Ideas for Modules
Many ideas have been proposed for Math Exploration Quilt modules.
Here is the current list:
- Magnetic Pendulum -- numerical simulation (described in the
Math Exploration Quilt overview page.
-- a river-crossing problem explored step-by-step
by several modules that span a very wide range of mathematics.
Starts with time=distance/rate and progresses through
the Pythagorean Theorem,
graphing, numerical optimization, curve-fitting,
- Population growth -- exponential increase, effects of resource
limits & competing populations,
cyclic behavior, phase plane graphs, chaos.
- Integers -- GCD, LCM, graphs of cyclic (and noncyclic!) behavior,
explore computational cost vs solution method, optimization by
continuous approximation, and how all this relates to the
- Graphing -- linear and logarithmic axes; "accurate" and misleading
- Polynomials -- graphs vs coefficients.
- Complex numbers -- graphical interpretation.
- Trigonometry -- basic trig functions (for right triangles)
- Curve fitting -- via polynomials, exponentials, rational functions;
effects of noise on fit.
- Calculus -- finite differences to derivatives; sums to integrals.
- Probability & random numbers -- dice games, card games, election
polls, Monte Carlo simulation.
- Iterative numerical solution of nonlinear equations.
- Optimization: numerical vs analytic.
- Money exchange & budgeting -- take a trip, but don't spend too
- titration -- change of pH vs amount of reagent added
- mixtures -- change of boiling/freezing temperature as function
of concentration. Change of concentration over time as a
result of freezing (also models heat transfer and phase change).
- Simple mechanics -- bouncing ball, damped pendulum (1D).
- DC circuits -- network voltage/current for simple resistor (linear)
and semiconductor (nonlinear) circuits.
- AC circuits -- network voltage/current over time for simple
RLC and semiconductor circuits.
- Economic models -- profit versus advertising budget, ...
To date, reasonably robust Excel workbooks have been generated only
for the first two ideas. Those workbooks can be accessed through
the hyperlinks in the above list.
However, several other Excel workbooks have been done as
quick-and-dirty prototypes designed to check out ideas. They
- 3-D Surface graphics
with a simple GUI
(Graphical User Interface) to control viewing angle.
- Solves an integer problem using brute
force. The problem is
"How many sheep, pigs, and chickens can you buy, given that
sheep, pigs, and chickens cost so much each, and you have
to spend exactly so many dollars?" This workbook
is interesting because it lets you easily explore what happens
as you change the prices. (Caution: such exploration can easily
lead you to conclude that these "exactly equal" problems are
insanely unrelated to anything that matters.)
- A potpourri of spreadsheets (several in one
workbook) addressing compound interest, calculation of pi
via inscribed/circumscribed polygons, and calculation of pi
via solution of a trigonometric equation using a series
expansion and successive refinement.