Unit 6: The Babylonians, the Egyptians, and Mathematics

Preparation

• History Web Lecture: The Babylonians and Egyptians created and developed mathematical procedures and used astronomical observations to solve particular problems; they do not seem to have been theoreticians, looking for the general solution to a type of problem, as the Greeks were later. Help your student see the connection between the practical problems of laying out fields and cities (measuring area and length), counting and measuring (trade), and keeping track of the calendar (planting and harvesting crops), and the study of geometry, arithmetic, and astronomy.

  Go over the forms of notation used by both Egyptians and the Babylonians. How are they similar? Different? Help the student realize how the notation of numbers can make it easy (or hard) to solve arithmetic problems.

• Science Web Lecture: The lecture covers some basic ideas in mathematics that have implications for science. In particular, we bring up the idea of discrete entities (ones that have a boundary that separates them from other things), and continuous entities, and the difference between counting and measuring. Another key point of this lecture is the use of formulae to calculate derived quantities from basic measurements, such as the calculation of areas from measurements of the sides of squares. This section may be easy or difficult, depending on the level of math background your student already has. The goal is not to memorize every formula presented, but to understand that a general formula is a powerful tool that allows us to determine a result in every conceivable case.

  This is the last of our "groundwork" units. We've talked about what science is, how individuals and societies can pursue it, what disciplined observation and experiment bring to scientific understanding of nature, and how we might use mathematics to help us keep track of and calculate interesting relationships. We will continue to use all of these tools throughout the year, so while it is not necessary to understand every possible ramification of concepts of physical law or the application of math to science, it is important that students have some sense of what science is, and what math is good for.

• Mastery Exercise: Exercise questions are largely practical applications of the concepts and terms in the weblecture, so students will have to do more analysis and less "looking up" the answer in this exercise.

• Discussion: The discussion will focus on the development of mathematics as a tool of expressing precise quantities, and on the ramifications of using calculations, especially if there are errors in the measured quantities.

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