So first click on point C and then on point B in the sketch. In the iterate menu box, click on structure and then select add new map. We still need to map the iterated process onto CB. When you have done this you should see a lighter image that looks like the following C Note: you may have to move the iterate menu box to have access to point C in your sketch. We want to map point B to point C, so now click on point C in the sketch. Now the B ⇒ and point B should highlight. So with the A ⇒ box highlighted, click on point A in the sketch. We want point A to be mapped to point A and point B to be mapped to point C. We have to tell Sketchpad where we want the iterated process mapped or placed. Using the arrow selection tool, deselect all objects and then select points A and B.
Construct segment trisector gsp5 generator#
To approximate the fractal we now need to iterate the generator construction process. We have now constructed the generator of Lévy’s curve. Now select points C and B and from the construct menu choose segment. Then, using the arrow selection tool, select points A and C and from the construct menu choose segment. Using the text tool, click on top point to label it as “C”. Now, in the display menu, choose hide objects. So, using the selection arrow tool, deselect all objects by clicking in blank space and then select the rotated segment, the original segment, the perpendicular line, and the midpoint. We now want to hide the portions of the construction that aren’t needed. Using the construct menu, choose intersection to create the point of intersection. Now, select the rotated segment and perpendicular line. If everything looks correct, press the rotate button and obtain the following image.
You should see a lighter image of the rotated segment in the sketch. Make sure the fixed angle radio button is selected (it should be by default) and enter 45 into the degrees entry space. Now select AB and from the transform menu choose rotate. You should see a bulls-eye animate briefly around point A. Now double click on point A to set it as a point of rotation. Using the selection arrow tool, deselect all objects. Now from the construct menu, select midpoint to construct a midpoint on the segment Bįirst select both the midpoint and AB, then, from the construct menu, select perpendicular to create a line perpendicular to the segment passing through the line. Using the selection arrow tool, select the line segment. Using the text tool, click on endpoints of our segment to label the points as “A” and “B” B Start with a blank sketch and construct a line segment using the straightedge tool. Time permitting we will discuss fractal or similarity dimension and applications of fractals in real world settings. We will use this process to create an approximation of a very simple fractal, Lévy’s curve, and a more complex fractal, the Koch curve, and its beautiful, pseudo-fractal counterpart, the Koch Snowflake.
To draw fractals with Sketchpad, one merely needs to be able to construct a generator from an initiator and successfully apply the iterate function. While finite iterations of the process will not create an exact image of the fractal, they can give us a reasonable approximation and The Geometer’s Sketchpad excels in this application. Fractal images defined in this way are also referred to as Iterated Function systems. Infinite repetition of the recursive process ultimately creates an infinitely complex image…our fractal. The starting image is called the initiator or seed and the second image is called the generator or first iteration. When using recursion, we must define a specific starting image and a process by which we will transform the first image into a second image. One of the most common ways of creating fractal images is to use a recursive definition, i.e. In simplest terms, fractal images are geometric figures that exhibit self-similar patterns in continually decreasing sizes. With a scope that spans the mathematics curriculum from middle school to college, The Geometer’s Sketchpad® brings a powerful dimension to the study of mathematics.” Understanding this, we will see that Sketchpad can be an incredibly useful tool for the study of fractal images.
Construct segment trisector gsp5 software#
INTRODUCTION According to the Key Curriculum Press website, the publisher of The Geometer’s Sketchpad, “Sketchpad is a dynamic construction and exploration tool that enables students to explore and understand mathematics in ways that are simply not possible with traditional tools-or with other mathematics software programs. ME2 by the Sea JRichard Rupp Del Mar College Using The Geometer’s Sketchpad to Explore Fractals Images and Iterated Function Systems
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