Math Forum Internet News

Volume 2, Number 51

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22 December 1997                                  Vol. 2, No. 51

                 THE MATH FORUM INTERNET NEWS

SimCalc | Non-Euclidean Geometry | Kwanzaa Math / Star of David
 

          SIMULATIONS FOR CALCULUS LEARNING - SIMCALC

            http://www.simcalc.umassd.edu/simcalc/

A knowledge of the mathematics of change is vitally
important to living and working in a rapidly evolving
democratic society. Problems involving rates, accumulation,
approximations, and limits appear in everyday situations
involving money, motion, planning, nutrition - virtually
any situation where varying quantities appear.

SimCalc aims to democratize access to the mathematics of
change for all students, providing software that combines
advanced simulation technology with innovative curricular
solutions. The project begins in the early grades with 
powerful ideas that extend beyond both classical calculus 
and traditional calculus reform

SimCalc MathWorlds v1.1b4 for the Macintosh was released
in November, 1997 and is available for download. You can
also obtain a current version from the Math Forum's FTP
archive:

   ftp://mathforum.org/software/mac/mathwords.hqx


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          NON-EUCLIDEAN GEOMETRY: SELECTED RESOURCES 
        
        
                  NONEUCLID - JOEL CASTELLANOS
                  
  http://riceinfo.rice.edu/projects/NonEuclid/NonEuclid.html
 
A software simulation that offers straightedge and compass 
constructions in hyperbolic geometry for use in high school 
and undergraduate education. This site offers an introduction,
over 25 pages of illustrated hypertext, exercises, and a 
discussion of why it's important for students to study 
hyperbolic geometry. Basic concepts include:

  - Non-Euclidean Geometry
  - The Shape of Space
  - The Pseudosphere
  - Parallel Lines
  - Postulates and Proofs
  - Area
  - X-Y Coordinate System
                    
NonEuclid software for Windows may be downloaded from the site.


Mac users might enjoy KALEIDOTILE, a tiling program based on 
the Geometry Center's display at the St. Paul Science Museum. 
You can use KaleidoTile to create and manipulate tessellations 
of the sphere, Euclidean plane, and hyperbolic plane. 

  http://www.geom.umn.edu/software/download/KaleidoTile.html

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THE GEOMETER'S SKETCHPAD GALLERY - BILL FINZER & NICK JACKIW

http://mathforum.org/sketchpad/gsp.gallery/poincare/poincare.html

A base sketch and downloadable scripts for interactive 
investigation of hyperbolic geometry using the Poincaré disk 
model. For example, one can easily discover that the 
construction of the incircle of a triangle that works in
the Euclidean plane also works in the hyperbolic plane.  

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HYPERBOLIC GEOMETRY (GEOMETRY AND THE IMAGINATION)

http://www.geom.umn.edu/docs/doyle/mpls/handouts/node37.html

An exercise that helps students see that since angular excess 
corresponds to negative curvature, the hyperbolic plane is 
a negatively curved space. 

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"Non-Euclidean Geometry," an essay covering the history of
this subject from Euclid's Elements through Riemann's 
spherical geometry, can be found via the MACTUTOR HISTORY 
TOPICS INDEX: 

http://www-groups.dcs.st-and.ac.uk/~history/HistoryTopics.html

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Last but not least, see David Eppstein's GEOMETRY JUNKYARD for 
more links to sites about hyperbolic geometry on the Web: 

http://www.ics.uci.edu/~eppstein/junkyard/hyper.html


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  KWANZAA MATH: THE MKEKA - DEBORAH LEWIS & CATHERINE WESTER

  http://www.whyy.org/smc/allen/ZwanWeb/Kwanzaa.math.426.html

Students apply their knowledge of math to create a mkeka,
the traditional woven mat that is one of the seven symbols
of Kwanzaa. They may then count all the rectangles and find
squares in the mkeka.

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                  STAR OF DAVID - JUDY BROWN
                  
http://dimacs.rutgers.edu/~judyann/LP/lessons/star.david.html

Students find the total number of triangles in the Star of
David pictured at the top of the page, and then count the
quadrilaterals and hexagons in the star.

Other Star of David activities might be created using:

MUTSUMI SUZUKI'S MAGIC STARS
  http://mathforum.org/alejandre/magic.star/

NORMAN SHAPIRO'S GEOMETRY THROUGH ART 
  
Coffee can geometry
  http://mathforum.org/~sarah/shapiro/shapiro.coffeecan.html
Find the angles
  http://mathforum.org/~sarah/shapiro/sum.angles.html
Find the hidden shapes
  http://mathforum.org/~sarah/shapiro/shapiro.find.shapes.html


Continuing Judy Brown's 12 Days of Christmas activity, see
"The Twelve Days of Christmas and Pascal's Triangle":

http://dimacs.rutgers.edu/~judyann/LP/lessons/12.days.pascal.html


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