History and Philosophy Of Science | History & Conceptual Fdn Math
X126 | 22905 | Karin Ekholm


X126

The aim of this course is to study the history and conceptual
foundations of geometry and to examine the role of geometry in the
visual arts and architecture during the Renaissance. Since our focus
will be on analyzing geometrical structures in maps, buildings and
paintings, the discussions and assignments require not only reading,
but close examinations of geometrical diagrams and works of art. We
will visit the Lilly Library to look at early editions of Euclid and
Ptolemy, as well as the IU Art Museum in order to better understand
perspective.

The course will begin by looking at Euclid’s Elements in order to
gain an understanding of the axiomatic-deductive method of
reasoning, and work through a selection of Euclid's theorems. We
will then examine how Ptolemy applied geometry to treating physical
phenomena, including charting the motions of the planets, making
maps of the earth and explaining vision.

Next we will discuss what happened to these texts after classical
Greek civilization degenerated, how Islamic science assimilated and
improved upon Greek thought, and focus on the “rediscovery” of the
texts in medieval and Renaissance Europe. Finally, we will look at
the way in which Brunelleschi, Toscanelli, Alberti, Pierro della
Francesca, Durer and Leonardo da Vinci assimilated Greek ideas about
geometry into their own work.