Ways to Remember the Meaning of Circumference, Radius, Diameter, and Chord

Date: 03/18/2004 at 16:20:34
From: Johnathan
Subject: Circle parts

If the minute hand touched the edge of the clock, would it be most 
like a diameter, radius, circumference, or chord of a circle?  I have
a hard time remembering what each of those means.

Date: 03/18/2004 at 16:45:45
From: Doctor Peterson
Subject: Circle parts

Hi, Johnathan.

You need to learn these words!  Since different people learn words in 
different ways, I'll show you a few ways to think about these circle
terms.

Some people just like pictures.  Here is a picture showing what each 
term refers to:

                      ooooooooo
                oooooo         oooooo
             ooo                   / ooo
           oo                     /     oo
         oo                      /        oo
        o                       /           o
       o                 radius/             o
      o                       /               o
     o                       /                 o
     o                      /                  o
    o                      /                    o
    o---------------------*---------------------o
    o                 diameter                  o
     o                                         o
  c  o                                         o  e
      o                                       o
    i  o                                     o
        o             chord                 o   c
      r  oo-------------------------------oo
           oo                           oo   n
         c   ooo                     ooo
                oooooo         oooooo    e
             u        ooooooooo
                  m                 r
                        f     e

Some people like definitions in words:

  The circumference is the outside of a circle, the distance around.

  A diameter is a segment through the center, from one side to the
  other.

  A radius is a segment from the center to the outside
  (circumference).

  A chord is any segment joining two points on the circumference.

Some people like to make connections with other words or ideas.  Here 
are some that may make the words memorable:

  "Circum-" means "around", as in Magellan's circumnavigation of
  the world (going around it); and it sounds like "circle", which
  is what the circumference really is!

  "Dia-" means "through"; and sometimes we say that two ideas are
  "diametrically opposed", meaning that they are on opposite sides,
  as far apart as possible.  The diameter connects opposite sides of
  the circle.

  "Radius" reminds us of radiation; rays go out from the center of
  the sun, for instance, in all directions. Picture the circle as the
  earth's orbit, and a ray of light going from the sun at the center
  out to the earth.

  A "chord" is like a cord stretched across the circle.  In fact,
  that's where the word comes from.  The Greeks saw an arc (part of
  a circle) as a bow, and a chord as the bowstring.  The word "arc"
  means "bow", as in "archery"!

Or, if you like silly little tricks for memory, try these, which I 
just made up:

  Circumference starts with a C, which is curved; it means the
  curved part of the picture, the circle itself.

  Diameter starts with a D, which looks like half a circle; the
  straight line on the left is the diameter.

  Radius ... well, the slanted straight line of the R goes out from
  the middle like a radius.

  And a chord is any line in a circle that isn't special!

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/