**Understanding Higher Math through Physics and Tinkering**

**Prerequisite:** Completion of Algebra II or Integrated Math III.

Have you wondered how much gas you would save if the highway speed limit were dropped to 55 miles per hour? Would you imagine that dropping paper cones may have some bearing to that question? In this course we will explore mathematical descriptions of objects in the real world through hands on projects. Students will build models using cardboard and paper to prove mathematical theorems. We will learn to use approximations effectively, and discover how they lead to the study of calculus in a natural way. We will also learn trigonometry and vectors, as well as a technique called dimensional analysis, which blends physics into algebra. Students will discover how to compute the volumes of unusual geometric objects using Cavalieri’s Principle, and use origami folding to shed new light on conic sections. We will test our mathematical results along the way by considering their physical meaning in extreme, and hopefully absurd, situations. In the process, we will get a sense of how numbers are used in science, as well as how physics inspires new mathematical ideas.

Topics:

- Trigonometric relations with origami
- Vector geometry
- Extreme-case reasoning
- Dimensional analysis
- Cavalieri's principle and volume computations
- Application of origami to trigonometry and conic sections
- Scaling components

**Grade requirement:** Open to all qualified students.

**Self-study and homework required:**
2-5 hours per class meeting.