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## Custom Apps

Algebra

 Function Iteration: Illustrate the graphical iteration process for functions. The function and initial value can be adjusted dynamically, and a time series plot showing the number of iterations versus the evaluated function values can be displayed. Linear Programming: Analyze an optimization situation graphically by using constraint inequalities and an objective function to find the minimum/maximum. Both two-dimensional (2-D) and three-dimensional (3-D) linear programming problems can be examined. The linear programming situation can be graphically analyzed one constraint inequality at a time, resulting in the determination of the feasible region. See the Solver in the spreadsheets for numeric solutions and more variables.

Geometry

 Triangle Congruence: Explore whether three specified side or angle measures are sufficient information to determine the existence of a unique triangle (or the congruence of two triangles). Rigid transformations are used to verify the congruence of two triangles. Alternatively, measures of two triangles can be displayed to check for congruence, or created triangles can be manipulated and compared by clicking and dragging. Tilings with Triangles or Quadrilaterals: Explore tiling the plane with congruent triangles or quadrilaterals using rotations of 180° about the midpoints of sides. Tilings with Regular Polygons: Explore tiling the plane with one or more regular polygons to create regular and semi-regular tessellations. Design by Robot: Create both simple and complex designs by entering program commands for the robot to draw and move. Explore SSA: Experiment with various side and angle measures to explore the side-side-angle condition for triangles. Determine which measurements or intervals of measurements determine no triangle, exactly one triangle, or two noncongruent triangles. Explore Similar Triangles: Explore whether two specified side or angle measures are sufficient information to create similar triangles. A sequence of size (dilation) and rigid transformations are used to verify the similarity of two triangles. Alternatively, measures of two triangles can be displayed to check for similarity or compared directly using the mouse. Explore Arcs and Angles: Explore the relationship between the measures of inscribed angles and their intercepted arcs. Features include the dragging the points on the circle to change the arc length or angle measure and display measures of angles and arcs. Explore Radians: Experiment with measuring angles in radians and with how radian measures are related to degrees and revolutions. Features include guessing a target value displayed in radians, degrees, or revolutions in another unit of measure. Slicing or Unfolding Polyhedra: Visualize common polyhedra and manipulate 3-D modeling options such as cutting and unfolding. Features include rotating the shape in 3-D space and displaying the vertices, edges, and faces of a solid and its topological dual. Transform options include truncate, punch, and stellate. Slicing Cones, Cylinders, and Spheres: Dynamically manipulate a plane slicing a single or double cone, cylinder, or sphere and view the corresponding conic section. Features include manipulation of the position of the plane of intersection and the cone itself, identification of the cross-section, and the option to display the wire frame. See also 3-D slicing in CAS. Surface of Revolution: Draw and manipulate a line or a connected series of line segments in two-dimensional space to simultaneously generate a surface of revolution in three-dimensional space. Features include choosing the axis of rotation, setting the angle of rotation, and showing the wire frame and quadrilateral faces of the surface of revolution.

Statistics

 Estimate Center: Estimate the mean of a distribution by dynamically finding the balance point of the histogram. Preloaded or user-entered data sets can be analyzed. Estimate Center and Spread: Estimate the mean of a distribution as in the Estimate Center app, and estimate the spread of a distribution by estimating a proportion (such as two-thirds) of the data within a distance of the mean. Preloaded  or user-entered data sets can be analyzed. Modeling: Estimate a curve of “best-fit” on a scatterplot and compare to the regression equation. Features include a movable “best fit” curve and display of the estimate function equation with the regression equation. Available models are linear, exponential, power, logarithmic, quadratic, cubic, quartic, polynomial, and sinusoidal. Alternatively, users can enter an algebraic function model. Randomization Distribution: Create an approximate sampling distribution of possible differences in means, medians, or standard deviations of two treatments by re-randomizing and, then, identify extreme events. Features include adjusting histogram settings and displaying the count or relative frequency of resampling results in each bar of the histogram. Distribution of a Sample: Explore the shape, mean, and standard deviation of distributions of sample means, medians, or standard deviations for various sample sizes. Results are displayed in a histogram as counts or relative frequencies. Summary statistics are available. Binomial Distributions: Vary the number of trials and the probability of a success on each trial to see how the shape, center, and spread of binomial distributions are affected. Conduct experiments and compare theoretical models of distributions to simulation results. Features include moveable sliders for p and n, comparison of simulation results with theoretical binomial or normal distributions, and simultaneous display of multiple distributions.

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