DCET Seccção de Matemática




António Araújo

CV detalhado
ORCID ID:0000-0003-0909-5782

I am an Assistant Professor (Professor Auxiliar) at Universidade Aberta. I got a Ph.D. in Mathematics (Geometry) from the University of Lisbon in 2011. Before that I had obtained a BSc. in Physics (1995) and a MSc. in Mathematics (1999) from the same university.

I did my Ph.D. in the area of contact geometry, namely in the classification of singularities of lagrangian varieties and the resolution of singularities.

Currently my main area of work is the application of geometry to the visual arts.

I developed geometrical methods for drawing handmande spherical perspectives in both the azimuthal equidistant ("360-degree fisheye") and equirectangular spherical perspectives. The arrival of VR panoramas created a renaissance for immersive perspective drawing. This put us, delightfuly, in the position of Brunelleschi or of Alberti after half a thousand years. I was happy to be in a position to work on such problems since I had a background in both mathematics and drawing, being an avid urban sketcher. So my work in mathematics and art now happily feed on each other.

I also have an interest in digital methods. I have developed the program Eq A Sketch 360 , to help demonstrate, teach, and draw spherical persepctives.

I am a sub-director of the Ph.D. in Digital Media Arts, a double title of UAb and UAlg.

Since july 2020 I am coordinator of CIAC-UAb, the UAb pole of the Center for Research on Science and Communication.

Since july 2020 I am the editor of the Maths-Art section of the Newsletter of the European Mathematical Society Newsletter.

I am a collaborator of CMAF-CIO, of which I was a member for many years before my research turned towards the applications to the visual arts and I joined CIAC.

I coordinated several courses in the past at Aberta. I was coordinator of the BSc. in Applied Mathematics and vice-coordinator of the MSc in Statistics, Mathematics and Computation (MEMC)

Here is a list of my main publications

In refereed journals (PT: Publicações em revistas com referee):

  • A. Araújo, O. Neto, Moduli of germs of legendrian curves , Annales de la Faculté des sciences de Toulouse, Vol XVIII, nº4, (2009), p. 645-657 (link)

  • A. Araújo, O. Neto, Limits of tangents of quasi-ordinary hypersurfaces, Proc. Am. Math. Soc., Volume 141, Number 1, January 2013, Pages 1-11 (link)

  • A. Araújo, Topologia, Anamorfoses, e o bestiário das Perspectivas curvilíneas, Convocarte Faculdade de Belas Artes da Universidade de Lisboa, no. 2 (Setembro 2016): 51-69 (link)

  • Araújo, A. (2018). Drawing Equirectangular VR Panoramas with Ruler, Compass, and Protractor. Journal Of Science And Technology Of The Arts, 10(1), 15-27. doi:http://dx.doi.org/10.7559/citarj.v10i1.471

    This paper has a companion page with aditional information.

  • António Bandeira Araújo (2018) Ruler, compass, and nail: constructing a total spherical perspective, Journal of Mathematics and the Arts, 12:2-3, 144-169, DOI: 10.1080/17513472.2018.1469378

    This paper has a companion page with aditional information.

  • Araújo, A.;Serranho, P. (2019). On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions, Journal of Computational and Applied Mathematics, Volume 359, Pages 55-68. https://doi.org/10.1016/j.cam.2019.03.019

  • Araújo, A. B. (2020). Explorations in Rational Drawing. Journal of Mathematics and the Arts, 14(1–2), 4–7. https://doi.org/10.1080/17513472.2020.1734437

  • Araújo, A. B., Olivero, L. F., & Rossi, A. (2020). A Descriptive Geometry Construction of VR panoramas in Cubical Spherical Perspective. Diségno, 6, 35–46. https://doi.org/10.26375/disegno.6.2020.06


  • A. Araújo, J. Cabral, O. Neto, Dessingularization of Legendrian Surfaces - The Quasi-Ordinary Case (link)

In refereed Proceedings (Proceedings com revisão por pares):

  • A. Araújo, Cardboarding Mixed Reality with Dürer Machines, 5th Conference on Computation, Communication, Aesthetics & X, Lisbon, 2017, 102-113. (link)

  • Araújo, António, Guidelines for drawing immersive panoramas in equirectangular perspective, in Artech 2017. International Conference on Digital Arts, 8 - "Interfaces of Tomorrow", Macau, 2017, 93-99. (link)

  • Araújo, António, Anamorphosis: optical games with perspective’s playful parent, in Recreational Mathematics Colloquium V G4G, Ludus, Lisbon, 2017, 71-86. (link)

  • A. Araújo, "A geometria (descritiva) da anamorfose e das perspectivas curvilíneas", Atas do Workshop "Matemática e Arte", 2017, Eds. S. Vinagre e A. I. Santos, Sociedade Portuguesa de Matemática, pp. 15-22.(link)

  • Araújo, A, Flores, M., Figueiredo, M., Anamorfoses e outras tecnologias imersivas no contexto da educação artística in Atas do II Colóquio - Desafios Curriculares e Pedagógicos na Formação de Professores, 2017, Eds. Maria Flores et al., Universidade do Minho, Instituto de Educação, Centro de Investigação em Estudos da Criança, pp.243-250 . (link)

  • Araújo, A.B., Let's Sketch in 360°: Spherical Perspectives for Virtual Reality Panoramas, in Proceedings of Bridges Stockholm 2018, 2018, Eds. E. Torrence et al., Tesselations Publishing, pp. 637-644. (link)

  • Araújo, A. B.; Olivero, L. F.; Rossi, A. - Boxing the Visual Sphere: towards a systematic solution of the cubical perspective. In Congresso de la UID, 41, Perugia, 2019. p. 33–40. doi:10.36165/1004 (link)

  • Araújo, A.B., Workshop-Drawing Equirectangular Perspectives for VR Panoramas with Eq A Sketch 360, in 2021 7th International Conference of the Immersive Learning Research Network (iLRN), 2021, pp. 1-3, doi: 10.23919/iLRN52045.2021.9459397

Book Chapters (Capítulo de livros):


At U. Aberta I have taught many different courses. My most usual ones are (differential geometry of) Curves and Surfaces, (Axiomatic) Geometry, History of Mathematics. I taught physics (mechanics and electromagnestism) for a few years, as well as several courses in statistics (sampling theory, descriptive statistics). Ocasionally I taught linear algebra, differential equations. I am now teaching Computer Graphics.

I have a deep interest in Bayesian probability as a generalization of logic, and I created the first courses in Bayesian probability at Aberta. I teach Bayesian Inference to both undergraduate and graduate students.

I have taught several open courses on arts and mathematics to general audiences of artists, programmers and teachers. My favorite course is perhaps the module I teach at our Doctorate in Media Arts. It used to be called "Topics of Geometry and Color Thory in Visual Representation". Now its called Geometry and Visual Immersion and is mostly based on my research on immersive anamorphosis.


Endereço electrónico: antonio.araujo@uab.pt

Endereço postal: Universidade Aberta, Departamento de Ciências e Tecnologia, Palácio Ceia, Rua da Escola Politécnica 141-7, 1269-001 LISBOA, Portugal

Última actualização: 18 de Agosto de 2018

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