07/18/2017
EUCLIDIAN CONSTRUCTION W/MAX – 9/11/2014 [v1]
My eight-year-old tutee Max and I receive a box full of drafting tools, and I immediately started teaching him how to use classical construction techniques (also known as Euclidian Construction) to make a 30°-60°-90° triangle first, and then to draft a pentagon.
In Classical Construction, you are limited to just using a compass and straight edge (plus markers like pencils and such). You quickly learn a “playbook” of sorts in which you learn to bisect lines, find perpendicular bisectors, bisect angles, build various triangles, polygons, circles and relationships and objects, scaling lengths by rational numbers and square roots, and so on.
One place to visit to develop such a playbook quickly is the Constructions page on OpenMathRef dot com.[1]
[1] http://mathopenref.com/tocs/constructionstoc.html
As an adjunct to these construction methods, to get a grounded sense of why these ancient techniques work and are so powerful, you might want to read at least the first six books of Euclid’s “Elements”, written circa 400 B.C. If you wish to purchase a printed copy, I highly recommend the Green Lion Press edition linked to below, which uses the acclaimed Heath translation of the original Greek texts on papyrus, and little scholarly analysis.[2] Or if you want a more scholarly analysis, the Dover edition which also makes use of the Heath translation is a good additional three-volume set to invest in.[3,4,5] Or if you are on a budget, you’ll also find an excellent free version on Project Gutenberg, and I recommend using the PDF version as the HTML version doesn’t always place the geometric figures at useful locations on the screen.[6]
Green Lion Press edition of Euclid’s “Elements” on Amazon (one volume of Books I-XIII):
[2] https://www.amazon.com/Euclids-Elements-Euclid/dp/1888009195/
Dover Press edition of Euclid’s “Elements” on Amazon (three volume set of Books I-XIII):
[3] https://www.amazon.com/Thirteen-Books-Elements-Vol-1-2/dp/0486600882/
[4] https://www.amazon.com/Thirteen-Books-Elements-Vol-3-9/dp/0486600890/
[5] https://www.amazon.com/Euclid-Thirteen-Books-Elements-10-13/dp/0486600904/
Euclid’s “Elements”, Books I-XI, on Project Gutenberg, translated by John Casey:
[6] http://www.gutenberg.org/ebooks/21076
Note that this “v1” video is incomplete. Future expansions of this video will show how to construct the same 30°-60°-90° triangle and pentagon inscribed within a circle of a given radius or diameter. And an even more future version will talk about how all of these constructions would be “scored” as to obtain the best score you want to eliminate any unneeded vertices and also produce an accurate construction in minimal time.
But for getting your feet wet about classical construction, this video between Max and I is a great place to start.
VIDEO AVAILABLE AT
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https://youtu.be/9ngkjc-x61Y
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PUBLIC DOMAIN NOTICE
This video is in the public domain, and can be used, shared, reshared, and edited for any purposes whatsoever. Please note that the Euclidian Baseball™ logo and its variants are trademarks and copyrighted artwork. No use of those logos is permitted without proper clearances obtained.
TECHNICAL INFORMATION
This video was recorded in 2014 by Max Ikner on an iPad Air. The video was then transferred to an iMac i7. The audio tracks were run through Levelator 2.0 to optimize the dynamic range of the recording, then recombined with the video and edited using iMovie 10.1.6 under macOS Sierra 10.12.5.