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GBK Geometry – 2012-13

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)

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GBK Geometry – 2012-13

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  1. GBK Geometry – 2012-13 Jordan Johnson Week One, Day Two

  2. 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

  3. 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.

  4. 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.

  5. Euclid & Alexandria

  6. Euclid’s Elements

  7. 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 wasreally easy, try a regularhexagon (i.e., one whosesides are all equal).

  8. 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.

  9. The Surfer’s & Spotter’s puzzles Spotter: Wants access to all corners Surfer: Wants access to all sides

  10. The Island • Equilateral triangular island • 12km on each side

  11. 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.

  12. 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.

  13. 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?

  14. 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.

  15. 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!

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