Details

The images Serlio I, II, III, and IV are similar to the corresponding images in the book of Serlio [3]. See http://digi.ub.uni-heidelberg.de/diglit/serlio1584/0074/image?sid=219b4952a0817e3ab12d0c6e48f4fce5 # current_page and http://digi.ub.uni-heidelberg.de/diglit/serlio1584/0075?sid=219b4952a0817e3ab12d0c6e48f4fce5.

"Serlio I" shows ovals with constant distance; one may say "parallel" ovals. The construction in this Demonstration uses three famous theorems of Euclid (ca. 360–280 BC) that were not known to Serlio (1475–1554?). The edges of the ovals consist of four segments of circles that are joined smoothly. This is easily done by using the theorems of Euclid: "If two circles touch one another, their midpoints and the point of contact lie on a straight line (III, 11and III, 12)." "The straight line from the center of a circle to the point of contact of a tangent and the tangent are perpendicular (III, 18)."

The plan of Saint Peter's Square is based on the configuration in the image Serlio IV.

In architectural literature the words "oval" and "ellipse" are often used synonymously, which is incorrect in a mathematical sense.

References

[1] T. K. Kitao, Circle and Oval in the Square of Saint Peter's: Bernini's Art of Planning, New York: New York University Press, 1974.

[2] P. L. Rosin, "On Serlio's Construction of Ovals," Mathematical Intelligencer, 23(1), 2001 pp. 58–69, 2001. http://users.cs.cf.ac.uk/Paul.Rosin/resources/papers/oval2.pdf.

[3] S. Serlio, Tutte l'opere d'architettura di Sebastiano Serlio Bolognese, Venice: Presso Francesco de'Franceschi Senese, 1584. http://digi.ub.uni-heidelberg.de/diglit/serlio1584.