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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Review Asg #25: From the Ch. 3 Algebra Review (p. 130): Exercises 1-24. Homework / Questions Clean-up. Homework. Play Hex.  Asg #26 will be: Ch. 4 Lesson 1 (pp. 134-138): Exercises #16-25, 31-39, 47-49. Bonus: Set III.

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review Asg #25: From the Ch. 3 Algebra Review (p. 130): • Exercises 1-24. • Homework / Questions • Clean-up

  3. Homework • Play Hex.  • Asg #26 will be: Ch. 4 Lesson 1 (pp. 134-138): • Exercises #16-25, 31-39, 47-49. • Bonus: Set III. • Due Tuesday, 11/6. • Asg #27 will be: Ch. 4 Lesson 2 (pp. 141-144): • Exercises #1-7, 20-24, 37-54. • Bonus: Set III • Due Thursday, 11/7 (per. 1-2) or Friday, 11/8 (per. 7).

  4. Today’s plan • Greeting • Review Asg #25: From the Ch. 3 Algebra Review (p. 130): • Exercises 1-24. • Lesson: Hex Follow-up • Homework / Questions • Clean-up

  5. Hex

  6. Hex: Follow-up • In pairs, discuss: • What questions occurred to you as you played Hex? • What have you noticed about how the game works?

  7. Hex • Theorem: • The first player of a Hex gamealways has a winning strategy. • Proof sketch (by John Nash): • Either the first or second player musthave a winning strategy; ties areimpossible and the game must end. • Extra stones on the board for a player always improve that player’s position. • Suppose the second player has a winning strategy. • The first player can play anywhere,and then use the second player’s winning strategy. • If the strategy calls for playing on a cell the player already played,they can play anywhere on that turn. • This way, the first player will win. There can be no winning strategy for the second player. • The second player doesn’t have a winning strategy,so the first player must.

  8. Location on the Hex Board

  9. Coordinate Geometryand Distance • Definitions / reminders: • The origin is the reference point whose coordinate(s) is/are zero. • one-dimensional vs. two-dimensional systems of coordinates • quadrants of a graph:

  10. Distance in two dimensions • Question: • Given points (x, y) and (z, w), how do you compute the distance between them? • Answer: • The Pythagorean Theorem!

  11. Examples • Find the distance between: • (5, 8) and (9, 11) • (-4, 2) and (3, 1) • (10, 54) and (5, 42)

  12. Homework • Play Hex.  • Asg #26 will be: Ch. 4 Lesson 1 (pp. 134-138): • Exercises #16-25, 31-39, 47-49. • Bonus: Set III. • Due Tuesday, 11/6. • Asg #27 will be: Ch. 4 Lesson 2 (pp. 141-144): • Exercises #1-7, 20-24, 37-54. • Bonus: Set III • Due Thursday, 11/7 (per. 1-2) or Friday, 11/8 (7)

  13. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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