Sum of Interior Angles of Polygons: A general Formula, and other updates

[Michael de Villiers]

Just to announce for those interested that my homepage at http://mysite.mweb.co.za/residents/profmd/homepage4.html has been updated with the following new items:
1) PME (1989) paper "A comparative study of two Van Hiele testing instruments"
2) Feb 2011, Math e-Newsletter with info regarding new books, websites, conferences, etc.
3) mathematical/mathematics education quote
4) mathematics/science cartoon

My dynamic geometry sketches Link at http://math.kennesaw.edu/~mdevilli/JavaGSPLinks.htm has been updated with the following (new & revised) sketches:
1) De Villiers points & Hyperbola of a triangle (updated)
2) A generalization of Neuberg & Simson line (updated)
3) Interior Angle Sum of Polygons: A general formula (new)
4) Some unproved conjectures (updated)

and the Student Explorations section with:
1) Cyclic quadrilateral rectangle result (new)
2) Interior Angle Sum of Polygons: A general formula (new) with introductory Logo (Turtle Geometry) activity
3) Quadrilateral Inequality involving Perimeter & Diagonals (updated)
4) Added links to 'Mathematical Digest' and 'School Maths'

[Michael de Villiers]

Perhaps it's necessary to point out that this general formula for the sum of interior angles of a polygon is derived from the exterior angles result, namely the Turtle Closed Path theorem.

Students understanding and acceptance of the Turtle Closed Path theorem as an axiom can easily be developed from carefully designed LOGO (turtle geometry) activities. The turtle movement can also be simulated, of course, by animation with other dynamic geometry software.