World of Education/World of Education.iso/world_f/feedback.zip/CATALOG.DOC

Text File | 1991-01-13 | 10KB | 156 lines

                               PEANUT Software


Over the years, these programs have evolved to the point where they are fairly
reliable.   However, there still might be difficulties.  If you can describe
what you did to make a program crash, or if you think of other improvements,
please let me know.  I am especially eager to hear of productive classroom
applications for any of the following programs:


GEOM allows the user to carry out high-precision geometric constructions in
the Euclidean plane.  Any construction that has been properly saved can be
carried out again and again on other similarly labelled figures by simply
recalling the name of the procedure.  (131000)

GUESS graphs randomly chosen functions and then challenges the user to name
that function.  By setting switches, one can specify the types of graphs that
will appear (polynomial, rational, sines, cosines, tangents, absolute values).
The parameters that need to be figured out are always small whole numbers.
Radian measure is used for angles.  This activity is successful with students.
The subprogram BLOBS is loosely modelled on Green Globs.  I have never used it
with students, but it seems to have some possibilities.  Finding an equation
for the line through two given points (working against the clock) is a fairly
worthwhile classroom exercise.  (117000)

CONICS graphs conic sections, which are presented to the computer as second-
degree equations, or through focus-focus or focus-directrix data.  (98000)

PLOT is a utility program that is built from three main subprograms:  PLOT2D
is a general-purpose grapher for curves in the xy-plane.  It works for all
graphs that are presentable in one of the explicit forms y=f(x), r=f(theta),
or parametrically x=f(t), y=g(t).  Special features allow one to see x=y
reflections, derivatives, sums of power series, composites, and the graphs of
curves that are given in implicit form F(x,y)=0.  PLOT3D is a general-purpose
grapher that will handle surfaces in xyz-space, once they are presented in
Cartesian form z=f(x,y), in polar form z=f(r,theta), or in parametric form
x=F(r,t), y=G(r,t), z=H(r,t).  Drawings are done in perspective.   Numerical
integration is available in 2- and 3-dimensional programs.  EULER provides
graphical and numerical solutions to ordinary differential equations.  First-
order equations of dimension two and three can be analyzed. Phase-plane
analysis of second-order equations is also possible.  (193000)

POLYHE allows the user to build drawings of three-dimensional polyhedra, in
perspective.   Among other things, this program will produce nice diagrams of
prisms and pyramids (with hidden lines either invisible or dotted).  Polyhedra
can be rotated and sliced into pieces.  (124600)

ARCADE is a collection of mathematical games:  KRYPTO is a mental arithmetic
game, which invariably enlivens an elementary class.  NIM and CHOMP are both
take-away games.  BOXES is a familiar paper-and-pencil game.  MEMORY is a
computerized version of the matching game in which the players try to remember
the positions of face-down cards.  It never forgets to shuffle!  LANDER is an
educational game program - a good workout in simple antidifferentiation.  This
problem works well with a class that has mastered all those routine free-fall
exercises and is ready for an application.   HEX plays the paper-and-pencil
game of the same name.  This is an interesting mathematical game.  Although
the computer has not been taught any masterful strategies, it will beat you if
you do not pay attention!  The program can also be used to simply print out
sheets of hex paper.  MAZES provides a realistic simulation of the problem of
escaping from a maze.  RUBIK is a simulation of the classic 3x3x3 cube puzzle.
(If your machine does not have high-resolution color graphics, then the cube
faces are distinguished by patterns rather than colors.)  No substitute for
the real thing!  (161000)

HP simulates a hand-held calculator, of the Hewlett-Packard variety.  That is
to say, first you enter the numbers, then you tell the calculator what to do
with them.  Why bother, you ask?  Well, this calculator has the capacity to
handle up to 250 significant digits, though it only operates in integer mode.
This makes it easy to find the GCD of 56491686164 and 69670785864 (which is
59372, by the way) - just key in the numbers and ask for the GCD.  Or, you can
painlessly find that C(20,8) is 125970.  It is also possible to discover that
sqrt(5) is 2.23606797749978969...    Class time can be productively spent in
trying to figure out ways to get non-integral answers with this calculator.
There is a notable subprogram: SUPERPOWERS allows one to display very large
powers of any base less than 214.  Printed output is available.  (69000)

MATPAC is a package of matrix procedures.  In rational mode, all operations
involve integers, so that calculations are carried out with perfect accuracy;
in decimal mode, about twenty significant digits are carried.  A few standard
geometric transformations (projections, rotations, and reflections) are built
in.  Matrices can of course be named and stored.  (131000)

LAB1 is a collection of subprograms:  BALL-in-the-CUP displays random
parabolic trajectories, then challenges the user to catch the projectile in
mid-flight.  One has to fit a quadratic equation to the given data to do this.
One can select either calculus or non-calculus mode.  In the former, angular
information plays an essential part.  MANY-BODY simulates the dynamics of a
system of bodies whose motion is governed by an inverse-square gravitational
law.  SUMS and PRODUCTS just calculates running partial sums (or products) of
given sequences.  You can step along one term (factor) at a time, or else let
it fly.  There is no graphing - just number crunching.  INDEF graphs a given
function f, then graphs a specified indefinite integral of f, shading in the
original graph as it goes.  For classroom purposes, one can pause during the
graphic integration process.  OSCILLATIONS simulates the oscillations of a
stretched string or of a hanging chain.  PARAMETRIC DEMO shows how a pair of
parametric equations team up to produce a dynamic plane curve.  (142000)

LAB2 is a collection of subprograms:  MAP2D produces various graphs relating
to two-dimensional transformations.  It operates in either real or complex
mode, and is useful when discussing changes of variable and Jacobians.  ROOTS
finds solutions to arbitrary equations of the form f(z)=0, where f is any
elementary function of a single variable.  The root search takes place in the
complex plane, so one must type z as the independent variable.  (131500)

LAB3 is a collection of geometric graphing subprograms:  There is a piece of
mathematical lab equipment that shows how the area of a QUADRILATERAL depends
on the lengths of the sides and on the angle made by two adjacent sides.  One
can flex the quadrilateral and thereby empirically explore a max-min problem.
One can draw a variety of STAR POLYGONS and other string art figures, which
could conceivably stir up some interest in questions of either a geometric or
combinatorial nature.  RAINBOW displays the internal reflection of a light ray
after it has been refracted by a spherical raindrop.  The data produced helps
to explain how rainbows are actually formed.  This program is useful in the
analysis of a very nice max-min problem, if only to draw some diagrams that
are difficult to do by hand.  One can simulate the bouncing of a ball on
BILLIARDS tables that are either ELLIPTICAL or POLYGONAL.  Finally, one can
draw an unlimited variety of CYCLOIDS.  (142000)

PROBA is a package of probability distributions, which give the user easy
access to standard tabular information and graphical displays of the same.
This is a fairly new program, but it has had some classroom use.  Students
find the graphic displays helpful.  (90500)

FEEDBACK is a program that allows the user to explore the strange types of
behavior that occur when a function is iterated.  For real functions of one
real variable, periodicity and chaos are represented both graphically (through
web diagrams) and sonically.  Orbits may be tabulated and examined.   There
are also three large subprograms:  MANDEL draws both the Mandelbrot set and
its associated Julia sets; zoom in on the fascinating world of quadratic
mappings in the complex plane; there are many procedures available to try.
FRACTAL draws more Julia sets; it operates in both real (two-dimensional) mode
as well as complex mode.  It draws ferns, snowflakes, etc.  POTPOURRI draws a
few special fractal curves (snowflakes, Peano curves, etc), as well as some
fractal aggregations that suggest crystals and vegetation.  (191000)

SKETCHER is a toy - just a computerized version of Etch-a-Sketch.  It does
allow the user to draw oblique straight lines and circular arcs.  (71000)

LIFE allows the user to watch the evolution of cellular automata, with rules
as formulated by J. H. Conway, or as formulated by the user.  (60000)


This software is free, and in a state of perpetual revision; current versions
are available at any time.  Approximate program sizes are noted above.  Allow
an additional 36K for graphics drivers on each disk, and an additional 15K for
documentation.  I can fill disks using any of the formats 360K, 1.2M, or 720K;
it is helpful if you format the disks to your liking.   My single request is
that you send a prepared mailer with your disks.  I am happy to write the
programs and copy them for you, but I do not have the resources or time to buy
stamps and wrap packages.


Richard Parris
Phillips Exeter Academy
Exeter NH      03833