Talk:Right angle (geometry)

first sentence

The first sentence has the word angle in it five times! Surely this is excessive! Hayford Peirce 12:56, 14 August 2008 (CDT)

Indeed, I had put that on watch for when I felt able to concentrate on editing it. But for now I'll just crush that capital... - Not to mention ten angles in the rest! - Ro Thorpe 14:45, 14 August 2008 (CDT)

Maybe we should keep it and nominate it prominently somewhere as: "The single most inglorious sentence of all of Citizendium. And maybe Wikipedia, too...." Hayford Peirce 16:19, 14 August 2008 (CDT)

Thank you for your feedback. I look forward to your alternative proposals. --Miguel Adérito Trigueira 01:54, 15 August 2008 (CDT)

some positive proposals

• The Merriam-Webster 11th Edition Collegiate Dictionary, pretty much the standard USA dictionary of today, defines a right angle as: "the angle bounded by two lines perpendicular to each other; an angle of 90 degrees or 1/2 pi radians."

• The Concise Oxford Dictionary, Fifth Edition of 1964, defines it thusly: "neither acute nor obtuse, of 90 degrees, made by lines meeting not obliquely but perpendicularly"

• The American Heritage Dictionary of the English Language, Third Edition, a pretty hefty book of 1992, weighs in with "n. mathematics. An angle formed by the perpendicular intersection of two straight lines; and angle of 90 degree."

Unfortunately the offered definition "created when two straight lines meet perpendicularly at 90 degrees to each other." although it is in line with all of the above source material creates a circular definition with perpendicular (geometry). An alternative, that does not depend on the definition of perpendicular, would be better. --Miguel Adérito Trigueira 04:23, 18 August 2008 (CDT)

• And finally, from the absolutely majesterial (and final authority) Merriam-Websters Unabridged International Dictionary, Second Edition, of 1932, "the angle bounded by two radii that intercept a quarter of a circle; one fourth of a round angle, or one half of a straight angle. Two lines forming right angles are perpendicular to each other."

• Even poor old Wikipedia has this to say: "In geometry and trigonometry, a right angle is an angle of 90 degrees, corresponding to a quarter turn (that is, a quarter of a full circle). It can be defined as the angle such that twice that angle amounts to a half turn, or 180°.

Though these are much better then the previous ones, the first part (using radii of a circle), though true, depends too much on other definitions. The definition proposed earlier relied only on the definition of straight lines, angles, and equality, which is simpler, requires less external knowledge, and is not circular.

One phrase though sticks out in both its accuracy and simplicity is "one half of a straight angle" (though "straight angle" needs to be explained.)

In this vein, how about "the angle formed by a line extended from another which bisects the angle formed by the line itself in half"? (only 2 uses of the "offending word") --Miguel Adérito Trigueira 04:23, 18 August 2008 (CDT)

From current revision "The right angle bisects the angle of the line into two equal parts" thats almost perfect, how about

"In Euclidean geometry, a right angle, symbolized by the L-shaped figure ∟, bisects the angle of the line into two equal parts." --Miguel Adérito Trigueira 06:03, 18 August 2008 (CDT)

None of them, you will note, repeat the word "angle" over and over and over and over.... Hayford Peirce 11:34, 15 August 2008 (CDT)

At no point, it has been noted, has anyone expressed any insistence on the repeated use of the "offending word". Substance was its motive, not form. Kindly restore the substance, of the original, in any form deemed worthy... --Miguel Adérito Trigueira 04:23, 18 August 2008 (CDT)

formatting

comment was "some positive reformatting; you can't use indented spaces in the Wiki format." I see you changed my formatting from

Mathematical language

to

Mathematical language

I would like to point out that the "indented spaces" are indeed valid in the Wiki format, and that it furthermore indicates that special formating is desired. The original formating was as intended. If you disagree with the formatting for other reasons, then we can discuss it here. --Miguel Adérito Trigueira 11:31, 15 August 2008 (CDT)

Would you *really* say that yours looks better on the screen than mine? Hayford Peirce 11:36, 15 August 2008 (CDT)

It is not question of looks. It is appropriate to show certain things as preformated blocks (using "Leading space" wiki notation). Think of it as a diagram, but with words. The formating tells us that the following text is of an exact nature. Such things include code fragments (computer program eg. Programming_language#Strongly-typed_vs._loosely-typed), definitions, formula, demonstrations, theories, axioms, and proofs. In this case a demonstration.

Also note that things will look different depending on which "skin" is selected on "my preferences", which browser is being used, and even which operating system is being used. --Miguel Adérito Trigueira 04:58, 18 August 2008 (CDT)