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Left Angles


Date: 06/01/99 at 22:13:07
From: greg
Subject: Geometry

What is a left angle? I know it is not a right angle and is not 90 
degrees. Our math teacher will give us a prize if we can get this 
question right. Please tell me!


Date: 06/02/99 at 08:26:44
From: Doctor Peterson
Subject: Re: Geometry

Hi, Greg.

There's no such thing as a left angle, unless someone has recently 
invented it just for fun. But this is a fascinating question for those 
of us who like both words and math. The word "right" has so many 
meanings that it can be confusing to figure out which one to pay 
attention to; a "right angle" has nothing to do with right- or left-
handedness.

Think about all the different things "right" can mean:

As an adjective or adverb:
    correct, true, proper ("the right thing to do")
    opposite of left ("my right hand")
    perpendicular ("a right angle")
    straight ("right toward the goal")

As a verb:
    correct ("righting wrongs")
    make upright ("right the boat")

As a noun:
    privilege ("I have a right to ...")

It's related to the Latin adjective "rectus," which is the past 
participle of the verb "rego" meaning "to direct, lead, or rule"; from 
these words we also get such words as "direct," "correct," "erect," 
"rectangle," "rectify," and "rectitude" (as well as "regulate" and 
"regal"). "Rectus" has pretty much the same range of meaning as 
"right" in English, as you can tell from this list: straight, upright, 
perpendicular, correct, proper.

The Greek equivalent is "orthos," which again means either "straight," 
"perpendicular," or "correct." Your orthodontist, of course, 
"straightens" your teeth, and "orthogonal" means a right angle. The 
basic meaning is "straight"; if you take this as "standing straight," 
it means "upright" or "vertical," which is where we get the meaning of 
perpendicular: a right angle is one that stands up straight. This was 
the word used by Euclid in geometry. Take "upright" figuratively, and 
you get the moral meaning of "upright"; and since a straight line 
isn't crooked and goes where it is supposed to, it is also "correct."

So I would say that we call a right angle "right" because it is 
"upright" or "erect." The real mystery is, why is the right hand 
called right? That's where the bias against left-handers comes in. 
Greek and Latin both have words for the right side (dexios, dexter) 
that are unrelated to their words for "straight." So it must be in 
English or its precursors that right-handedness became "right" - the 
"correct" hand to use if you want "dexterity."

Here's a diagram to show how the various meanings are related:

                          +--> perpendicular
                         /
    straight ---> upright ---> proper
            \
             +---------------> correct ---------> right (hand)
    \_______________________________________/
                 orthos, rectus
    \________________________________________________________/
                               right

Since a "right" angle has nothing to do with left and right, there's 
no reason for a "left" angle to exist.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Definitions
Elementary Two-Dimensional Geometry
Middle School Definitions
Middle School Two-Dimensional Geometry

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