The Farmer and the Mathematician II: more mathematical investigations using Geometry Expressions

This is Mr. Ottman's second book about a corny farmer and his mathematician friend. Our farmer uses a Center Pivot Irrigation System – those long stretches of wheeled scaffolding, sometimes up to a half-mile in length, rotating around a fixed point attached to his water source. This presents real world geometry problems concerning how to fit a circular or semi-circular irrigated plot into a polygonal (usually rectangular, sometimes triangular or even trapezoidal) field. As in the first book, we demonstrate to the student that Mathematics is not just for calculating the price of produce in the grocery store. Here we have a fresh batch of examples of mathematics in action using our symbolic geometry software, Geometry Expressions, with images from Google Earth. The process of mathematical modeling is both critical to using mathematics in the world around us, and to developing an understanding and appreciation for the true utility of mathematics. A mathematician or engineer would first be given a problem to solve. They would also be given constraints, or a set of rules and conditions that must be followed. From that, the scientist would attempt to create a mathematical representation of the problem. Often, real problems are much too complex and it is necessary to constrain, or simplify them further. This is very similar to the approach that a student would take to gain insight into a problem by solving a simpler, related one. Geometry Expressions is written to mirror this process. It is a constraint-based geometric and algebraic modeling program that allows the student to investigate problems in both a numeric and symbolic representation. So join the Farmer and his mathematical instructor, Sophie, as they fly over Texas, investigating interesting geometrical ideas and stumbling over important mathematical concepts. The content is appropriate and adaptable for students in a range of courses from Algebra and Geometry up through and including Calculus. The book comes complete with black line masters and detailed teacher notes for every lesson.