Write a report on Ramsey theory.
The Garden House of Ostia was constructed in the 2nd century, in the city of Ostia,
whose population reached 50,000 at its peak. 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 archeologists 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.
"A Roman Apartment Complex," by Donald J. Watts
and Carol Martin Watts. Scientific American, December 1986, pp. 132-139.
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.
Make drawings of geometric figures on a piece of rubber inner tube. Demonstrate to
the class various ways in which these figures can be distorted.
The problem shown in the News Clip was first published by John Jackson in 1821. Without the poetry,
the puzzle can be stated as follows: Arrange nine trees so they occur in ten rows of three trees
each. Find a solution.