Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Equilateral triangles on a sphere
Name: julie a corder, pam swan, candice korb, and natalie bauman
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:
Our eighth grade geometry class has been assigned a six-week project. We have to cover the surface of a sphere with equilateral triangles of any size. We are working in partners; one pair has a sphere with a diameter of 4 inches, the other 6. Our research has shown that since no straight lines can be drawn on a sphere, and since spherical triangles all have angles with measures with a sum greater than 180, getting plane triangles to lie on a spherical surface is impossible. We have been told to just make the triangles as small as possible, so that the error is not visible.


Replies:
Julie, Pam, Candice and Natalie - the solution to the problem is that you can only "strictly speaking" do it correctly when the triangles are really tiny - infinitesimally small in fact. By using small, but not infinitely small, triangles, you are making an approximation. Did you actually measure those angles for spherical triangles? Try comparing the sum of the angles for a large spherical triangle with the sum for a smaller one. You should find that the smaller one has a sum much closer to 180 degrees. Remember that the lines for a spherical triangle must be "locally straight" so you cannot just follow "lines of latitude" which are curved - the lines you draw must be more like "lines of longitude."

Anyway, if you actually did try covering the sphere with little triangles, congratulations! It has kind of like making a circle out of little straight-line segments, which is the sort of thing computers do all the time of course.

asmith



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory