NetLogo Models Library:
This is a Solo version of the HubNet activity called Perimeters and Areas by Embodied Agent Reasoning, or PANDA BEAR. PANDA BEAR Solo can be used as a standalone activity or as an introduction to PANDA BEAR.
PANDA BEAR is a microworld for mathematics learning that lies at the intersection of dynamic geometry environments and participatory simulation activities. Whereas PANDA BEAR involves many people controlling individual vertices of a shared, group-polygon, in PANDA BEAR Solo, an individual user controls all of the vertices of a polygon. The measures of perimeter and area of the polygon are foregrounded in the environment. The model user can be given challenges regarding the polygon's perimeter and area as suggested in the THINGS TO TRY section.
SETUP initializes the model to create a polygon containing NUMBER-VERTICES vertices. GO allows the user to move the vertices around with the mouse. The PERIMETER and AREA monitors update automatically as the vertices move around. The PANDA plot shows both of those measures over time as a record of the user's actions as they work towards a goal. SETUP-PLOT resets the plot to start a new challenge with the same polygon. The MOVE-FD, MOVE-BK, TURN-RIGHT, and TURN-RIGHT buttons change the red vertex's location and heading. The STEP-SIZE and TURN-AMOUNT input boxes control the amount of movement of the MOVE-FD, MOVE-BK, TURN-RIGHT, and TURN-RIGHT buttons.
In a triangle, for an individual vertex, moving "between" the other two vertices minimizes the perimeter for a given area.
In a triangle, when all three vertices attempt to form an isosceles triangle, and equilateral triangle is formed.
Strategies that work for challenges at the triangle level often work at the square level as well.
As the number of vertices is increased, the polygon that maximizes the area given a perimeter and minimizes the perimeter given an area gets closer and closer to a circle.
With three vertices, make the area as big as possible while keeping the perimeter at or below 25.
With three vertices, make the perimeter as small as possible while keeping the area at or above 25.
Increase the number of vertices in the polygon from three to four (and beyond - approaching a circle) and do the above.
Modify the challenges in a patterned way. For example, with four vertices, doubling the allowed perimeter should quadruple the maximum area.
Add different methods of movement. For example, instead of turning and going forward and backward, the user could be allowed to move the red vertex in the 4 cardinal directions.
Allow the user to give the vertices movement rules to follow over and over so that the group-polygon "dances".
This model uses links to form the sides of the polygon, each vertex is linked to exactly two other vertices. The sum of the lengths of all the links is the perimeter of the polygon.
The area calculation is based on information found here: http://mathworld.wolfram.com/PolygonArea.html
Thanks to Josh Unterman for his work on this model.
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Copyright 2007 Uri Wilensky.
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