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Explanation of functionalities

Drag the filled circles on the top and bottom line of the initial marked box to change their position.
  • Increase or decrease number of boxes: Double or halve the number of marked boxes (increase or decrease the number of iterations of Pappus' Theorem by one). If you increase the number of marked boxes, the box operations $\tau_1$ and $\tau_2$ are applied to all the existing marked boxes (i.e., you apply Pappus' Theorem to all the marked boxes).
  • Reset: Set the top and bottom parameter to 0.5 and the number of marked boxes to one.
  • Make boxes symmetric: Set the top and bottom parameter to 0.5.
  • Modify the canvas size: Increase or decrease the size of the canvas (drawing area for the Pappus Curve) by 50px or fit the canvas to the size of your browser window.
  • Show or hide curve or boxes: Show or hide the set of top and bottom points of marked boxes, or show or hide the boundaries of the open convex interiors of marked boxes.
  • Computation of box dimension: To compute the box dimension of the set of top and bottom points of the marked boxes one needs to specify a finite sequence of $k$ coordinate meshes of grid sizes $\delta_k$. If you increase or decrease the number of meshes, you increase or decrease $k$ by one. Here, we use $\delta_k \propto 0.5^k$. After choosing $k$ click on Compute Box Dimension to compute the box dimension of the given set of top and bottom points.

Additional Notes

The design of this web page was inspired by Richard Schwartz' Java applet about iterating Pappus' Theorem. The source code was written by Anne and Fabian Kißler.