### Volume 2, Number 51

 ``` 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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 \|/ 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. \|/ 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. \|/ "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 \|/ 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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. \|/ 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problem of the Week http://mathforum.org/geopow/ Internet Resources http://mathforum.org/~steve/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ ```