Appreciating the Gravity of the Situation

The fountain above, located in Siena, Italy, contains many quadratic functions, one of which is labeled. (Image courtesy of Wikimedia Commons, CC-A-SA)

This course uses fountains and photo editing to explore quadratic equations that model gravity. Students should already be a bit familiar with quadratic equations before doing this project, but do not need to remember every single thing — reminders are included, and the course is designed as a low-pressure, explorative experience.

Our main idea here will be to see how math is used to describe and discover features of the real world, not just numbers on a chalkboard, and to have a bit of fun along the way.

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Fieldwork Goals Materials Fieldwork Instructions Lab Work 1: Data Presentation and Organization Goals Data Organization Visual Aid Preparation Lab Work 2: Analysis Goals Building the Function, Step 1: Dealing with Time Building the Function, Step 1.5 Dealing with Time & — SPOILERS Building the Function, Step 2: Dealing with Height Building the Function, Method 2 Validation Goals Peer Review Previous Research Results Error Brainstorming Thread Reaction Time Updated Functions Extensions Goals Questions and Brainstorming Open Thread Calculus: Initial Speed of the Water and Water Pressure My Example