Unwrapping Involutes
Website Address:https://www.curriki.org/oer/Unwrapping-Involutes-680734
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As you pull the paper off of a grocery store tube of cinnamon rolls, several things happen at the same time: the seam of the wrapped portion of the paper forms a helix on the cylindrical tube; the line tangent to the helix follows the edge of the unwrapped paper to its corner; and the corner of the paper traces the involute of the base of the cylinder. One can similarly obtain the involute of any other base curve. This Demonstration illustrates a few such cases. It also shows the relationship of the construction to the geometry of the tangent developable surface of the seam.
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As you pull the paper off of a grocery store tube of cinnamon rolls, several things happen at the same time: the seam of the wrapped portion of the paper forms a helix on the cylindrical tube; the line tangent to the helix follows the edge of the unwrapped paper to its corner; and the corner of the paper traces the involute of the base of the cylinder. One can similarly obtain the involute of any other base curve. This Demonstration illustrates a few such cases. It also shows the relationship of the construction to the geometry of the tangent developable surface of the seam.
