{"id":11878,"date":"2020-02-25T15:23:09","date_gmt":"2020-02-25T14:23:09","guid":{"rendered":"https:\/\/blog.uchceu.es\/arquitectura\/?p=11878"},"modified":"2020-06-01T10:48:04","modified_gmt":"2020-06-01T08:48:04","slug":"fractal-geometry-coil-architecture","status":"publish","type":"post","link":"https:\/\/blog.uchceu.es\/arquitectura\/en\/fractal-geometry-coil-architecture\/","title":{"rendered":"International fractal geometry: a COIL module in Architecture"},"content":{"rendered":"

Mathematics is one of those subjects that many people are afraid of, dreading its impossible concepts: variables, calculus and fractal geometry. But then you haven\u2019t met the person who teaches this at ESET, CEU\u2019s school of architecture.<\/p>\n

She has a PhD in mathematics, so she was always bound to love numbers, but she also sees teaching as a vocation. After you talk to CEU lecturer Luc\u00eda Hilario<\/strong>, it\u2019s obvious why students end up finding numbers so interesting when studying with her! In our conversation with Luc\u00eda we explored the meaning of maths, what its practical applications are and, most especially, how maths has been given an international and innovative twist at the University. The solution to that equation was to use an approach called COIL \u2013 Collaborative Online International Learning<\/strong><\/a>.<\/p>\n

\"La
Luc\u00eda Hilario has pioneered the COIL module in fractal geometry in Architecture<\/figcaption><\/figure>\n

Luc\u00eda, you\u2019ve been one of the first to take up the gauntlet of this ground-breaking COIL initiative and you\u2019ve done so boldly, with modules for Mathematics, Theory of Architecture, and Construction of Foundations and Structures. What led you to include this module in your course?<\/strong><\/p>\n

The reason is clear: it\u2019s down to the kind of students we have, who are from all over the world. For them, being able to interact with people at the Florida International University<\/strong><\/a> is very positive, because it makes their experience here even more international. It\u2019s something that makes the internationalization of ESET that much more tangible.<\/p>\n

Personally, as soon as this project was proposed, I knew what I wanted to do. I teach on both the Business Management and Architecture degrees, but at ESET the group of students I teach is smaller. So, given their international profile as well, it made it that much easier to try out my first COIL module with them.<\/p>\n

This module forms part of the Mathematics course. Was it easy to incorporate it within the course?<\/strong><\/p>\n

The Mathematics course is taught over both semesters of the first year, and I always try to give the students the mathematical tools needed for physics and structural calculations<\/strong>. And then I also look at the kind of maths that really connect with the professional practice of architects: we study the golden ratio<\/strong>, the catenary curve<\/strong>, fractal geometry<\/strong>, etc. And I\u2019m always trying to encourage learning by doing. So, for example, soon we\u2019re going to visit the Ciudad de las Artes in Valencia, so that I can get an architect to explain what kind of surfaces have been used in its construction.<\/p>\n

\"Geometr\u00eda
The Ciudad de las Artes in Valencia, an environment full of interesting surfaces and structures<\/figcaption><\/figure>\n

I don\u2019t think that my course is one of those that undergraduates hate<\/em> because I always try to give them tools that they can use in architectural projects, such as geometry. It\u2019s also true that the degree of knowledge students have when starting the course can be quite uneven, and it\u2019s important to bear this in mind. So, in the first few months, I focus on finding a balance between the stronger and weaker students in maths.<\/p>\n

But I\u2019m always trying to introduce new things into the course, such as conic sections and the golden ratio, which were already used in buildings in Ancient Greece and yet which are still absolutely relevant today.<\/p>\n

So, you\u2019re after a perfect proportion possessing balance and beauty. What other mathematical concepts do you teach that have an architectural application?<\/strong><\/p>\n

Another key concept for architecture is conical sections<\/strong>. Remember that a building may contain many circles, ellipses, parabolas and hyperbolas. The catenary curve<\/strong> is another example, which Gaud\u00ed used so much in his buildings. Or parametric curves and surfaces<\/strong>, which are very important in CAGD (Computer Aided Geometric Design): NURBS, B-spline, rational B\u00e9zier curves, B\u00e9zier curves, etc.<\/p>\n