Find several objects with curved surfaces. One might be a sphere (large or small ball, an orange, grapefruit, canteloupe, etc.); one should be something less regular--a squash, banana, lampshade, inner tube--think of something original.
| Cut out some of the angles on the included sheet, cutting on the dotted lines. | |
| Tape the angle onto a curved surface so that it lies as flat as possible. Trim the margins if necessary. | |
| Cut off part of one of the rays of an angle to make a line segment, and tape it onto the surface to form a triangle, with tape at the two new vertices. | |
| Once you have a triangle lying on the surface, remove it, keeping its triangular shape. | |
| Cut the middle of one or more of the sides so that the pieces lie flat on the table. | |
Measure each of the angles with a protractor; also measure the lengths of the sides.
Record all the information in a table, including a qualitative description of what the surface looked like where the triangle was.
Compute the sum of angles in your triangle and record it in the table.
If your triangle has a right angle, label the right angle C and the other angles A and B. Label the side opposite C with a c, the side opposite B with a b, and the side opposite A with an a. Compute c2; compute a2+b2 and record both values in the table.
Repeat the process of making and measuring triangles for different locations on the surface; for large surfaces, try a small triangle, then a large triangle in the same spot.
Make a cone out of paper and use it as another surface; make some triangles on it; record the results.
Make a cylinder out of paper and use it as another surface; make some triangles on it; record the results.
For comparison, make a few plane triangles, including some right triangles; record the results.
To the Math 129 home page
To CSUSB Math Department home page
To Susan Addington's home page