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   ooooo   ooooo  .oooooo.  oooooooooooo       HOE E'ZINE RELEASE #832
   `888'   `888' d8P'  `Y8b `888'     `8  "A Short Lesson In Applied Calculus
    888     888 888      888 888           (or: How I Learned to Stop Hating 
    888ooooo888 888      888 888oooo8       Math and Love the Aluminum Can)"
    888     888 888      888 888    "                  by Ior
    888     888 `88b    d88' 888       o               9/20/99
   o888o   o888o `Y8bood8P' o888ooooood8
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        when newton and leibniz concurrently discovered/invented calculus,
 they had little idea of how it would revolutionize industry.  today,
 calculus is used for many things, far beyond the boring textbook examples of
 'if a hollow object created by rotating curve y = x^3 - 2x^2 around the x
 axis is being filled up by water at a rate of blah blah yadda yadda how long
 will it take for the object to be completely full?' analog electronics
 engineers use calculus to decide on the proper resistors to use when
 building that fancy new p8-12389752 gHz computer you're contemplating
 purchasing. architects might use it to understand the actual space of a room
 under and arching roof.  and professors might use it to bore high school and
 college students.

        regardless, we owe some of the most astounding feats of modern
 engineering to calculus.

        the best example of this is the typically underappreciated aluminum
 can.

        stop for a minute and think about the aluminum can.  you probably use
 at least one a day.  it doesn't seem like anything special.  however, the
 virtues of the aluminum can cannot be examined enough.  the aluminum can is
 optimized for several things.  let's list those:

        -- the can is optimized for maximum volume.
        -- the can is optimized for a minimum of physical space.
        -- the can is optimized for a minimum of physical weight.
        -- the can is optimized for maximum integrity.

        the first two optimizations are actually fairly simple problems to
 solve for anyone who has had a first year calculus course.  the third
 optimization is possible with aluminum, a space age material made possible
 only through the use of calculus.

        it's the last optimization that is truly mindboggling. even just
 observing a single aluminum can full of a carbonated soda, the implications
 of this optimization are incredible.  the authors lack of knowledge about
 the amount of carbonation in soft drinks means that the exact amount of
 pressure exerted outwards on the can is not known.  it can easily be assumed
 to be over 1 atmosphere, if it weren't there would never be a problem with
 carbonated sodas fizzing over the edge of the can when opened.

        this optimization is even more spectacular when observing the
 aluminum can in groups.  the groups being referred to here are not just the
 packs of six cans or the flats of 24.  these groups are most easily seen at
 large warehouse stores such as price-costco.  frequently, a single full
 aluminum can will be supporting easily another 20 or more cans directly on
 top of it!  even the human spine would fracture if a single human were to
 support 20 other humans vertically.  yet there is no doubt that the aluminum
 can could carry over 50 times its own weight with direct vertical
 compression.

        truly, the aluminum can is a marvel of the manufacturing process and
 is only possible through the great math of calculus.  next time you finish a
 soda or a beer, do not simply throw the can in the recycling.  instead,
 pause to look at the can.  to notice its perfect shape, its meticulous
 design, and its dazzling abilities.  only when one has contemplated this
 thouroughly may the can be discarded.

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 [ (c) !LA HOE REVOLUCION PRESS!       HOE #832 - WRITTEN BY: IOR - 9/20/99 ]