Calculating Using Dates AD and BC

Date: 11/25/2003 at 09:17:56
From: Theodore 
Subject: How do you work the BC & AD math problems

How do you calculate how many years there are between dates where one
is given in years B.C. and the other is in years A.D.?  For example,
how many years were there from 15 B.C. to 63 A.D.?

Do you start with zero or not?  I just start with zero and add the
B.C. amount, then add the A. D. amount.  Is that correct?

Date: 11/25/2003 at 12:21:14
From: Doctor Peterson
Subject: Re: How do you work the BC & AD math problems

Hi Theodore.

Thanks for writing to Dr. Math.  As discussed here

  Year 0
    http://mathforum.org/library/drmath/view/52475.html 

there was no year 0; that forces us to make an adjustment when we 
compare A.D. and B.C. dates.  If there were a year 0, the time line 
would look like this:
                   __________________________________
                  /                                  \
  <-+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-->
     -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9

(I've put the numbers between the marks because a given year spans 
the time from Jan 1 one year to Jan 1 the next.)

Then you could find the time from, say, June 1, 5 B.C. to June 1, 7 
A.D. by subtracting a negative number:

  7 - -5 = 7 + 5 = 12 years

That amounts to what you do: there are 5 years before 0, and 7 years 
after, making a total of 12.

But in fact there was no year zero, because the people who invented 
the B.C./A.D. system didn't know about the number zero yet.  (That 
was, of course, long after the year zero, but still a long time ago!) 
So reality looks like this:
                   _______________________________
                  /                               \
  <-+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-->
     -9 -8 -7 -6 -5 -4 -3 -2 -1  1  2  3  4  5  6  7  8  9

To make that, I just deleted one year's worth from a copy of the 
first version--and that's all you have to do to find the difference 
between dates.  After you subtract the first date from the second, you 
subtract one year if the non-existent year zero would have been 
between them.

  (7 - -5) - 1 = 12 - 1 = 11 years.

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

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

Date: 11/25/2003 at 20:29:40
From: W. Theodore 
Subject: Thank you (How do you work the BC & AD math problems)

Dr. Math, I would like to say thank you for your help.  I am home-
schooled and my text has nothing to say about that topic. 

Thanks again!