1 / 13

GBK Geometry

In today's lesson, we delve into the exciting game of Hex while exploring the concepts of distance in geometry. We'll review winning strategies, demonstrating that the first player always has an advantage. Using the Pythagorean Theorem, students will practice calculating distances between points in two dimensions. Homework assignments will enhance understanding, covering exercises from Chapters 4, Lessons 1 and 2. Let's engage in pair discussions and ensure a comprehensive review of the day's topics. Get ready for a thorough exploration of geometry!

yehuda
Télécharger la présentation

GBK Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GBK Geometry Jordan Johnson

  2. Today’s plan – Period 1 • Greeting • Hex Review • Lesson: Distance • Homework / Questions • Clean-up

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

  4. 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.

  5. Location on the Hex Board

  6. 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:

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

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

  9. Homework • Asg #26: 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)

  10. Today’s plan (Periods 2 & 7) • Greeting • Warm-up: Distance • Review Theorems • Homework / Questions • Clean-up

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

  12. Homework • Asg #26: 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!

More Related