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relations between the 5 shapes
by G. A. Sarcone & M. J. Waeber
math relations between the 5 basic shapes of the Tangram puzzle
shown below will allow you to create and/or solve new interesting
geometric puzzles. The small isosceles triangle B, the
square C and the rhomboid D of the Tangram all
have the same area, but their surfaces are different.
Actually, the square C has the smallest perimeter (4a < 2(a+b)).
The large isosceles triangle E is 4 times the size of
the small isosceles triangle A, but curiously its perimeter
is only 2 times as big!
©1992-2007, Sarcone & Waeber, Genoa
Sarcone & Waeber, Genoa
geometrical shapes in fig. a) and b) seem to be identical...
It's obvious that they are made with the same 4 Tangram pieces,
but thanks to the table above, we can calculate the perimeter
of each geometric figure and find that the perimeter of second
diagram is approx. 1.03 times larger than the first one.
The math expression is:
Pb / Pa =
substituting the value "b" with "a2",
we obtain: 1.0327...
you form a perfect trapezium as shown in fig. c below using
all 7 tan pieces? The table above will be helpfull to determine
wether the puzzle is possible or not...
del Matematico, G. Sarcone, 2001
13th convex shape...
1942, Fu Traing Wang and Chuan-Chih
Hsiung (also known as Xióng Quánzhì,
in Chinese: 熊全治) proved that there are
convex tangram configurations (cf. "A theorem
of the tangram", The American Mathematical Monthly,
n. 49, pp. 596-599). Well... Here below, you'll find 12 convex
polygons you can form with the Tangram puzzle. Can you guess
which is the 13th convex tangram configuration? Mail us your
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