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NCTM0604

# NCTM0604 - School of Science Indiana University-Purdue...

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1 School of Science Indiana University-Purdue University Indianapolis Carl C. Cowen, Dean IU PU I School of Science President, Mathematical Association of America NCTM Annual Meeting, St. Louis April 27, 2006 The St. Louis Arch and Other Mathematically Interesting Shapes

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2 School of Science Indiana University-Purdue University Indianapolis Introduction The Catenary: physical description Making a model of the St. Louis Arch The Catenary: mathematical description Comparison between catenaries, parabolas, and hyperbolas Ruled Surfaces The Challenges facing us in Math Sources
3 School of Science Indiana University-Purdue University Indianapolis The Catenary: physical description A catenary is the curve formed by a flexible cable of uniformly distributed weight when hung from supports at two points. Galileo thought this curve would be a parabola, but Leibniz, Huygens, and the Bernoulli brothers showed otherwise. Jefferson is given credit for the English word ‘catenary’

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4 School of Science Indiana University-Purdue University Indianapolis Catenary through (-1,1); (0,0); (1,1)
5 School of Science Indiana University-Purdue University Indianapolis

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6 School of Science Indiana University-Purdue University Indianapolis Catenary through (-1,1); (0,0); (1,1) v p
7 School of Science Indiana University-Purdue University Indianapolis

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8 School of Science Indiana University-Purdue University Indianapolis
9 School of Science Indiana University-Purdue University Indianapolis The St. Louis Gateway Arch is an inverted catenary, 630 feet wide at the base and 630 feet tall: its equation is

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10 School of Science Indiana University-Purdue University Indianapolis Catenary through (-1,1); (0,0); (1,1)
11 School of Science Indiana University-Purdue University Indianapolis Catenary and parabola

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12 School of Science Indiana University-Purdue University Indianapolis Catenary, parabola, and hyperbola
13 School of Science Indiana University-Purdue University Indianapolis

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14 School of Science Indiana University-Purdue University Indianapolis
15 School of Science Indiana University-Purdue University Indianapolis

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16 School of Science Indiana University-Purdue University Indianapolis
17 School of Science Indiana University-Purdue University Indianapolis

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18 School of Science Indiana University-Purdue University Indianapolis
19 School of Science Indiana University-Purdue University Indianapolis Ruled surfaces A surface is called a ‘ruled surface’ if through each point of the surface, there is a line lying entirely in the surface.

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