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?

Regular Polygon Interior Angles

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 TransformRotate.

5. Rotate 108 degrees.

6. Continue to rotate new segments until pentagon is closed.

“Regular” Polygon Angle Measures

“Regular” Polygon Angle Measures

Regular Polygon Interior Angle Formula

…where “y” is the measure of each interior angle

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?

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. TransformRotate.

5. Rotate 77.14 degrees.

6. Continue to rotate new segments until pentagon is closed.

How many vertices are in your shape?

How can you explain this?

Hint: Turn 3.5 into a fraction