Maple Application Centre: New Applications

Procedures and a Maplet™ for Analysing Linear Programming Problems.
Submitted by P.H. Stikker

This maplet application is an educational tool used to help students explore concepts of linear programming, including feasible regions, feasible solutions, corner points, objective functions, objective values, and optimal solutions of the dual of a linear program.

In the maplet window, students may move the objective function within the graph as well as set the objective value experimentally, which allows the student to understand the meaning of an optimal solution geometrically. Students can change colours and save settings and values within the maplet for future use. You can download this maplet at http://www.adeptscience.com/go?pg=O68.

Maplet™ For 3 Distributions
Submitted by P.H. Stikker

Another educational tool created by Stikker, this maplet allows the user to explore the world of statistical distributions. Stikker’s maplet teaches three classic distributions: Normal, Binomial and Poisson. The user may decide which distribution he or she wishes to use or ask the maplet for help in deciding which distribution would best suit their needs. Stikker also provides probability tables and a standard deviation calculator to make learning statistics easier. You can view this maplet at http://www.adeptscience.com/go?pg=O72.

Reconstruction of 2-D Images
Submitted by Bruno Guerrieri

With the help of the listdensityplot command in Maple, Guerrieri implemented an algorithm to reconstruct 2D images. This application was inspired by the article, “How to resurrect a cat from its grin” that appeared in Mathematical Recreations. Given a rectangle divided into a grid, we can reconstruct the contents of the grid (meaning the colour associated to each block) by placing ray emitters on the southern and eastern borders of the rectangle and sensors on the northern and western borders. The values that are read in at the sensors represent the amount of absorption undergone by each ray. This data can be used to reconstruct the layout of the rectangle. To learn more about image reconstruction in Maple, visit http://www.adeptscience.com/go?pg=O73.

Stochastic Model of Filling a Box with Spheres
Submitted by Lee R. Partin

Partin uses Maple to fill a box of given dimensions with spheres of a given radius. He uses a stochastic model to program a procedure that randomly fills a box with balls. The goal is to determine whether the arrangement of spheres can fit into the box. The process begins by placing a first layer of balls and then determining whether it is possible to place a second layer on the first layer, and so forth. To view this worksheet and gain a better understanding of the process involved, visit maplet at http://www.adeptscience.com/go?pg=O74.

Circular Membrane Oscillation Using Maple
Adapted from the worksheet of D. Frenkel, L. Golebiowski and R. Portugal CBPF and PUC-Rio/1996

This worksheet explores in depth the classic problem of a vibrating circular membrane. Frenkel, Golebiowski and Portugal were able to use the wave equation to animate the motion of a vibrating circular membrane over time. This worksheet is full of exciting and interesting animations that help visualise the phenomenon perfectly. You can view this worksheet and learn more about circular membrane oscillation at http://www.adeptscience.com/go?pg=O75.

Article: Maple Application Centre: New Applications