polyominoes

1. polyominoes Hongan le, Adriana V., and Ogechi Smash 1st years July 13,2010

2. What is an polyonminoe? Polyonminoe- 2-dim shape -generalization on a domino

3. answer • Longest perimeter: 2n+2 • Polyominoe Theorem 1: the perimeter, whether shortest or longest, will always remain an even result as long as the shape is a square. Reason being that every side have another side parallel to it • Polyominoe Theorem 2: When you configure the squares to solid mass with no gaps, then you would have the smallest perimeter

4. 1st Result • Polyoninoe Theorem 1: Longest perimeter: 2n+2 • Why? • Arrangement of squares ●The arrangements at the top exemplify the longest perimeter ●The arrangement at the left doesn’t display the longest perimeter

5. 2nd Result ● Polyominoe Theorem 2: The perimeter of a polyominoe is always an even number regardless of the area ●Why?

6. 3rd Result ●Polyominoe Theorem 2: When you configure the squares to solid mass with no gaps, then you would have the smallest perimeter ●Why? ●The arrangement of squares ●These are some examples of polyominoes with the smallest perimeter

7. 4th and Final Result ●Polyominoe Theorem 4: The shortest perimeter formula: y= square root of n, then round up to the ones, times 4 Explain: What just happened here?

8. Continuation of the Final Result

9. = the largest perimeter possible = the smallest perimeter possible.

10. question • If n is the area then find the shortest and longest perimeter of the polyominoe? • Create a formula for the longest and shortest perimeter for polyominoe. • Then graph the function in the problem above. *explain process.

11. Applications • Why should people care about polyominoes? In other words, what’s the point? • Architect • City planners, taxicabs • Infrastructure ●Polyominoes can apply to maps in that it can lead one to finding either the shortest distance possible or the longest distance possible to another location relative to one’s original location