Dissection of a Vase
What is this about?
A Mathematical Droodle
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Copyright © 1996-2015 Alexander BogomolnyThe 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?
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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
- I. Moskovich, Leonardo's Mirror and Other Puzzles, Dover, 2011
Equidecomposition by Dissiection
- Carpet With a Hole
- Equidecomposition of a Rectangle and a Square
- Equidecomposition of Two Parallelograms
- Equidecomposition of Two Rectangles
- Equidecomposition of a Triangle and a Rectangle
- Equidecomposition of a Triangle and a Rectangle II
- Two Symmetric Triangles Are Directly Equidecomposable
- Wallace-Bolyai-Gerwien Theorem
- Perigal's Proof of the Pythagorean Theorem
- A Proof Perigal and All Others After Him Missed
- Dissection of a Vase
- Curvy Dissection
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Copyright © 1996-2015 Alexander Bogomolny| 49551954 |
