slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
School of Science Indiana University-Purdue University Indianapolis PowerPoint Presentation
Download Presentation
School of Science Indiana University-Purdue University Indianapolis

Loading in 2 Seconds...

play fullscreen
1 / 37

School of Science Indiana University-Purdue University Indianapolis - PowerPoint PPT Presentation


  • 164 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'School of Science Indiana University-Purdue University Indianapolis' - brooklyn


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

School of Science

Indiana University-Purdue University Indianapolis

The St. Louis Arch and Other Mathematically Interesting Shapes

Carl C. Cowen, Dean

IUPUI School of Science

President, Mathematical Association of America

NCTM Annual Meeting, St. Louis

April 27, 2006

1

slide2

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

2

slide3

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 aparabola, but Leibniz, Huygens, and the

Bernoulli brothers showed otherwise.

Jefferson is given credit for the English word ‘catenary’

3

slide4

School of Science

Indiana University-Purdue University Indianapolis

Catenary through (-1,1); (0,0); (1,1)

4

slide5

School of Science

Indiana University-Purdue University Indianapolis

5

slide6

School of Science

Indiana University-Purdue University Indianapolis

p

v

Catenary through (-1,1); (0,0); (1,1)

6

slide7

School of Science

Indiana University-Purdue University Indianapolis

7

slide8

School of Science

Indiana University-Purdue University Indianapolis

8

slide9

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

9

slide10

School of Science

Indiana University-Purdue University Indianapolis

Catenary through (-1,1); (0,0); (1,1)

10

slide11

School of Science

Indiana University-Purdue University Indianapolis

Catenary and parabola

11

slide12

School of Science

Indiana University-Purdue University Indianapolis

Catenary, parabola, and hyperbola

12

slide13

School of Science

Indiana University-Purdue University Indianapolis

13

slide14

School of Science

Indiana University-Purdue University Indianapolis

14

slide15

School of Science

Indiana University-Purdue University Indianapolis

15

slide16

School of Science

Indiana University-Purdue University Indianapolis

16

slide17

School of Science

Indiana University-Purdue University Indianapolis

17

slide18

School of Science

Indiana University-Purdue University Indianapolis

18

slide19

School of Science

Indiana University-Purdue University Indianapolis

• Ruled surfaces

A surface is called a ‘ruled surface’ if through each point of the surface, thereis a line lying entirely in the surface.

Clearly a plane is a ruled surface.

But also, so is a cylinder!

And more!!

19

slide20

School of Science

Indiana University-Purdue University Indianapolis

Hyperboloid of one sheet

20

slide21

School of Science

Indiana University-Purdue University Indianapolis

St Louis Science Center: Hyperboloid, one sheet

21

slide22

School of Science

Indiana University-Purdue University Indianapolis

park, Ann Arbor: part of Hyperboloid, one sheet

22

slide23

School of Science

Indiana University-Purdue University Indianapolis

  • Not educating enough people in science, technology, engineering and math
  • Need to diversify our math and science workforce
  • Middle school and high school are the critical times
  • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html

23

slide24

School of Science

Indiana University-Purdue University Indianapolis

  • Not educating enough people in science, technology, engineering and math
  • Need to diversify our math and science workforce
  • Middle school and high school are the critical times
  • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html

24

slide25

School of Science

Indiana University-Purdue University Indianapolis

  • Not educating enough people in science, technology, engineering and math
  • Need to diversify our math and science workforce
  • Middle school and high school are the critical times
  • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html

25

slide26

School of Science

Indiana University-Purdue University Indianapolis

  • Not educating enough people in science, technology, engineering and math
  • Need to diversify our math and science workforce
  • Middle school and high school are the critical times
  • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html

26

slide27

School of Science

Indiana University-Purdue University Indianapolis

  • Explosion in biological research and progress
  • The mathematical sciences will be a part
  • Opportunity: few mathematical scientists are biologically educated few biological scientists are mathematically educated

Dr. Rita Colwell: “We're not near the fulfillment of biotechnology's promise. We're just on the cusp of it…”

27

slide28

School of Science

Indiana University-Purdue University Indianapolis

  • Explosion in biological research and progress
  • The mathematical sciences will be a part
  • Opportunity: few mathematical scientists are biologically educated few biological scientists are mathematically educated

Report Bio2010: “How biologists design, perform, and analyze experiments is changing swiftly. Biological concepts and models are becoming more quantitative…”

28

slide29

School of Science

Indiana University-Purdue University Indianapolis

  • Explosion in biological research and progress
  • The mathematical sciences will be a part
  • Opportunity: few mathematical scientists are biologically educated few biological scientists are mathematically educated

NSF/NIH: “Emerging areas transcend traditional academic boundaries and require interdisciplinary approaches that integrate biology, mathematics, and computer science.”

29

slide30

School of Science

Indiana University-Purdue University Indianapolis

Main Points

• Sophisticated math is everywhere around us

• New mathematics is being created every day and it is being used to improve our lives

• We must use our influence to help counselors, parents, and students understand the amazing variety of careers that can be built on an education in math and science

• We must dramatically increase participation of women and other underrepresented groups in college and post-graduate math and science

30

slide31

School of Science

Indiana University-Purdue University Indianapolis

Sources

• Mathematical Association of America

• American Mathematical Society

• Association for Women in Mathematics

• National Association of Mathematicians

• SACNAS – Society for the Advancement of Chicanos and Native Americans in Science

31

slide32

School of Science

Indiana University-Purdue University Indianapolis

Convergence

On-line Magazine that uses history to teach mathematics

32

slide33

School of Science

Indiana University-Purdue University Indianapolis

Mathematical Moments: explanations of math used in the modern world

33

slide34

School of Science

Indiana University-Purdue University Indianapolis

MAA Online - Columns:

34

slide35

School of Science

Indiana University-Purdue University Indianapolis

URL’s for the Sources

www.science.iupui.edu/ccowenwww.maa.org convergence.mathdl.org/ www.maa.org/news/columns.htmlwww.ams.org www.ams.org/ams/mathmoments.htmlwww.awm-math.org/www.math.buffalo.edu/mad/NAM/www.sacnas.orgen.wikipedia.org

35

slide36

School of Science

Indiana University-Purdue University Indianapolis

Model of the St Louis Arch3 feet bead/ball chainFast curing epoxy (comes in a pair of tubes)plastic cup to mix epoxy in spoon to mix epoxy withstand to hold “arch”thread to tie chain to standtie string to ends of chain to tie chain to standmix epoxy thoroughly, add chain to coat chain with glue, trying to keep string out of gluehang chain on stand with string, let cureturn upside down

36

slide37

School of Science

Indiana University-Purdue University Indianapolis

Cylinder/Hyperboloid ruled surface device2 disks of cardboard, about 6 inches diameter1 foot long dowel 3/8” diameter or a long TinkerToy rod35 feet of yarn or string, cut into pieces about 1 foot long punch holes at center of cardboard disks to accommodate the dowel/rod snuglyslit disks about 3/8” in, along radius at 32 equally spaced points on rimsinsert rod into center holes and position disks near ends of rod insert lengths of yarn into slits so that each end of each yarn piece is held in one slit on top disk, one on bottompulling disks apart to slightly stretch yarn, with yarn pieces perpendicular to ends, get a cylinderbut by twisting end disks relative to each other so yarn pieces are not perpendicular, create a hyperboloid of one sheet.

37