id: 06664672
dt: j
an: 2016f.00945
au: Gomes, Luis Teia
ti: Pythagoras triples explained via central squares.
so: Aust. Sr. Math. J. 29, No. 1, 7-15 (2015).
py: 2015
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: F60 G40 A30
ut: Pythogorean triples; history of mathematics; geometric construction
ci:
li:
ab: Summary: Very much like today, the Old Babylonians (20th to 16th centuries
BC) had the need to understand and use what is now called the
Pythagoras’ theorem $x^2 + y^2 = z^2$. They applied it in very
practical problems such as to determine how the height of a cane
leaning against a wall changes with its inclination. In this paper,
Luis Teia Gomes presents an alternative method that uses squares rather
than circles to geometrically describe the Pythagorean triples, and how
they are interconnected. The triangles formed by the triples in
Pythagoras’ or Plato’s families can be geometrically interconnected
via intermediate central squares ‒ this forms the basis of the
central square theory. This pattern of parent ‒ child triple
relationship allowed the geometric construction of both sequences,
which seem to behave in a similar manner. From the perspective of
central square theory, the Pythagoras’ or Plato’s families are
expressed not only as a sequence of triples, but also by their
connecting sequence of squares. (ERIC)
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