Second Brazilian Conference on Statistical Modelling in Insurance and Finance, (N. Kolev and P. Morettin, editors), Institute of Mathematics and Statistics, University of São Paulo (2005), pp 45 - 54. PDF

4. "Copulas with fractal supports" (with G. A. Fredricks and J. A. Rodríguez Lallena), Insurance: Mathematics and Economics, 37 (2005), pp. 42-48. PDF

5. "The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas" (with M. Úbeda Flores), C. R. Acad. Sci. Paris, Ser I, 341 (2005) pp. 583-586. PDF

6. "Proof without words: A triangular sum," Mathematics Magazine, 78 (2005), p. 395. PDF

7. "Some properties of Schur-constant survival models and their copulas," Brazilian Journal of Probability and Statistics, 19 (2005) pp. 179-190. PDF

1. "Best-possible bounds on sets of bivariate distribution functions" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Journal of Multivariate Analysis, 90 (2004), pp. 348-356. PDF

2. "The symmetric footrule is Gini's rank association coefficient" (with M. Úbeda Flores), Communications in Statistics - Theory & Methods, 33 (2004), pp. 195-96. PDF

3. "Proof without words: Four squares with constant area," Mathematics Magazine, 77 (2004), p. 135. PDF

4. "Proof without words: Every octagonal number is the difference of two squares," Mathematics Magazine, 77 (2004), p. 200. PDF

5. "A comparison of bounds on sets of joint distribution functions derived from various measures of association" (with M. Úbeda Flores), Communications in Statistics - Theory & Methods, 33 (2004), pp. 2299-2305. PDF

6. "Proof without words: A triangular identity," Mathematics Magazine, 77 (2004), p. 395. PDF

1. "Kendall distribution functions" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Statistics & Probability Letters, 65 (2003), pp. 263-268. PDF

2. "Paintings, plane tilings, and proofs," Math Horizons, November 2003, pp. 5 - 8. PDF

3. "An improved remainder estimate for use with the integral test," The College Mathematics Journal, 34 (2003), pp. 397-399. PDF

4. "Properties and applications of copulas: A brief survey," Proceedings of the First Brazilian Conference on Statistical Modelling in Insurance and Finance (J. Dhaene, N. Kolev, and P. Morettin, eds.), Institute of Mathematics and Statistics, University of São Paulo (2003), pp. 10 - 28. PDF

5. "Proof without words: The cube as an arithmetic sum," Mathematics Magazine, 76 (2003), p. 136. PDF

1. "Concordance and copulas: A survey," Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 169-178. PDF

2. "The Bertino family of copulas" (with G. A. Fredricks), Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 81-92. PDF

3. "Some new properties of quasi-copulas" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 187-194. PDF

4. "Multivariate Archimedian quasi-copulas" (with J. J. Quesada Molina, J. A. Rodríguez Lallena, and M. Úbeda Flores), Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena eds.), Kluwer Academic Publishers, Dordrecht (2002), pp. 179-186. PDF

5. "Proof without words: The area of a salinon," Mathematics Magazine, 75 (2002), p. 130. PDF

6. "Proof without words: The area of an arbelos," Mathematics Magazine, 75 (2002), p. 144. PDF

7. "Proof without words: Lunes and the regular hexagon," Mathematics Magazine, 75 (2002), p. 316. PDF