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Exploring Geometry on the Sphere Lesson Plan

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Lesson Plan #:AELP-GEO0002
AUTHOR: Kirsten Davis, Salt Lake City, UT

Date: 1994

Grade Level(s): 6, 7, 8, 9, 10, 11, 12


  • Mathematics/Geometry

OVERVIEW: This particular activity allows students to discover that not all geometry is Euclidean.

OBJECTIVES: The students will:
1. Learn and use new vocabulary words (great circle, geodesic, spherical angle, spherical triangle, Euclidean geometry).
2. Measure spherical angles to the nearest degree.
3. Discover facts about spherical triangles.
4. Explain facts about spherical triangles to others.


  • beach balls
  • string
  • non-permanent markers
  • protractors
  • paper towels
  • water

1. The day before the activity have students go to the library for 15 minutes to look up the vocabulary words.
2. The day of the activity, divide the class into groups of three.
3. Give materials to student teams.
4. Have student teams construct 3 very different sized spherical triangles on a beach ball using string and markers.
5. Have each group measure and record the measure of each angle. Calculate and record the angle sum for each triangle.
6. Have each team enter their findings on a chart (overhead or chalkboard).

1. As a class, make comparisons between the different lines of the table.
2. Have students come up with a generalization about what is happening with the angle sums according to triangle size.
3. Discuss the various careers and topics that have applications for non-Euclidean geometry.
4. Have students write their conclusions in the form of a letter to a fellow geometry student who has not done this activity.
5. Encourage students to share learned knowledge with parents.

March 1995: This lesson plan is the result of attending the Park City Mathematics Institute’s High School Teachers Program (1994-1995). The teachers are from various sites around the United States. Their objective as a whole is to promote and implement classroom reform in the content and teaching of high school mathematics. Teachers stay in contact by newsletters and regional site meetings.