id: 06439700
dt: j
an: 2015d.00485
au: Britz, Thomas; Mammoliti, Adam; Sørensen, Henrik Kragh
ti: Proof by picture: a selection of nice picture proofs.
so: Parabola 50, No. 3, 5-15 (2014).
py: 2014
pu: AMT Publishing, Australian Mathematics Trust, University of Canberra,
Canberra; School of Mathematics \& Statistics, University of New South
Wales, Sydney
la: EN
cc: E50 K20 G40 E60
ut: proving; picture proofs; sum of consecutive integers; binomial
coefficients; sum of squares; Ramsey theory; combinatorics; Euclidean
geometry; Pythagorean theorem; triangle area; infinity; sets; power of
a set; cardinality; natural numbers; number pairs
ci:
li:
ab: From the text: Just like any other cultural group, mathematicians like to
tell stories. We tell heroic stories about famous mathematicians, to
inspire or reinforce our cultural values, and we encase our results in
narratives to explain how they are interesting and how they relate to
other results. We also tell stories to convince others that our results
are valid, and preferably also to explain why they are true. These
stories are what you know as “proofs". You might think (perhaps with
some trepidation) of proofs as formal, written sequences of logical
steps. However, proofs can come in a variety of formats, some of which
are more active or intuitive than a formal written proof. In this
article, we show how proofs can be in the form of pictures, and we show
a selection of these picture proofs that we find particularly elegant
and instructive.
rv: