Spirolaterals
Introduction
A spirolateral is "created by drawing a set of lines; the first at a unit, then each additional line increasing by one unit length while turning a constant direction." (The Art of Spirolaterals by Robert J. Krawczyk.) Here is a paper relating spirolaterals to multiplication: http://educ.queensu.ca/~fmc/january2003/Spirolaterals.html. Here are some examples using different angles and number of sides before repeating the process. |
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Instructions look like:
turn 90 degrees
move one step
turn 90 degrees
move two steps
turn 90 degrees
move three steps
Now repeat these three operational pairs and you will find that you eventually end up where you started.
Another example:
turn 45 degreesRepeat this septet of paired turn-move commands and sure enough, you are at the beginning.
move one step
turn 45 degrees
move two step
turn 45 degrees
move three step
turn 45 degrees
move four step
turn 45 degrees
move five step
turn 45 degrees
move six step
turn 45 degrees
move seven step
Not all combinations of angles and operation lengths produce closed forms. For example:
turn 90 degrees
move one step
turn 90 degrees
move two steps
turn 90 degrees
move three steps
turn 90 degrees
move four steps
will work its way off the page.
Instructions
To run the program:Set the angle (angle) and the number of steps in one iteration (nTurns).Click the green flag to clear the display before trying another spirolateral.
---- Slide the little ball below the variable's display to increase/decrease its value.
Set the length of the first segment (lenFactor). The second segment will be 2 * lenFactor, the third will be 3 * lenFactor, etc.
Hit the space bar to draw the first set of segments. Continue hitting the space bar for additional sets.
If the drawing goes outside the Scratch display window, the figure will be corrupt. Shorten the segment length (lenFactor), click the green flag, and hit the space bar to try again.
The x and y position of the drawing tool ( a sprite) is displayed to see when the drawing is closed. Drawings begin at (0, 0), so (x, y) at (0, 0) shows closure. Beware: "computer error" will cause closed figures to return to (x, y) very close to (0, 0), but not necessarily exactly (0, 0).