Exercises for Digitizer

Developing lesson plans.

1. (Calculus) Using Digitizer, devise a plan to determine which size egg (small, medium, large)is the most economical. (We define economical by the largest volume-to-cost ratio.)
   
   
2. (Statistics) Using the Pixel error feature, estimate how much error there may be in the measurement of the area of a circle. Account also for the fact that the you have finitely sampled the points on the circle.
   
   
3. (Basic) Using digitizer determine the area of the following polygon. You can copy the image to your hard drive and import it using the browse function. The scale should be accurate.
   
   
4. (Basic algebra) Devise a lesson plan that shows how the area of an object changes with the change in scale. Similarly, Devise a lesson plan that shows how the length of an object changes with the change in scale. Ask the students to compare the changes.
5. (Trigonometry) Devise a plan to show the angle of windshields of three different vehicles.
   
   
6. (Statistics & Trigonometry) What is the average angle of a compact acutomobile windshield.
   
   
7. (Basic algebra) What is the ratio of the areas of a square and octogon having the same diameter?
   
   
8. (Calculus) Using digitizer data taken from the graph of a function, use the trapezoidal and Simpson's rule to estimate the area under the curve.
   
   
9. (Calculus) Find the volume of an ellipsoid.
   
   
10. (Algebra) Is the St. Louis arch a parabola?
    
    
11. (Algebra) Use the relations between the area of an ellipse and its semi-major and semi-minor axes to show that the football below is not an ellipsoid. Discuss possibility of error.
    
12. (Algebra) What kind of spiral is the cinnimon bun? Make a lesson plan.
    
    
13. (Algebra) The bar graph below has only approximate heights shown. Using Digitizer, find them precisely - i.e. to within one decimal place.
14. (Statistics) Do criminals have beady eyes? Using digital images of various people, determine the average distance between the eyes and the height of the face. (Here you will need to define the height of a face - not that easy.)
    
    
15. (Basic & Statistics) Here's a tough one. Find the diameter of the sequoia tree below at left. Not that the hard part is making the correct scale. Discuss the error involved. You might use the Pixel error. You might make several digitized points and use averages. Discuss the problems of performing the same measurements on the sequoia tree at the right.
    
    
16. (Algebra & Geometry & Calculus ) Among the very first curvilinear areas computed by the ancient Greeks was the lune. A lune is the excess of the intersection of two circles. In fact, the intersection can produce two lunes. Find the area of a lune. Can you find the relation between the area of the lune and of the radii of the circles combined with the distance between the circles?
    
17. Find a new application for digitizer in any area and develop a mathematics learning plan for undergraduate or high school students to execute.
18. Using Excel determine how to parse the following set of numbers into three columns.

    0 (230,150) 1 (207,93) 2 (150,70) 3 (93,93) 4 (70,150) 5 (93,207) 6 (150,230) 7 (207,207)

    This Text-to-Columns application is a little trickier than the one discussed in the Digitizer notes.