While at a Chinese restaurant, looking at a place mat with info on the
Chinese Zodiac, I thought of a way to make its cyclical nature easier
for a 6-year-old to understand.  Like the way, in trigonometry, it is taught
that radian angle measure wraps around the circle--how about repeating
the 12 Chinese zodiac sign names along a spiral? Leaving space to write
family and friends' names would be a touch the makers of the place mats
had left out.  Hopefully it would be a fun chart for a 6-year-old to fill in.

It occured to me that the only thing I knew that could produce a
smooth spiral with precise placement of labels according to a formula
would be PostScript, through a program I might hopefully be able to write.
What I didn't know was that I'd have to use cubic splines to do the job right.


If you want to go into the details of when exactly a Chinese New Year starts,
here's what I found...

 The Winter Solstice occurs on Dec 21 or 22 under the Julian Calendar
    (the leap day system keeps it that way).

 The first day of the Chinese New Year is the day of the 2nd new moon
    after the Winter Solstice (based on 120 degrees East meridian, as of 1928,
    prior to that, calculations were based on Beijing time (116E).
    This is 30 to 59 days later, depending upon the age of the moon at
    Winter Solstice.  That corresponds to 21 Jan to 21 Feb on the
    Julian Calendar (the discrepancy probably lies in the occasional use of
    leap days in the Gregorian Calendar to synchronize it with the equinoxes).

 So technically, the Gregorian Year of your birth is not all you need to know
 to determine your animal sign under the Chinese Zodiac.

 Chinese New    Gregorian
  Year's Day      Date

     4706      26 Jan 2009
     4705       7 Feb 2008
     4704      18 Feb 2007
     4703      29 Jan 2006
     4702       9 Feb 2005
     4701      22 Jan 2004
     4700       1 Feb 2003
     4699      12 Feb 2002
     4698      24 Jan 2001
     4697       5 Feb 2000
     4696      16 Feb 1999
     4695      28 Jan 1998
     4694       7 Feb 1997
     4693      19 Feb 1996
     4692      31 Jan 1995

  Some sources on the web:
     http://www.math.nus.edu.sg/aslaksen/calendar/chinese-talk.pdf
     http://www.chinapage.com/newyear.html

 Chinese Zodiac...  [based on a Chinese restaurant's paper place mat]
   RAT    - You are ambitious yet honest.  Prone to spend freely.  Seldom
            make lasting friendships.
   OX     - Bright, patient and inspiring to others.  You can be happy by
            yourself, yet make an outstanding parent.
   TIGER  - Tiger people are aggressive, courageous, candid and sensitive.
   RABBIT - Luckiest of all signs, you are also talented and articulate.
            Affectionate, yet shy, you seek peace throughout your life.
   DRAGON - You are eccentric and your life complex.  You have a very
            passionate nature and abundant health.
   SNAKE  - Wise and intense with a tendancy towards physical beauty.  Vain
            and high tempered.
   HORSE  - Popular and attractive to the opposite sex.  You are often
            ostentatious and impatient.
   SHEEP  - Elegant and creative, you are timid and prefer anonymity.
   MONKEY - You are very intelligent and are able to influence people.
            An enthusiastic achiever, you are easily discouraged and confused.
   COCK   - A pioneer in spirit, you are devoted to work and quest after
            knowledge.  You are selfish and eccentric.
   DOG    - Loyal and honest, you work well with others.  Generous yet
            stubborn and often selfish.
   BOAR   - Noble and chivalrous.  Your friends will be lifelong, yet you are
            prone to marital strife.  Avoid other Boars.

 Compatibility summary (inferred by Robert):
   4 in either direction (120 degrees) are the most compatible signs.
   6 in either direction (180 degrees) is the least compatible sign (exc. Boar).