2012 Fall MAA Meeting (MD DC VA Section) ppt
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Roanoke Valley Reef Project MAA MD-DC-VA Section Meeting VMI - October 2012
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This is the powerpoint presentation that Caren Diefenderfer and Jan Minton gave at the Fall 2012 Meeting of the MD/DC/VA Section Meeting of the MAA
Transcript of 2012 Fall MAA Meeting (MD DC VA Section) ppt
Roanoke Valley Reef Project
MAA MD-DC-VA Section MeetingVMI - October 2012
Jan Minton Caren DiefenderferRoanoke College Hollins University
From
To
The Institute For Figuring Hyperbolic Crochet Coral Reef, with urchins by Christine Wertheim and sea slug by Marianne Midelburg.Photo © The Institute For Figuring (by Alyssa Gorelick)
with Mathematics
along the way
Smithsonian Museum of Natural History
Euclidean Elliptical Hyperbolic
Types of Geometry
Plane Geometry (standard high school geometry)
Spherical Geometry is a special case of Elliptical Geometry. Geometry on a sphere.
This is the question of the evening.
“For God’s sake, please give it up. Fear it no less than the sensual passions, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.”
- Wolfgang Bolyai (1775-1856) to his son, Janos Bolyai, regarding the study of hyperbolic geometry.
A point and its immediate neighboood
Disk (Flat) Cap Saddle
Like a Pringle Potato Chip!
Euclidean Spherical Hyperbolic
Euclidean Spherical Hyperbolic
Euclidean plane is flat
Spherical plane is shaped like a ball.
Hyperbolic plane??An infinite Pringle?
What about lines?
Euclidean Spherical Hyperbolic
Straight lines
Circles (great circles)
Curves (arcs or circles)
What about parallel lines?
Euclidean – under control
Spherical – Every pair of great circles intersect and so there are no parallel lines in spherical geometry.
What about parallel lines?
Hyperbolic A Strange New World
The Sum of Angles in a Triangle
Euclidean Spherical Hyperbolic
Exactly 180 degrees
More than 180 degrees
Less than 180 degrees
Two Models of Hyperbolic Geometry
The Poincaré Disk Lines
The Open Half Plane Two Types of Lines
Poincaré Disk Open Half Plane
Triangles
Poincaré Disk Open Half Plane
Violating the Parallel Postulate
Hyperbolic Distance in the Poincaré Disk
Definition: Given points P and Q in the Poincare Disk, the hyperbolic distance from P to Q is defined as
|ln((PM/PN)/(QM/QN)| = |ln([(PM)(QN)]/[(PN)(QM)])where M and N are the points on the boundary of the disk on the line that goes through P and Q.
Hyperbolic Distance in the Open Half Plane
Definition: Given points P and Q in the Open Half plane, the hyperbolic distance from P to Q when P=(x1,y1) and Q=(x2,y2) is
arcosh(1+((x2-x1)^2 (y2-y1)^2)/(2y1y2)).
How about some Hands On models?
{3,7} Polyhedral Model
Hyperbolic Soccer Ball
Paper Annuli
DainaTaiminaCrocheting Adventures with Hyperbolic Planes
Bookseller/Diagram Prize for Oddest Title of the Year for 2009
2012 Euler Book Prize
Crocheting Adventures with Hyperbolic Planes is a novel approach to geometry that has brought a whole new audience to mathematics. In this respect it has greater outreach potential than any book we have previously considered. It is truly a book where art, craft, science, and mathematics come together in perfect harmony.
To Figure:To form or shape, to trace, to reckon or calculate, to represent in a diagram or picture, to ornament or adorn with a design or pattern.
The mission of the Institute For Figuring is to contribute to the public understanding of scientific and mathematical themes through innovative programming that includes exhibitions, lectures, workshops, and participatory, community based projects.
Margaret Wertheim
TED talk: The Beautiful Math of Coral
US Satellite Reef Projects in
Arizona MaineCalifornia New YorkFlorida North CarolinaIllinois UtahIndiana VirginiaDist. of Columbia
And Around the World
AustraliaEngland
GermanyIrelandJapanLatvia
I made a mistake. What should I do?
It doesn’t
matter …
keep
going!
Roanoke Valley ReefRoanoke College
Olin Gallery January 25 – March 1, 2013
Opening LecturePaul Snelgrove, Biological Oceanographer
Memorial University of Newfoundland
Echo Sounding Hollins University
Eleanor D Wilson MuseumJanuary 10 – March 2, 2013
Institute for Figuring Hyperbolic Crochet Coral Reef
www.crochetcoralreef.orgRoanoke College Project
www.roanoke.edu/coralreefEmail
Roanoke Valley Reef on facebook!
