id: 06664518
dt: j
an: 2016f.01026
au: Bentley, Brendan
ti: Why the golden proportion really is golden.
so: Aust. Math. Teach. 72, No. 1, 10-14 (2016).
py: 2016
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: G40 M80
ut: golden ratio; golden proportion; mathematics and arts
ci:
li:
ab: Summary: Why do certain objects or images such as a piece of furniture, an
item of clothing, or even a flower appear visually attractive? The most
obvious factors must involve aspects such as size, colour, movement and
discrepancy such as in looking at a Salvador Dali painting. Yet there
is another subtle factor associated with shape that also can demand,
and even attract, attention. This factor concerns the relationship
between dimensions such as width and height. One such phenomenon is
referred to as the Golden Proportion. Expressed mathematically, this
represents a ratio coefficient of 1\,:\,1.62. Taken out of context,
such a figure sounds strange. Indeed, it seems almost bizarre to inform
someone that they like something because it is 1.6 times higher than it
is wide. However, this article presents many examples of phenomena that
appear consistent with such a notion. Herein, the author argues that
the analysis of the Golden Proportion engages students in varied
mathematical thinking. Specifically, such an analysis invokes
measurement, ratio, rational number, and proportion. Most vitally,
investigating the Golden Proportion, finding it within the world, and
being able to describe its dimensional properties, provides remarkably
rich learning opportunities which can foster the awareness of
proportional reasoning. (ERIC)
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