# Oakland East Bay Math Circle NonEuclidean Geometry Worksheet by langstonwalker

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```									      Oakland East Bay Math Circle: Non­Euclidean Geometry Worksheet

Using the rubber bands and spheres you have, follow the instructions below to test
the rules of geometry.  Remember that in elliptic geometry, a “straight line” is really
a great circle (a circle that has the same diameter of the sphere it’s on).

1.  Use three rubber bands to create different triangles on the sphere.  Make four
different triangles and use your protractor to measure all three angles inside the
triangle.  Try to make very different triangles.  Write the angles below.

Triangle 1:  __________       __________       __________

Triangle 2:  __________       __________       __________

Triangle 3:  __________       __________       __________

Triangle 4:  __________       __________       __________

2.  For each of the triangles you made, find the sum of the angles on the inside of the
triangle.

Triangle 1:  __________    +  __________    +  __________    =  __________

Triangle 2:  __________    +  __________    +  __________    =  __________

Triangle 3:  __________    +  __________    +  __________    =  __________

Triangle 4:  __________    +  __________    +  __________    =  __________

3.  Are the sums of the angles of the triangle 180 degrees?

4.  Now use the rubber bands to make three different right triangles. Use the
measuring tape to measure the lengths of the three sides in millimeters, and write
them below.

Triangle 1:  __________      __________      __________

Triangle 2:  __________      __________      __________

5.  Do these sides satisfy the Pythagorean theorem?

(First smallest side)2 + (Second smallest side)2 = (Hypotenuse)2

Triangle 1:  (__________)2 +  (__________)2 =  (__________)2

Triangle 2:  (__________)2 +  (__________)2 =  (__________)2

6.  What’s different between the geometry we’re used to (Euclidean geometry) and
the geometry on a sphere (Elliptic geometry) that might account for these
differences?

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