Diagonal (pronounced dahy-ag-uh-nl
or di-ag-nl (both uses U & non-U)
(1) In mathematics, connecting two nonadjacent angles or
vertices of a polygon or polyhedron, as a straight line.
(2) In mathematics, a set of entries in a square matrix
running either from upper left to lower right (main diagonal, or principal
diagonal ) or lower left to upper right (secondary diagonal ).
(3) In number theory, as the broken diagonal, in the theory
of magic squares, a set of n cells forming two parallel diagonal lines in the
square.
(4) In linear algebra, as diagonal matrix, a matrix in
which the entries outside the main diagonal are all zero.
(5) In geometry, extending from one edge of a solid
figure to an opposite edge, as a plane (joining two nonadjacent vertices).
(6) In category theory, as diagonal morphism, a morphism
from an object to the product of that object with itself, which morphism is
induced by a pair of identity morphisms of the said object.
(7) Something with or assuming an oblique direction; having
slanted or oblique lines or markings; having a slanted or oblique direction.
(8) In typography, a virgule (a slash), known also as a solidus
(used in computing file systems variously as forward slash & back slash or
slash & slosh (the generalized term the diagonal mark).
(9) In design, any line or pattern using diagonals; something
put, set, or drawn obliquely.
(10) In fabrics, a cloth marked or woven with slanting
lines or patterns
(11) In manège, of a horse at a trot, the state in which the
foreleg and the hind leg, diagonally opposite, which move forward
simultaneously.
(12) In zoological anatomy, of or related to the
cater-corner (diagonally opposite) legs of a quadruped, whether the front left
and back right or front right and back left.
(13) In chess, one of the oblique lines of squares on a
chessboard (the mode in which a bishop may be moved).
1400s: From the Middle French diagonal From the Latin diagōnālis, the construct being the Ancient
Greek διαγώνιος (diagṓn(ios)) (from angle to angle) + the Latin -ālis (the
third-declension two-termination suffix (neuter -āle) used to form adjectives of relationship from nouns or
numerals). The construct of the Greek diagōnios, was dia- + γωνία (gōnía) (angle; corner), from the primitive Indo-European root genu- (knee; angle). The dia- prefix was from the Ancient Greek prefix δια- (dia-), from διά (diá) (through, across, by, over) and was most productive, the
familiar forms including diadem, diacritical, diagnosis, diagram, diameter,
dialect, dialogue & diatribe. The adjective diagonal (implied in diagonally) (extending
as a line from one angle to another not adjacent) dates from the early fifteenth
century and was from the Old French diagonal, from the Latin diagonalis, from diagonus (slanting line), from the Ancient Greek diagōnios. It emerged as a noun in the 1570s in the
sense of “a straight line drawn from one angle to or through another not
adjacent, in a plane or solid figure".
The specific technical meaning in chess describes "a line of
squares running diagonally across a board" and is the mode in which a
bishop may move). Diagonal is a noun
& adjective,
diagonality is a noun and diagonally is an adverb;
the noun plural is diagonals.
Defying the tyranny of the horizontal line: Lindsay Lohan’s
hand-written notes made during one of her court appearances in Los Angeles,
July 2010. Even on the Reddit subs where
exist the planet’s most unforgiving critics, most were so taken with the
neatness of the lettering, the diagonality attracted barely a comment.
A
diagonal measurement is defined usually by describing a line between the bottom
left and the upper right corners (or vice versa) of a square or rectangle. It has a nuanced value when used of computer
monitors, televisions and such because it has to be read in conjunction with
the aspect ratio of the device. A 19
inch (monitor sizes usually expressed in inches although the French will always
include a metric conversion) monitor in a 16:9 aspect will be very different from
a 19 inch 4:3 device. In computing, what
began in typography, as diagonal marks (the virgule (often called a slash of solidus
(/) and the later “back slash (\)) are used in computing file systems to
separate directories & sub-directories (now familiar as folders) from file
names. Under MS/PC-DOS, OS/2 &
Windows, a file called myfile.txt to a sub-directory called text in a directory
called user on D: drive would be displayed in the path D:\user\text\myfile.txt
(although under DOS it would be in upper case).
The Windows crowd call these diagonal marks “back slashes” and the
solidus they call “forward slashes” and they’re used for other purposes. The Unix crew think this childish and insist
a solidus is a “slash” and there’s no such thing as a back-slash which real
people call a slosh.
Notable moments in diagonal (canted) headlamps
The one-off, 1938 Jaguar SS100 fixed head coupé (FHC) “Grey
Lady” which demonstrates the traditional placement when four lights were used.
The inclination designers for decades felt to use a diagonal arrangement for headlights began innocently enough in the pre-war
years when it emulated the usual practice of placing a pair of driving lamps or
for lights inboard of the main headlamps and lower down, mounted typically on
the bumper bar or its supporting brackets.
Most headlamps until the late 1930s were in separate housings, as were
the auxiliary devices and even cars which integrated them into the coachwork
adopted the same geometry. This was due
in part to the evolutionary nature of automobile styling which has often tried
to avoid the “shock of the new” and in part to regulations, especially those
which applied in the US.
Jaguar S-Type (1963-1968, left), Vanden Plas Princess R
(1964-1968, centre) and Volvo 164 (1968-1975, right).
Although most would regard the technique which
essentially integrated the driving lamps/fog lamps into the coachwork as just a
variation on the diagonal theme, professional designers insist not; they say
this is just wrapping enveloping bodywork around an existing device. Also, the professionals prefer the term “canted
headlamps” because “diagonal” has a more precise definition in mathematics.
Rover 3.5 Coupé (P5B 1967-1973, left) and Packard Coupe
(1958) (right)
While the US manufacturers usually re-tooled in 1957-1958
after regulations had been changed to allow quad head-lamps, the British were
often fiscally challenged and needed to continue to use existing sheet
metal. A design like the Vanden Plas
Princess R (and the companion Wolseley 6/99 & 6/110 (1959-1968)) has sufficient
space to allow the diagonal placement but the Rover P5 (1958-1967) with its
wider grill precluded the approach so the expedient solution was to go
vertical. Although obviously just “bolted
on”, such was the appeal of the P5B it just added to the charm. It could have been much worse because less
charming was the 1958 Packard Coupe, produced by Studebaker-Packard, the
company an ultimately doomed marriage of corporate convenience which seemed at
the time a good idea but proved anything but. Studebaker-Packard lacked the
funds to re-tool to take advantage of the rules allowing four head-lamps but
without the feature their cars would have looked even more hopelessly outdated
than they anyway did so cheap fibreglass “pods” were produced which looked as “tacked
on” as they were. They were the last
Packards made and Studebaker’s demise followed within a decade.
1963 Zunder
The Zunder ("spark" in German) was produced in
Argentina between 1960-1963 and used the power-train from the Porsche 356. The body was fashioned in fibreglass and was
one of the many interesting products of the post war industry in Brazil and
Argentina, the history of which is much neglected. By the standards of time, it was well-built
but as a niche product, was never able to achieve the critical mass necessary
to ensure the company’s survival and production ceased in 1963 after some 200
had been built.
Buick Electra 225 (First generation 1959–1960, left) and
(Lincoln) Continental Mark III (1958-1960, right). The Buick adopted horizontal headlamps in
1960.
In the late 1950s, most US manufacturers did have cash to
spend and the industry spirit at the time was never to do in moderation what
could be done in excess although by comparison with the Lincoln, the Buick
verged on the restrained. Tellingly, the
Buick sold well while the Continental was such a disaster Ford considered
sending Lincoln to join Edsel on the corporate scrapheap and the nameplate was
saved only because it was possible at low cost to re-purpose a prototype Ford
Thunderbird as the new Continental.
Rarely has any replacement been such a transformation and the 1961
Continental would influence the design of full-sized American cars for twenty
years. It used horizontally mounted head-lamps.
1961 Chrysler 300 G.
Chrysler’s “Letter Series 300” (1955-1965) coupes and
convertibles were the brightest glint in the golden age in which Detroit’s power
race was played out in the big cars, an era which would be ended by the
introduction of the intermediates and pony cars in the 1960s. The 300G (1961) was visually little changed
from the previous year’s 300F but the simple change to diagonal headlamps was
transformative. There were those who
didn’t like the look but generally it was well received and as a first
impression, the feeling might have been Chrysler had mastered the motif in a
way the Continental Mark III proved Ford just didn’t get it.
1961 DeSoto Adventurer (left), 1962 Dodge Dart (centre)
and 1963 Dodge Polara (right).
However, Chrysler’s designers in the early 1960s may have
decided they liked diagonal headlamps which was good but seemingly they liked
them so much they though the buyers should be offered as many permutations of
the idea as could be made to work on a production line. What’s remarkable is not that the public didn’t
take to the approach but that it took the corporation so long to admit the
mistake and try something more conventional.
Just to hedge their bets, while Dodge, Plymouth and DeSoto all had
headlamps mounted at an obvious degree of cant, on the Chryslers the effect was
so subtle one really needed to hold a spirit level to the front end to confirm
there was an slant, albeit one imperceptible to the naked eye. The one division which never were the diagonal
way was the Imperial but it’s headlamp treatment was more bizarre still.
1961 DeSoto styling proposal (September 1958) for the
1961 range.
For DeSoto, things could have looked worse even than they
did, some of the implementations of the diagonal motif which went as far as
clay models or actual metal prototypes so bizarre one wonders what external influences
were being studied (or inhaled). As it turned out,
1961 would be the end of the line for DeSoto, a nameplate which had been
successful as recently as the mid 1950s.
Its demise was little to do with diagonal head-lamps (though they didn’t
help) but a product of Chrysler’s other divisions expanding their ranges up and
down, encroaching on a market segment DeSoto once found so lucrative. The phenomenon was a harbinger of the
eventual fate of marques like Mercury, Pontiac, Oldsmobile and Plymouth.
Clockwise from top left: Fiat 8V (1952-1954),
Gordon-Keeble GK-1 (1961-1967), Jensen C-V8 (1962-1966) and Triumph Vitesse
(1962-1971).
Perhaps surprisingly, the French majors were never enamored,
presumably because Citroën and Renault didn’t like to be imitative and Peugeot
were too conservative. Some of the Europeans
did dabble with the idea, embracing it as an expression of modernity although the
then radical treatment of the head-lamps sometimes struck a discordant note
when they were grafted onto something where the rest of the platform was so
obviously from one or two generations past.
Fiat’s exquisite 8Vs didn’t all get the diagonal look but those which
did remain the most memorable of the few of the breed built. An unqualified aesthetic success was the
Gordon-Keeble built to aviation standards and powered by a Chevrolet V8. It deserved to succeed but floundered as much
of the British industry did in the era because of a lack of capitalization and
an accounting operation which didn’t match the quality of the Engineering. More successful was the Jensen C-V8 but while
the distinctive front end now makes it much prized by collectors, at the time
it was less admired and its very presence served only to emphasize how
antiquated the rest of the styling had become.
For its replacement, Jensen tuned to an Italian styling house and the
Interceptor, introduced in 1966 and remembered for the vast expanse or rear
glass, is now thought a classic of the era.
The one which sold best was the Triumph Vitesse, one of a number of
variations built on the robust and versatile separate chassis of the Herald
(1959-1971) including the Spitfire and GT6.
Somewhat the BMW M3 of its day, the Vitesse’s front end actually lived
on in India (though without the lusty six cylinder engines) but curiously, the
inner headlights weren’t fitted.
Gilding the lily: The Lancia Fulvia coupé (1965-1976)
before & after.
The lovely, delicate lines of the Lancia Fulvia were
perfect and really couldn’t be improved.
The unfortunate facelift with the canted lights was no improvement.
