How would you draw a square if you were not allowed to measure its sides or angles?
Locations: Palo Alto
Cost: $110/hr.
Recommended hours: 6-7.5
Goals:
This course consists of creating geometric constructions – segments, angles, polygons, etc. – using only a compass and a ruler. We will use these tools, along with a writing utensil of course, to accomplish tasks such as cutting a segment in half, drawing an equilateral triangle, and creating a right angle — all without needing to measure anything!
Another aspect of the course is analysis of the motivations for performing constructions, and the role of these techniques in the history and foundation of mathematics. Constructions prompt questions about types of numbers as we take whole numbers and transform them into rational numbers, irrational numbers, or primes. Geometry as most students learn it is heavily based on algebra; this course can provide a visual or geometric analogue of common algebraic concepts.
Students who stay actively engaged in the learning process during the summer perform better during the school year.
