Project Ideas

Measurement of many types of complicated shapes in a variety of ways is quite simple using data and digital images. Here is a collection of images.

  Volumes
  1. Egg - volume of revolution problem. You need just the image and a single measurement of the egg's length. Alternatively, give the diameter of the axial cross-section to add a small level of difficulty.
  2. Water tower - a volume of a cylinder problem. You need a distant image of a water tower to eliminate parallax and one measurement. The easiest measurement to obtain is a portion of the circumference of the base which can be obtained by pacing.
——— Areas
  1. Area of a polygon. Here you will need the algorithm as explained in the polygon project.
  2. Approximate the area of an ellipse. Compare with the formula for the area of an ellipse where a and b are the semi-major axes. Approximate the area of a circle.
  3. Establish that a vertically compressed circle is an ellipse. Are all oval shapes necessarily ellipses. (e.g. Consider the Decartes ovals.
  4. Area of the front elevation of a hotel. Here you will need a single measurement again. But how to get it? If the front elevation is quite large, all familiar objects next to it such as an automobile are really two small to use for accurate scaling. Here you may consider enlarging the image to make an scale which in turn will give a larger scale for the original picture. Note that from a horizontal measurement, the vertical measurement is obtained as well.
  Shapes
  1. It that shape a circle? See the circle project. This can be applied for example, to determine if the roof of the astrodome is round.
  2. Is an egg an ellipsoid?
  3. Is that shape a rectangle? Here you can compute the angles of the vertices or alternatively verify that the Pythagorean theorem holds. This requires computing the distance between diagonal points.
  Angles
  1. What is the angle of the handicap ramp?
  2. What is the angle of a stairway? See the stairway project.
  Length
  1. Find the distance between two points. A simple application of the Pythagorean theorem.
  2. Find the circumference of any polygon. Applications: Find the distance through a maze. Find the shorted distance between two points over a map with specified paths.
  3. Determine the ratio of the major-minor axes of an ellipse.
  4. Approximate the circumference of an ellipse by selecting many points around the circumference and Here the exact formula, you will recall, is complex.
  5. Verify the formula for an ellipse. Find the constant, semi-major axes, etc.

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Can you think of ideas? If so, please email to Don Allen.