1. Formula-Free Geometry

2. Area and Volume

3. Exact Geometry Easy! Pretty easy! 11 1 1

4. Inexact Geometry 1 No formula for green area

5. Random Procedure  Drop a point at any location within the square  The likelihood of a point falling inside the region is determined by the proportion of area that the shaded region fills Uniform Random Occurring with equal probability

6. Random Points 1

7. Real Geometry Can we use this for real problems? 25000 km YES!

8. Real Geometry Use a computer to generate MANY random points 25000 km

9. Real Geometry

10. 10 cm

11. Today’s Challenge

12. Circle in a Square 2

13. Simulated Random Points Use the NXT Brick to…

14.  Find average of five estimates  Find the percent error relative to 3.14159  Find the ‘standard error’ of samples  Tighter error  better confidence

15. How Close? Standard Error