Report

GBK GEOMETRY – 2012-13 Jordan Johnson Week One, Day Two TODAY’S AGENDA Greetings Syllabus signatures? (~1 min) Review Rules (~5 min) Euclid, Constructions, and Equilateral Triangles (~10 min) First Geometric Construction (~10 min) GeoGebra demo (~10 min) Homework / Questions (~5 min) Clean-up YESTERDAY’S WORK: RESPECT In 5 minutes, answer this question in as many ways as possible: What does “respect” mean, and how can we demonstrate respect here? Now: For each of those two questions, choose the three answers that seem most important to you as a group. Be ready to share your results. RULES Now consider the second question: How can we demonstrate respect here? Choose one answer to the second question that seems most important to you as a group. Goal: simple rules that say what we do want to see in class at all times. Each group: produce one card with a rule, from one of your ideas. EUCLID & ALEXANDRIA EUCLID’S ELEMENTS CONSTRUCTIONS & EQUILATERAL TRIANGLES Equilateral triangle: one whose sides are all of equal length (and angles are all of equal size) Task: Draw a line segment of length 12cm using your ruler; label its ends A and B. Set your compass to the length of the segment, and draw an arc centered at A, then another arc centered at B. Label the intersection point C. Bonus: If that was really easy, try a regular hexagon (i.e., one whose sides are all equal). CONSTRUCTIONS & EQUILATERAL TRIANGLES This was a construction: a figure designed to satisfy given conditions. (In this case: all sides are of equal length.) “Construct” usually means using a compass and a straightedge. THE SURFER’S & SPOTTER’S PUZZLES Spotter: Wants access to all corners Surfer: Wants access to all sides THE ISLAND Equilateral triangular island 12km on each side THE SPOTTER Goal: Choose a location for his house Minimize the sum of the distances from the house to the vertices A, B, and C. THE SPOTTER Scale drawing of the island: 1cm = 1km Example 1: House at D AD = 4.4km, DB = 9.1km, DC = 7.9km Total distance: 21.4km Example 2: House at E AE = 10.4km, EB = 5.1km, EC = 6.9km Total distance: 22.4km. THE SPOTTER Using your triangle from yesterday or a new one (12cm on each side) as a model: Choose several points on the island For each point: Measure the distance to each corner Add up the distances. What do you believe is the best place for the house? …and how many km of path must the spotter clear? What about the worst place? …and how many km to clear from there? HOMEWORK Same homework as yesterday: your bio / introduction email. Due Friday. Posted online at the course Web site. Tomorrow: Bring your supplies (compass, ruler, notebooks, protractor). Bring your signed syllabus form. CLEAN-UP / REMINDERS Pick up all trash / items. Put all borrowed items back in place. Push in chairs (at front and side tables). See you tomorrow!