id: 06113462
dt: j
an: 2013a.00618
au: Barkan, Stanley
ti: If not, then what if as well? Unexpected trigonometric insights.
so: Math. Enthus. 9, No. 1/2, 19-36 (2012).
py: 2012
pu: Information Age Publishing (IAP), Charlotte, NC; University of Montana,
Department of Mathematical Sciences, Missoula, MT
la: EN
cc: G60
ut: trigonometric identities; problem posing; Euclidean geometry
ci:
li:
ab: Summary: In performing an exercise of “what if not", one can end up with
a paucity of structure. Adding alternative structure can be a rich
source of discovery, as we present here. The framework of this
presentation is the original voyage of discovery, from a trivial
geometric problem to the derivation of some unexpected trigonometric
formulae based on regular polygons. The original “voyage" has been
changed only sufficiently to make the text readable.
rv: