2. Are there instances in which the word or its variants are actually
found in modern (ok, post-modern for some folks) geometry textbooks at
the primary, secondary or early university level in the United States?
Elsewhere?
3. Where parallelepiped usage is extant in parts of Europe, South America
and Japan, does the concept survive in geometry courses, or is its usage
limited to the jargon of architecture or arcane mathematical discussions?
>>
In the fall of 1997 I taught an undergraduate course in computer graphics
(I teach in night school at Richard Stockton College, but as an "adjunct",
not a professor). The text was Donald Hearn and M. Pauline Baker _Computer
Graphics, 2nd edition, C version_ (Upper Saddle River NJ: Prentice Hall,
1997), sections 12-4 and 12-5 uses the word "parallelepiped" without
definition.
Specifically, the book was discussing "view volumes" and "clipping" in 3
dimensions. What this means is that you can model an arbitrarily large
object, but you display only the portions of the object that fall within
the "view volume". The process of identifying those portions inside the
view volume (and discarding those outside) is called "clipping".
"For a parallel projection, the ... view volume form[s] an infinite
parallelepiped"
"With an orthographic parallel projection, the six planes form a rectangular
parallelepiped, while an oblique parallel projection produces an oblique
parallelepiped view volume.
One student asked me who invented the word "parallelepiped"? Remembering
that Dr. John Dee had something to do with the first translation of Euclid
into English, I said it was Dee, and proceeded to entertain the class with
a few Dr. John Dee stories.
I might add that Hearn and Baker recommend the use of quaternions for 3-d
transformations in computer graphics.
"Parallelepiped" also occurs in H. S. M. Coxeter _Introduction to Geometry_
(the title page is missing from my copy so I can't give a proper
bibliographic citation) pages 127-128, 223, and 309. On page 228 Coxeter
says
In the tongue-twisting word "parallelepiped" we stress the syllable
"ep," belonging to the Greek prefix epi, which occurs also in such
words as "epithet" and "epicycloid."
Aside to Senhor Romulo Lins: you wrote << 'Shoe box' is also a very
common expression among teachers for the 'paralelepipedo retangulo.' >>
This produces a play on words in English, since a 'paralelepipedo
retangulo' paving block is known in English as a "cobblestone", and
in English a shoemaker is a "cobbler".
James A. Landau