Archives For Geometry


[easyazon_image align=”left” height=”250″ identifier=”1587170663″ locale=”US” src=”” tag=”douloschristo-20″ width=”205″] Today is the birthday of Norton Juster, the author of the side-splittingly hilarious kids book [easyazon_link identifier=”0394820371″ locale=”US” tag=”douloschristo-20″]The Phantom Tollbooth[/easyazon_link].  

In the wake of The Phantom Tollbooth‘s success, Juster wrote [easyazon_link identifier=”1587170663″ locale=”US” tag=”douloschristo-20″]The Dot and the Line: A Romance in Lower Mathematics[/easyazon_link], which was inspired by Edwin A. Abbott’s novel [easyazon_link identifier=”048627263X” locale=”US” tag=”douloschristo-20″]Flatland: A Romance of Many Dimensions[/easyazon_link].  I just spent several days writing a paper in tribute to my friend and mentor David Neuhouser, who introduced me to Flatland (which I talk about in my new book [easyazon_link identifier=”083084449X” locale=”US” tag=”douloschristo-20″]Reading for the Common Good[/easyazon_link]) and would have loved Juster’s book.

The Dot and the Line was turned into a short film by Chuck Jones, the renowned animator and producer of Looney Tunes, etc. It seems fitting to share this film here today…

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“Distinctively Particular Ways of Thinking
About the Spaces We Inhabit

A Review of
The First Six Books of The Elements of Euclid

By Oliver Byrne.

Reviewed by Chris Smith.

The First Six Books of The Elements of Euclid
By Oliver Byrne.

Two Volume Set in Clamshell Case: Taschen, 2010.
Buy now: [ Amazon ]

Oliver Byrne - EUCLID'S ELEMENTSA dozen years ago this Fall, I was just starting my graduate studies in philosophy of science, working toward a PhD.  I was particularly interested in the ways that humankind has historically understood and talked about the spaces that we inhabit.  But as I got further and further into my research, I grew increasingly frustrated with the depth of layer upon layer of abstraction inherent in contemporary systems of geometry and physics.  Eventually, I got to the point at which I could no longer continue to be so heavily invested in these abstract worlds and I had to take a break from my graduate studies for my own sanity.

One hundred and fifty years before my graduate school experience, a little known Irish mathematician and surveyor by the name of Oliver Byrne had a similar experience.  Byrne’s frustrations – aimed particularly at the way geometry was taught – led him to craft one of the most elegant geometry books ever printed.  And now thanks to Taschen Books, Byrne’s book The First Six Books of The Elements of Euclid, is back in print. As its title implies, Byrne’s work is an adaptation of Euclid’s Elements, but its novelty lies in its use of color to identify specific figures.  Consider, for instance, the following proof which Byrne offers in the book’s along with its parallel in the traditional rendering of Euclid to demonstrate the contrast between the two methods:

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Euclid alone has looked on Beauty bare.
Edna St.Vincent Millay

Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.