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This is a draggable line on an xy-coordinate system that dynamically updates the equation of the line. Here is an idea of what the sketch looks like:
The midpoint quadrilateral, constructed by connecting the midpoints of any quadrilateral, is always a parallelogram. Under what conditions is it a rhombus? Use this sketch to investigate. Here's a picture of the sketch:
This is a sketch of a tessellation made in the pattern of a Navajo rug.
This sketch was created recursively, replicating a segment and an angle thus creating various polygons when the angle is changed.
Parallelogram Area vs. Perimeter
This is a figure which is minimally constrained to be a parallelogram with constant area and perimeter.
Here's what the sketch looks like:
Here is an animation of a pendulum. You can vary its length and amplitude. Take some data. What is the dependence of the period on these two parameters. Does it behave like a physical pendulum?
This is a dynamic perspective drawing of a road and a railroad track receding into the distance.
This is a dynamic polygon generator created using the same techniques as in N-gon but using two different angles and two different lengths of segments, all of which are changing at different rates.
Here are five scripts that demonstrate ways to use Sketchpad to investigate random phenomena.
2D Fractal Mountain Script
Generate a random, fractal skyline.
3D Landscape Script
Generate a 3-D landscape using random fractals.
Select a starting point and a segment that specifies how large the steps are. The depth of recursion indicates how many steps will be taken. Each step is in a random direction.
Select any two segments and run the script. You will get a collection of random length toothpicks within the parallelogram defined by the segments.
With a simple script, you can model the motion of a ball in a uniform gravitational field. With a bit more work, you can find the focus and directrix of the resulting parabola. Finally, you can animate a ball along the path. This sketch could present some very good challenges for advanced students!
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