Dissection of a Vase
What is this about?
A Mathematical Droodle


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Discussion

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Copyright © 1996-2017 Alexander Bogomolny

The applet is intended to help raise and answer a question about a shape (that might remind one of a vase) whose border consists of six quarter circles drawn with the same radius:

Given the radius, say R, of the arcs, what is the area of the vase?


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

The top of the vase if complemented by four circular sectors with central angle of 90° becomes a square of the side equal to the diameter of the arcs and circles, i.e., 2R. One of the sectors (the lowest) is already inside the intended square; the other three find there locations by dragging the scroll bar and come from the remaining three quarters of a circular part of the vase. It follows that - by dissection - the area of the vase equals that of the square.

References

  1. I. Moskovich, Leonardo's Mirror and Other Puzzles, Dover, 2011

Equidecomposition by Dissiection

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Copyright © 1996-2017 Alexander Bogomolny

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