This demo illustrates matrix-vector multiplication Ax, computed as linear combinations of the columns of A. Animation is done using a Java applet.
Search Results (75)
In most introductory linear algebra courses, prominent applications of transformations or mappings are moving (rotating, reflecting, translating), resizing (contracting, expanding), changing the shape (shearing, projecting) objects in the plane. A typical problem in such courses is to write the matrix of a transformation that changes points in such prescribed ways. The goal of this demo is to help students more easily visualize such transformations on a wide class of plane objects.
The purpose of this demo is to illustrate the use of the method of cross sections to find estimates of the volume of physical objects. The objects in this demo are not solids of revolution. The demo presented here utilizes Mathematica. Mathematica 5 notebooks are provided. The notebooks can be modified to approximate volumes of other objects for which a cross section approach is appropriate and a digital photograph is available.
This demo incorporates combines the visualization of approximating rectangles together with a graph of the approximate areas as a function of the number of rectangles. Thus, the limiting behavior of the approximating sums can be observed on the graph.
This demo estimates the area of a circle or triangle using a probability experiment employing the Monte Carlo technique. We also indicate how to use our approach to estimate the area of a polygonal region.
This demo illustrates two methods for computing the area of a triangle (and other regions) using the coordinates of the vertices. Both methods lead to interesting extensions which can provide topics for student investigation at a variety of academic levels.
This demo provides students with a concrete understanding of the average rate of change for physical situations and for functions described in tabular or graphic form. Animations in gif and Quicktime format are available, as well as Excel programs for classroom or student use.
This demo develops a procedure for randomly allocating bacteria to a fixed number of droplets from a total of 100 droplets using a probability experiment employing the Monte Carlo technique.
This demo provides a visual foundation and geometric intuition for best fit (least squares) models of data sets of ordered pairs using lines or parabolas. MATLAB routines are included.
THis demo provides an application of linear combinations to construct colors displayed on computer screens. This colorful demo provides a realistic example of linear combinations in action. BOth MATLAB and Java routines are included.
This demo demonstrates how to draw a circle using a carpenter's square, also known as a steel, framing, or rafter square.
This demo illustrates how a carpenter can draw an ellipse on wood or a sheet of wall board using simple tools. A "jig" can be used to demonstrate the technique and there are software animations to illustrate the use of the "jig".
This demo develops a function that measures the power of the signal of a cell phone as a user moves in a cellular network and then determine the position in the network when the signal is a maximum.
This demo illustrates a simple physical method for determining the centroid of an irregular region.
This demo develops a procedure for randomly allocating chocolate chips to cookies using a probability experiment employing the Monte Carlo technique.
This demo shows the development of the sine and cosine functions and their graphs by 'wrapping' around a circle. A MATLAB routine is included.
This demo illustrates the use of statistical simulation to find a rule which will lead to the prediction of probabilities.
This demo collection approaches probability through demos and experiments by using simulations via the Monte Carlo method. The collection includes interactive experiments for estimating the area of a circle, simulation of a network, allocation problems, creation of a rainbow, and choosing segments & drawing circles within a circle.
This is a gallery of animations for illustrating selected families of conic sections. Included are GSP and Excel files.
This demo provides a visual development for the "locus of points" definitions of the conic sections.