\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2012e.00029}
\itemau{Swetz, Frank J.}
\itemti{Similarity vs. the ``in-and-out complementary principle": a cultural faux pas.}
\itemso{Math. Mag. 85, No. 1, 3-11 (2012).}
\itemab
Summary: Modern investigators of early Chinese mathematical classics have often attributed a recognition and application of the principles of geometric similarity to the authors and commentators of these works. In problem situations involving the use of sighting poles and the determination of a remote distance, Chinese mathematicians frequently employed proportionality relations involving the sides of relevant pairs of right triangles. In such situations the modern western observer sees similarity; however, the Chinese employed a concept now called ``the in-and-out-complementary-principle" IOCP. They did not use geometric similarity. This article identifies the issues of confusion and examines the concept and application of IOCP.
\itemrv{~}
\itemcc{A30 G40}
\itemut{in-out principle; Chinese mathematics; geometry; proportionality relations}
\itemli{doi:10.4169/math.mag.85.1.3}
\end