Paseos Matemáticos por Granada. Un estudio entre Arte, Ciencia e Historia

22 September, 2021

Álvaro Martínez-Sevilla

This books presents a study between Art, Science and History. It contains perhaps the first proposal for a systematic study of mathematics that it can be found in the monumental heritage of a city. With 22 Walks that contain the analysis of many monuments, it reveals how they show functional mathematics (which have allowed a construction effective in its architectural purposes), decorative (mathematics that have served with its geometric arrangement to make more beautify the building) or symbolic (mathematics that expresses with an universal language a sense of programmatic proposal which wants to transcend its epoch).

Editorial: University of Granada
Year: 2017
Pages: 416 + DVD
ISBN: 978-84–338–60-7

These mathematics have always been present and have linked from the science to the monumental heritage. Numerous treatises on geometry and architecture are the base on which most of these monuments were built. But without a user guide, the lack of practice of these rules in the most recent architecture has led us to forget their existence and the way to recognize them. It is not just a matter of seeing mathematical figures in a building, but of finding the lantent design guidelines that make it be considered more beautiful or symbolically significant. In this way, it has been extremely useful diferent software programs, symbolic computing programs and graphic representation, but the most relevant has been the GeoGebra program. With a long history, this dynamic geometry software is capable of interacting with reality, drawing mathematical layers on images. This characteristic allows us to use methods which also use the AI, such as, obtaining information from reality that is then processed through expert knowledge or finding the patterns that are under the building. The dynamic nature of this software makes the exploration of such patterns very flexible, saving scaling, orientation and adaptation tasks.

With more than 700 images in total and more than 400 built with mathematical layer, the book contains a great variety of mathematics present in monumental architecture which includes examples of remarkable proportions, uses of conics and special curves, tessellations, modulation of facades or plants, symmetries, homothecies, functional constructive analysis, significant measurements on images, use of geometric places and regular graphic design structures, among other questions of a mathematical nature. All of them located in the historical-artistic context, interpreted according to their monumental style and historical time which builds a story about the monument mixing mathematics, history of science, art and technology as complementary disciplines for a more complete understanding of the analyzed monument.