Planimeter Applet

Java capable browser required

Try This!

  1. Select "data/us.jpg" from the drop down box at the middle right.
  2. Wait a long time for it to download.
  3. Scroll the map down until you see the scale for the continental U.S.
  4. Select the "ruler" checkbox.
  5. Drag the mouse from the beginning of the scale to the end (500 miles)
  6. Click on the text box after "ruler", and enter "500"
  7. Click on the "scale name" checkbox.
  8. Click on the text box after "scale name" and enter "miles".  (Technically, this particular text box is a placebo.)
  9. Scroll the map until you see Ohio.
  10. Click on the "move" checkbox.
  11. Click the mouse about 1/3 of the way from Springfield IL toward Chicago.
  12. Click on the "clear and trace" checkbox.
  13. Trace the outline of Ohio (press the mouse button somewhere on the perimeter of Ohio and then move the mouse around the perimeter while holding the button down and be careful to finish at your starting point.)
  14. Look at the value in the text box after "wheel reading."  The number there should be about 40000.
  15. The area of Ohio is 41,222 square miles.

Planimeter Applet Guide

  1. Structure of the Instrument
  2. The Wheel
  3. Tracer Arm Movement
  4. Tracer Arm Rotation
  5. Doubling Back Movement
  6. Position of the Pivot
  7. Path of the Pivot
  8. Measuring Twice or in the Opposite Direction
  9. The Zero Circle
  10. Mathematical Definitions
  11. Areas Measured
  12. Corrections for Rotation of the Tracer Arm
  13. Mathematical Expressions of Areas
  14. Formula for Area
  15. Formula for the Zero Circle
  16. Proof of the Zero Circle
  17. Formula for the Wheel Reading
  18. Description of the Wheel Reading
  19. Significance of the Wheel Reading
  20. Geometric Interpretation of the Wheel Reading
  21. Purpose of the Java Applet
  22. Organization of the Applet Window
  23. Colors in the Drawing Area
  24. Some Areas Not Represented
  25. Table of Area Colors
  26. Planimeter Consists of Narrow Lines
  27. Numeric Values of Areas
  28. Selection of the Sample
  29. Selection of the Drawing Mode
  30. Tracing in the Drawing Area
  31. Tracing Modes
  32. Clearing
  33. Move and Resize Modes
  34. Resize Modes
  35. Resizing Effects in the Drawing Area and Textboxes
  36. Negative Numbers in Textboxes Implement Special Features
  37. Scaling Modes
  38. Ruler Mode

Larry Leinweber, Proprietor

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