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In-Class Activities
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7.6 In-Class Activities
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Activity 1
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The Curved Space of a 2-Sphere
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Triangles on a 2-sphere
Blow a balloon into an approximately nice spherical shape. Define the north and south poles on your balloon. Draw a set of longitudes using a fine marker. Draw the equator as well.
Form a triangle with 2 longitudinal lines and the equator, draw it out with a thick marker.
Measure the interior angles of the triangle and find the sum of the three angles.
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Geodesics on a 2-sphere
A geodesic is a generalised notion of a straight line. It is the shortest distance between two points in space. It is the line whereby a non-accelerated body will move on.
Blow another balloon into a sphere. Mark out two points on the balloon and call them NiuLang and ZhiNΓΌ. How would you draw the shortest distance, aka the geodesic, between them?