1. 3.14.15 9:26.53 A. M.

2. L IFE OF P I By: Amanda Meiners meinersaj@live.com Western Illinois University Graduate Student SIU Mathematics Education Conference 3.14.15 9:26.53 A. M.

3.  Use the piece of string you selected, find a way to calculate the distance around the entire circle.  Measure how many times can you approximately use it until you have gone around the entire circle.

4. F IND THE LONGEST CHORD OF THE CIRCLE. This is the definition of diameter.

5. F IND THE LONGEST PERPENDICULAR BISECTOR TO THE DIAMETER. What do we call this? Radius

6. W E WANT TO FIND 3 UNIQUELY, EQUAL CHORDS. H OW CAN WE DO SO ? Using the tangent lines of the outside edge of the circle folded into the centroid (aka the center of the circle)

7. W HAT KIND OF SHAPE HAVE WE CURRENTLY ? W HAT ARE THE PARTICULAR ATTRIBUTES OF THIS SHAPE ?

8. P ICK YOUR FAVORITE CORNER AND FOLD IT ACROSS TO THE MIDPOINT OF THE OPPOSITE SIDE OF THE EQUILATERAL TRIANGLE.

9. M IDPOINT TO O PPOSITE S IDE When we fold 1 vertex what occurs? When we fold 2 vertices what occurs? When we fold all 3 vertices what occurs? (Isosceles) Trapezoid Parallelogram Equilateral Triangle

10. H OW DOES THIS COMPARE TO PREVIOUS SHAPES WE HAVE ENCOUNTERED ?

11. W HAT IF WE BRING ALL 3 VERTICES TOGETHER ? Triangle pyramid Platonic Solids: Tetrahedron

12. N OW UNFOLD AND START WITH THE LARGEST EQUILATERAL TRIANGLE AGAIN.

13. F OLD EACH CORNER ACROSS TO THE CENTER.

14. V ERTICES TO CENTER Folding 1 vertex to center. Folding 2 vertices to center. Folding 3 vertices to center. Isosceles Trapezoid (still just elongated) Nothing too special Regular Hexagon

15.  Within this hexagon what kind of triangles do we have ?  How do these compare to the previous triangles that came about?

16. F OLD SO THAT THE THREE SMALLEST SIMILAR TRIANGLES ARE ON TOP OF ONE ANOTHER.

17. W E NOW HAVE 1 OF THE FACES OF ANOTHER PLATONIC SOLID. I COSAHEDRON. B REAK INTO GROUPS OF 20 STUDENTS WORKING TOGETHER

19. P LATONIC SOLIDS CAN ARE DEFINED WHEN WE HAVE A COUPLE THINGS OCCUR.  Euler’s formula = F+V-E = 2 always  Only 5 Platonic Solids occur  At each vertex the angle is < 360 degrees  Tetrahedron: 180 degrees  Icosahedron: 300 degrees