Better than Optimal by Taking a Limit?

Autor/in	Betounes, David
Titel	Better than Optimal by Taking a Limit?
Quelle	In: College Mathematics Journal, 43 (2012) 5, S.379-386 (8 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0746-8342
DOI	10.4169/college.math.j.43.5.379
Schlagwörter	Structural Elements (Construction); Problem Solving; Calculus; Geometry; Geometric Concepts; College Mathematics; Mathematics Instruction; Mathematics Activities + Suchen Sie Ihr Suchwort? Problemlösen; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Geometrie; Elementare Geometrie; Mathematics lessons; Mathematikunterricht
Abstract	Designing an optimal Norman window is a standard calculus exercise. How much more difficult (or interesting) is its generalization to deploying multiple semicircles along the head (or along head and sill, or head and jambs)? What if we use shapes beside semi-circles? As the number of copies of the shape increases and the optimal Norman windows approach a rectangular shape, what proportions arise? How does the perimeter of the limiting rectangle compare to the limit of the perimeters? These questions provide challenging optimization problems for students and the graphical depiction of the geometry of these window sequences illustrates more vividly than sequences of numbers, the concept of limit. (As Provided).
Anmerkungen	Mathematical Association of America. 1529 Eighteenth Street NW, Washington, DC 20036. Tel: 800-741-9415; Tel: 202-387-5200; Fax: 202-387-1208; e-mail: maahq@maa.org; Web site: http://www.maa.org/pubs/cmj.html
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10