Sphere Presentations -
One Problem Per Person
Briefly review related content that applies to the geometry of
the plane / Euclidean geometry / flat geometry.
Discuss why the general topic is important in mathematics and the
Summarize diverse perspectives of your sphere problem in your own words.
through a given point, only one line can be drawn parallel to a given line.
Is this true on the sphere?
Do right triangles on the sphere satisfy the Pythagorean Theorem?
Can we construct a square on a sphere? Explain.
Can we construct every convex polyhedron on a sphere, like a soccer
ball [a spherical version of a truncated icosahedron]?
Are there spherical polyhedra that have no flat equivalents?
Is SAS (side-angle-side) always true for spherical triangles on the surface of a perfectly round beach ball? Explain.
For part 2 of your presentation, searches like
"parallels are important"
or a search word related to your problem and then (with and without
quotations) words like
important, interesting, useful, or real-life applications.
You might also pick some specific fields to see if
there are applications:
Pythagorean theorem chemistry
For part 3 of your presentation,
you do not need to prove an answer or completely
resolve the issue on the sphere. You should look for various perspectives
related to spherical geometry, and summarize those in your own words.
Try different combinations of search terms related to your problem
along with words like sphere,
spherical, earth, spherical geometry, or double elliptic geometry.
Vary your word combinations:
Polyhedra on a sphere
yield very different results, and quotations can be helpful if there
are too many results