Mathematical Visualization, Polygonal Number Theory, and Proofs without Words

[In press] Tri–Penta–Hepta–Nona. College Mathematics Journal.  https://doi.org/10.1080/07468342.2026.2723801

[2026] Constructing Triangular Numbers from Spiral Growth of Pentagonal Numbers. The Mathematical Intelligencer.  https://doi.org/10.1007/s00283-026-10564-9

[2026] A Sum-to-Product Identity for k-gonal Numbers with Indices Differing by Two. The Mathematical Gazette.  https://doi.org/10.1080/00255572.2026.2629243

[2026] A Difference Theorem Involving Centered Polygonal Numbers. Mathematics Magazine, 99(4), 427–428.  https://doi.org/10.1080/0025570X.2026.2627856

[2026] Relating Decagonal Numbers to Other Figurate Numbers. The College Mathematics Journal. https://doi.org/10.1080/07468342.2025.2525694

[2026] Polygonal Number Similarity. Humanistic Mathematics, 16(1), 124–133.  https://doi.org/10.5642/jhummath.ADON7075

[2025] Cuisenaire Proof Without Words: Sum of Pentagonal Numbers. Mathematics Magazine, 98(4), 332–333.  https://doi.org/10.1080/0025570X.2025.2535268

[2025] Hex and Nonagonal Numbers Relationship via the Floret Pentagonal Tiling. College Mathematics Journal, 56(4), 316.  https://doi.org/10.1080/07468342.2024.2394363

[2025] A Symmetric Difference Identity Involving Polygonal Numbers. College Mathematics Journal, 56(2), 152.  https://doi.org/10.1080/07468342.2024.2385883

[2024] Tri–Hepta–Penta. Mathematics Magazine, 97(5), 573.  https://doi.org/10.1080/0025570X.2024.2402195

[2024] Visualizing Symmetric Polygonal Number Identities. Symmetry: Culture and Science, 35(3), 295–298. https://doi.org/10.26830/symmetry_2024_3_295

[2024] Triquetra Theorem: A Relationship of Triangular, Square and Pentagonal Numbers. College Mathematics Journal. 55(2), 159–160.  https://doi.org/10.1080/07468342.2023.2234798

[2024] A Pattern Block Dissection to Square the Regular Dodecagon. College Mathematics Journal. 55(4), 344–345.  https://doi.org/10.1080/07468342.2024.2302793

[2024] Regular Dodecagon Quadrature with Pattern Blocks Manipulatives. The Mathematical Intelligencer, 46, 42–45.  https://doi.org/10.1007/s00283-023-10264-8

[2023] Dissecting a Star of David into Polygonal Numbers. The Mathematical Intelligencer 45, 38–41. https://doi.org/10.1007/s00283-022-10211-z

[2023] Covering a Star Number with Pentagonal Numbers. College Mathematics Journal 54(1), 63.  https://doi.org/10.1080/07468342.2022.2153554

Linear Algebra and Research in Undergraduate Mathematics Education (RUME)

[In press] Visualizing the Diagonalization of the Householder Matrix in a MATLAB-GeoGebra Assisted Digital Learning Environment. International Journal of Mathematical Education in Science and Technology.  https://doi.org/10.1080/0020739X.2026.2737755

[2026] Visualizing the Spectral Theorem for Symmetric Matrices in a Dynamic Geometry Environment. Book of Abstracts for the 27th Conference of the International Linear Algebra Society (p. 120). Virginia Tech: Blacksburg, VA, USA.

[2025] Visualizing Symmetric Matrices in a CAS-Assisted Learning Environment Using MATLAB. Symmetry: Culture and Science, 36(4): 409–416.  https://doi.org/10.26830/symmetry_2025_4_409

[2023] Visualizing Laguerre Polynomials as a Complete Orthonormal Set for the Inner Product Space Pₙ in a Technology-Assisted Learning Environment. International Journal of Mathematical Education in Science and Technology, 54(7), 1298–1314.  https://doi.org/10.1080/0020739X.2022.2093795

Publications in Other Languages

[2026] Pattern Block – Ähnlichkeiten. Mathematik Lehren, 258, 50–51.

[2021] Similitude des Nombres Polygonaux. Quadrature, 121, 21–22.  https://zbmath.org/1494.11009

[2019] Mit Teilern und ihren Summen spielen. Mathematik Lehren 215, 11–13. [Caglayan & Günter] https://www.friedrich-verlag.de/friedrich-plus/sekundarstufe/mathematik/zahlen-groessen/mit-teilern-und-ihren-summen-spielen-337

[2018] Visualizando a composta de rotações através de um software de geometria dinâmica. Gazeta Matemática 186, 22–26.  https://gazeta.spm.pt/getArtigo?gid=1488

[2017] Une propriété de la comatrice d'une matrice inversible. Quadrature 104, 40–41.  https://publimath.fr/aaq17017/