id: 05988802
dt: j
an: 2012a.00489
au: Walter, Marion; Crossfield, Don
ti: From chords of circles to triangular numbers to volumes of spheres.
so: Math. Teach. (Reston) 103, No. 8, 616-621 (2010).
py: 2010
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G40
ut: circles; intersecting chords theorem; area; dynamic interpretation; plane
geometry; product of segment of chords; three-dimensional analogs;
generalization; spheres; circular cross sections; perpendicular planes
ci:
li:
ab: From the introduction: This “Delving Deeper” article is a bit
different: It is inspired by a problem that Don Crossfield posed in
{\it The Oregon Mathematics Teacher} and from which interesting
mathematical discoveries emerged. To preserve a sense of the evolution
of the ideas, we have presented this discussion in epistolary form. For
example, the conversation that unfolds here takes place between two
imaginary characters, Hypatia and Ptolemy. Also, we have eliminated
casual talk and confusing references that occurred in the actual
conversations but have not cleaned up the mathematical questioning,
wondering, loose ends, and problem posing. Our goal is to share the
excitement and intrigue of collaborative mathematical exploration.
Although the result is a fictionalized account of our conversations, we
have made it as faithful a representation as possible of the way the
mathematical ideas developed.
rv: