The Nature of Mathematics, 12th Edition
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Chapter 8 Projects

Section 8.2 Individual Research

Individual Research Project 8.2

Historical Quest: The Garden House of Ostia was constructed in the 2nd century, in the city of Ostia, whose population reached 50,000 at its peak. (See the "What in the World" comment at the beginning of Chapter 7.) This city was a major port of Rome, which was about 25 km away. The Garden Houses are of interest because of the geometry used in its construction. The key to its construction, according to archaeologists Donald and Carol Watts, is a "sacred cut." In searching the records of the architect Vitruvius they found that the basic pattern begins with a square (called the reference square) and its diagonals. Next quarter circles centered on the corners of the square are drawn, each with a radius equal to half of the diagonal. The arcs pass through the center of the square and intersect two adjoining sides; together they cut the sides into three segments, with the central segment being larger than the other two. By connecting the intersection points, you can divide the reference square into nine parts, as described in the article. At the center of the grid is another square that can serve as the foundation for the next sacred cut. Experiment by drawing or quilting some "sacred cut" designs.

References:
"A Roman Apartment Complex," by Donald J. Watts and Carol Martin Watts. Scientific American, December 1986, pp. 132-139.

An historical reference, along with a very interesting site on the Garden Houses of Ostia is found at this site:
http://www.ostia-antica.org/indexes.htm

Individual Research Project 8.3

The German artist Albrech Durer (1471-1528) is not only a Renaissance artist, but also somewhat of a mathematician. Do some research on the mathematics of Durer.