Rubber Band Area
Rubber Band Area
Below there are 5 points with a tight rubber band wrapped around all of them, creating a shape. 4 of the points are arranged in a square. 1 of the points is rotating around the center of the square, as shown. The amount of rotation can be controlled using the slider.
GOAL: Write a function that takes the amount of rotation as input and outputs the area of the space inside the rubber band.
<iframe scrolling="no" title="ConvexHull-PerimeterRotation" src="https://www.geogebra.org/material/iframe/id/cgVGTPhu/width/1048/height/650/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="1048px" height="650px" style="border:0px;"> </iframe>
Extensions
- Is the function continuous? Is it differentiable?
- When is the perimeter changing the fastest?
- All 4 corners of the square can be moved. Can you generalize your function to work for squares of any side length?
- Move the corners to create quadrilaterals other than squares and try to write functions for those.
- What other questions can you ask about this situation?