OFFSET
3,2
COMMENTS
I do not know which of these values have been proved to be minimal.
Turning over is allowed. The pieces must be bounded by simple curves to avoid difficulties with non-measurable sets.
REFERENCES
G. N. Frederickson, Dissections: Plane and Fancy, Cambridge, 1997.
H. Lindgren, Geometric Dissections, Van Nostrand, Princeton, 1964.
H. Lindgren (revised by G. N. Frederickson), Recreational Problems in Geometric Dissections and How to Solve Them, Dover, NY, 1972.
LINKS
Stewart T. Coffin, Dudeney's 1902 4-piece dissection of a triangle to a square, from The Puzzling World of Polyhedral Dissections.
Stewart T. Coffin, The Puzzling World of Polyhedral Dissections, Chapter 1. (See section "Geometrical Dissections".)
Geometry Junkyard, Dissection
Gavin Theobald, Triangle dissections
Vinay Vaishampayan, Dudeney's 1902 4-piece dissection of a triangle to a square
EXAMPLE
a(3) = 1 trivially.
a(4) <= 4 because there is a 4-piece dissection of an equilateral triangle into a square, due probably to H. Dudeney, 1902 (or possible C. W. McElroy - see Fredricksen, 1997, pp. 136-137). Surely it is known that this is minimal? See illustrations.
Coffin gives a nice description of this dissection. He notes that the points marked * are the midpoints of their respective edges and that ABC is an equilateral triangle. Suppose the square has side 1, so the triangle has side 2/3^(1/4). Locate B on the square by measuring 1/3^(1/4) from A, after which the rest is obvious.
For n >= 5 see the Theobald web site.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 11 2005
STATUS
approved