Difference between revisions of "Hyperbolic Geometry Exercises"

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{{Exercises}}
 
{{Exercises}}
 
<ol>
 
<ol>
<li>One</li>
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<li>Draw a Poincaré disk, and draw four geodesics that don't cross.</li>
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<li>Draw a Poincaré disk, and draw four geodesics through the center point.</li>
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<li>Copy the Poincaré disk shown below, and draw three geodesics through the point that don't cross the line shown.
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[[Image:hyp-ex-3.svg]]
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</li>
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<li>All hyperbolic triangles have angles adding up to less than 180°.  Call the amount under 180° the "defect" of the triangle.  What is the upper limit for the defect of a hyperbolic triangle?
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</li>
 
</ol>
 
</ol>

Revision as of 23:52, 12 April 2007


  1. Draw a Poincaré disk, and draw four geodesics that don't cross.
  2. Draw a Poincaré disk, and draw four geodesics through the center point.
  3. Copy the Poincaré disk shown below, and draw three geodesics through the point that don't cross the line shown. Hyp-ex-3.svg
  4. All hyperbolic triangles have angles adding up to less than 180°. Call the amount under 180° the "defect" of the triangle. What is the upper limit for the defect of a hyperbolic triangle?