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Proof-By-Colors Euclid

Math Lint for this week discusses Oliver Byrne's version of the The First Six Books of the Elements of Euclid, which is now listed for sale at only $22,500. The special approach of this edition was its use of colors to "simplify" both Euclid's propositions and his related proofs of these same propositions.

I know, so what. You don't happen to have $22,500 lying around...but, its the University of British Columbia to the rescue!

UBC's Mathematics Department spearheaded a project that created digital photographs of each page of this version of Euclid's Elements. And, it is now available to you at no cost via the internet.

The sample page is Proposition 6 in Book II, which on the surface level is a proposition involving the "applying of areas" using rectangles and gnomens. On another level, this proposition illustrates the advent of "geometrical algebra" in that it also can be used to solve the quadratic x2 + nx = m2. This connection can be found by reading the corresponding commentary from either Heath or David Joyce. I might add that David Joyce's on-line Java-based version of a "dynamic" Euclid's Elements was suggested on MathNexus several years ago.

So, if you enjoy geometry or you teach geometry (unfortunately not always equal groups), then browse through UBC's fantastic contribution. Use it in your classes...and you might see how students are able to follow the proof of a proposition easier with colors than with symbols. Then wait for the question: Is this the way we will have to do it on the test?