Shapes of Constant Width

1. Shapes of Constant Width Susan Morgan Melissa Rodriguez NSFFall2011

3. What shape makes the best manhole cover? Why?

4. What’s the pattern? NSFFall2011

5. Frantz Reuleaux Known as the father of Kinematics • Born in 1829 in Eschweiler, Germany. • Received BA in Engineering from University of Bonn in 1854 • Teacher at the Swiss federal Institute of Technology 1856-1864 • Professor- Mechanical Engineering, University of Berlin 1864-1879 • President- University of Berlin 1868- 1879 • Believed in using scientific principles and analyzed mechanical devices using new methodology • Most known for his kinematics pairs and for the Reuleaux Triangle NSFFall2011

6. Applications of Reuleaux Triangles NSFFall2011

7. Applications of Reuleaux Triangles Wankel Engine Drilling a Square Hole NSFFall2011

8. Construction Supplies  Ruler Pencil Compass NSFFall2011

9. Construction of the Reuleaux Triangle Part I Construct an equilateral triangle Part II Place the tip of your compass on one of the triangle’s vertices Draw an arc between the two other vertices Repeat with the tip on the 2nd and third vertices NSFFall2011

10. Construction of the Reuleaux

11. Bruge Notre Dame Eglise, Belgium

12. NSF FALL 2010

13. Activity #2 NSFFall2011

14. NSFFall2011

15. Other Shapes

16. How do you define width?

17. Other Shapes • Star Application • http://www.cut-the-knot.org/Curriculum/Geometry/CWStar.shtml

18. Conclusion NSFFall2011