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17 November 2016

"Infinite Acres" / a solid with Finite Volume and Infinite Surface / you can fill it with This Much olive oil, but you can never buy enough paint to paint it


Sound ON / FULL SCREEN mode

A recent post was my preliminary design sketch for the USA's Wars Without End Memorial in Washington D.C. This is the 15th year of continuous warfare in Afghanistan and Iraq involving USA military (and intelligence) personnel. Both wars were declared by President George W. Bush, and have continued throughout the 8-year presidency of Barack Obama

Barring some kind of "November/December/January Miracle," warfare involving US military personnel will continue when the presidency of Donald Trump begins on 20 January 2017.

All previous USA wars, however protracted, ended. 


But so far as we can tell or test, these are America's first and only Wars Without End. We can clearly date the starts of the War in Afghanistan and the War in Iraq.

But there is no End in sight, for either war. (If you can stand on a chair and see an End to either or both wars, please Leave A Comment. Please provide details more substantive than Wishin' and Hopin'.)

My design for the Memorial uses a mathematical solid with a strange property: It has a Finite Volume (e.g., for filling it with liquid), but has an Infinite Surface (i.e., you can never buy enough paint to paint its outside). The name of this odd solid is, alternatively, Gabriel's Horn or Torricelli's Trumpet. (The Archangel Gabriel blows this magic horn to announce Judgment Day.)

Some years ago I saw the above film and -- well, I was smote. It was astonishing enough to encounter this strange solid, but the math that defined it was comfortably within my modest comprehension of the differential and integral calculus.

At that time, I couldn't find this cartoon film on the Internet. But I was so astonished by this clear explanation of what surely (to calculus dumpkopfs) must be an impossible object that, via e-mail, I asked permission of the film's author to post it. And Professor Melvin Hendrikson of Purdue University (Indiana USA) graciously granted his permission.

Professor Hendrikson explains the rest of this magic far better and more entertainingly than I could.

The Wars Without End Memorial post's nature was military and political, and Vleeptron will have more to say about the implications and consequences of America's Wars Without End.

This animated cartoon explains the quite simple math behind this strange object. (It must be quite simple, because I understand it.)


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