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Graphing Graphing Tools and DynamicGeometry Software
Tools and Dynamic GeometrySoftware
bDiscussants
Lilaine E. Canobis,Jodeth Demonteverde,Jonna Lyn Gegantoni,Charlyn Estimera,
Aji Garacho, Aldren Padernilla
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Introduction
Most data is meaningless to most
people unless it is visualized. Stepping
beyond familiar visualizations like bar charts
and pie charts, there are many approaches
to visualizing data, from mapping (e.g.,
color coding a map to show voting patterns)
to visualizing networks (e.g., the linksbetween people).
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WINPLOT
Winplot is a general-purposeplotting utility, which can draw (andanimate) curves and surfaces presented in a variety of formats.
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Winplot can generate both 2D and 3D
plots of functions and sequences. Itcan also "animate" these plots usingup to 23 variables and theircorresponding sliders. At the presentonly one slider may be animated at atime. It also has a variety of exportoptions including EPS, SVG, PiCTeX,
and Metafile, as well as simplecopying to the Windows clipboard.
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Winplot is a graphing program written byRichard Parris, a teacher at Phillips ExeterAcademy in Exeter, New Hampshire. Mr.
Parris generously allows free use anddistribution of the software, and providesfrequent updates. Although the program isfree, it is of top quality and easy to use.
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These instructions expand onthose found in the program's help
menus; they discuss sometechniques of two-dimensionalplotting, useful in an algebra orcalculus class. It is assumed thatthe reader has already installedthe program in Microsoft Windows,and is familiar with the basic
workings of that operating system.(These instructions apply to theAugust 22, 2008, version ofWinplot.)
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A notable strength of Winplot is itsability to plot graphs that are typically
not available on other (especially free)plotting software, such as implicitfunctions, slope fields, and intrinsiccurves (curvature defined by arclength).In addition, several standard calculusoperations can be performed on thefunctions, including generating graphs
of cross-sectional solids and solids ofrevolution, tracing trajectories on slopefields given an initial point, andcalculating line and surface integrals.
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GEOMETERS SKETCHPAD
The Geometer's Sketchpadis a popularcommercialinteractive geometrysoftwareprogram for exploringEuclideangeometry,algebra,calculus, and other areasofmathematics. It was created by Nicholas
Jackiw. It is designed to run onWindows95orWindows NT 4.0or later andMac OS8.6or later (includingMac OS X). It also runsonLinuxunderWinewith a few bugs.
Sketchpad 4 working with triangle trisectors.
http://en.wikipedia.org/wiki/List_of_interactive_geometry_softwarehttp://en.wikipedia.org/wiki/List_of_interactive_geometry_softwarehttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Windows_95http://en.wikipedia.org/wiki/Windows_95http://en.wikipedia.org/wiki/Windows_NT_4.0http://en.wikipedia.org/wiki/Mac_OS_8http://en.wikipedia.org/wiki/Mac_OS_8http://en.wikipedia.org/wiki/Mac_OS_Xhttp://en.wikipedia.org/wiki/Linuxhttp://en.wikipedia.org/wiki/Wine_(software)http://en.wikipedia.org/wiki/Wine_(software)http://en.wikipedia.org/wiki/Linuxhttp://en.wikipedia.org/wiki/Mac_OS_Xhttp://en.wikipedia.org/wiki/Mac_OS_8http://en.wikipedia.org/wiki/Mac_OS_8http://en.wikipedia.org/wiki/Windows_NT_4.0http://en.wikipedia.org/wiki/Windows_95http://en.wikipedia.org/wiki/Windows_95http://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/List_of_interactive_geometry_softwarehttp://en.wikipedia.org/wiki/List_of_interactive_geometry_software -
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Geometer's Sketchpad includes the traditional
Euclidean tools of classical geometric constructions;
that is, if a figure (such as the pentadecagon) can beconstructed with compass and straight-edge, it can
also be constructed using this program. However, the
program also allows users to employ transformations
to "cheat," creating figures impossible to constructunder the traditional compass-and-straight-edge
rules (such as the regular nonagon). Objects can also
be animated. The program also allows the
determination of the midpointand midsegments ofobjects.
http://en.wikipedia.org/wiki/Pentadecagonhttp://en.wikipedia.org/wiki/Nonagonhttp://en.wikipedia.org/wiki/Midpointhttp://en.wikipedia.org/wiki/Midpointhttp://en.wikipedia.org/wiki/Nonagonhttp://en.wikipedia.org/wiki/Pentadecagon -
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Grape
(Computers),orGRAphicsProgrammingEnvironment is asoftwaredevelopment environmentformathematical visualization, especiallydifferential geometry and continuum
mechanics.In 1994, it won the EuropeanAcademic Software Award.
The termgraphicalrefers to theapplications; the programming itself is mostly
based onC. GRAPE was developed by theUniversity of Bonn in Germany and is availablefor free for non-commercial purposes. It hasnot been developed actively since 1998.
http://en.wikipedia.org/wiki/Softwarehttp://en.wikipedia.org/wiki/Mathematical_visualizationhttp://en.wikipedia.org/wiki/C_(programming_language)http://en.wikipedia.org/wiki/C_(programming_language)http://en.wikipedia.org/wiki/Mathematical_visualizationhttp://en.wikipedia.org/wiki/Software -
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Cabri Geometry
Cabri Geometryis a commercialinteractivsoftwareproduced by the French companyteaching and learning geometry and trigon
was designed with ease-of-use in mind. Thallows the user to animate geometric figursignificant advantage over those drawn onblackboard.
http://en.wikipedia.org/wiki/Interactive_geometry_softwarehttp://en.wikipedia.org/wiki/Interactive_geometry_softwarehttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Interactive_geometry_softwarehttp://en.wikipedia.org/wiki/Interactive_geometry_software -
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Relationships between points on a
geometric object may easily bedemonstrated, which can be usefulin the learning process. There arealso graphing and display functionswhich allow exploration of theconnections between geometry andalgebra. The program can be run
underWindowsor theMac OS.
http://en.wikipedia.org/wiki/Microsoft_Windowshttp://en.wikipedia.org/wiki/Mac_OShttp://en.wikipedia.org/wiki/Mac_OShttp://en.wikipedia.org/wiki/Microsoft_Windows -
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GEOGEBRA
GeoGebrais aninteractivegeometry,algebra, statisticsandcalculusapplication, intended for learning andteaching mathematics and science from
primary school to university level.GeoGebra is available onmultipleplatformswith its desktop applicationsforWindows,Mac OSandLinux, with its
tablet apps forAndroid,iPadandWindows,and with itsweb applicationbasedonHTML5technology.
http://en.wikipedia.org/wiki/Interactive_geometry_softwarehttp://en.wikipedia.org/wiki/Interactive_geometry_softwarehttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Cross-platformhttp://en.wikipedia.org/wiki/Cross-platformhttp://en.wikipedia.org/wiki/Windowshttp://en.wikipedia.org/wiki/Mac_OShttp://en.wikipedia.org/wiki/Linuxhttp://en.wikipedia.org/wiki/Android_(operating_system)http://en.wikipedia.org/wiki/IPadhttp://en.wikipedia.org/wiki/Windows_Storehttp://en.wikipedia.org/wiki/Web_applicationhttp://en.wikipedia.org/wiki/HTML5http://en.wikipedia.org/wiki/HTML5http://en.wikipedia.org/wiki/Web_applicationhttp://en.wikipedia.org/wiki/Web_applicationhttp://en.wikipedia.org/wiki/Windows_Storehttp://en.wikipedia.org/wiki/IPadhttp://en.wikipedia.org/wiki/Android_(operating_system)http://en.wikipedia.org/wiki/Linuxhttp://en.wikipedia.org/wiki/Mac_OShttp://en.wikipedia.org/wiki/Windowshttp://en.wikipedia.org/wiki/Cross-platformhttp://en.wikipedia.org/wiki/Cross-platformhttp://en.wikipedia.org/wiki/Calculushttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Interactive_geometry_softwarehttp://en.wikipedia.org/wiki/Interactive_geometry_software -
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Its creator, Markus
Hohenwarter,started the project in2001 at the University of Salzburg,continuing it atFlorida Atlantic
University(2006
2008),Florida StateUniversity(20082009), and now at
theUniversity of Linztogether withthe help of open-source developers
and translators all over the world.
http://en.wikipedia.org/wiki/University_of_Salzburghttp://en.wikipedia.org/wiki/Florida_Atlantic_Universityhttp://en.wikipedia.org/wiki/Florida_Atlantic_Universityhttp://en.wikipedia.org/wiki/Florida_State_Universityhttp://en.wikipedia.org/wiki/Florida_State_Universityhttp://en.wikipedia.org/wiki/University_of_Linzhttp://en.wikipedia.org/wiki/University_of_Linzhttp://en.wikipedia.org/wiki/Florida_State_Universityhttp://en.wikipedia.org/wiki/Florida_State_Universityhttp://en.wikipedia.org/wiki/Florida_Atlantic_Universityhttp://en.wikipedia.org/wiki/Florida_Atlantic_Universityhttp://en.wikipedia.org/wiki/University_of_Salzburg -
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After a successful Kickstartercampaign, GeoGebra expandedtheir offerings to include aniPad,anAndroidand aWindows Store
appversion.
http://en.wikipedia.org/wiki/Kickstarterhttp://en.wikipedia.org/wiki/IPadhttp://en.wikipedia.org/wiki/Android_(operating_system)http://en.wikipedia.org/wiki/Windows_Storehttp://en.wikipedia.org/wiki/Windows_Storehttp://en.wikipedia.org/wiki/Windows_Storehttp://en.wikipedia.org/wiki/Windows_Storehttp://en.wikipedia.org/wiki/Android_(operating_system)http://en.wikipedia.org/wiki/IPadhttp://en.wikipedia.org/wiki/Kickstarter -
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Constructions can be made with points,vectors, segments, lines, polygons,conic sections, inequalities, implicitpolynomials and functions. All of them
can be changed dynamically afterwards.Elements can be entered and modifieddirectly via mouse and touch, orthrough the Input Bar.
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GeoGebra has the ability to use
variables for numbers, vectors andpoints, find derivatives andintegrals of functions and has afull complement of commands likeRoot or Extremum. Teachers andstudents can use GeoGebra tomake conjectures and to
understand how to provegeometric theorems.
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GeoGebra has the ability to use
variables for numbers, vectors andpoints, find derivatives andintegrals offunctions and has a fullcomplement of commands like Rootor Extremum. Teachers andstudents can use GeoGebra tomake conjectures and to
understand how to provegeometric theorems.