1. Continuous vs. Discrete Functions Continuous – temperature conversion – growth over time – velocity of an object – cost of cab ride – depreciation of car Discrete – tax credit for kids – change machine – outcomes for dice roll – formula: an interior angle of regular polygon?

2. Regular Polygon Interior Angles

3. Draw a Regular Pentagon in Sketchpad 1.Make a segment. 2.Double-click one endpoint to “mark it.” 3.Now, select the segment and the other endpoint. 4.Go to Transform  Rotate. 5.Rotate 108 degrees. 6.Continue to rotate new segments until pentagon is closed.

4. “Regular” Polygon Angle Measures

6. Regular Polygon Interior Angle Formula …where “y” is the measure of each interior angle

7. Can we break this “discrete” function? Is there anything that prevents us from putting a decimal number into the equation? What if we tried to calculate the interior angle measure of a regular 3.5-gon? What would the angle measure be?

8. Draw a Regular 3.5-gon in Sketchpad 1.Make a segment. 2.Double-click one endpoint to “mark it.” 3.Now, select the segment and the other endpoint. 4.Transform  Rotate. 5.Rotate 77.14 degrees. 6.Continue to rotate new segments until pentagon is closed.

9. How many vertices are in your shape? How can you explain this? Hint: Turn 3.5 into a fraction