Date: 10/19/98 at 15:58:19 From: Ann Warger Subject: "Year 0" While working with my eighth grade Algebra class, we came across the fact that between 10 B.C. and 10 A.D. there were really 19 years rather than 20. The book stated that there is no year 0. The only information I could find on this was from a History college professor who said that this is accurate, because the year between 1 B.C. and 1 A.D. is , historically, the 14th year of the reign of Augustus. Do you have any more information that you could pass on to me? I am also now unsure how to answer the questions in my other textbooks that really use B.C./A.D. as an example of a number line with 0 as the origin. Our social studies teacher is also wondering how she should treat this. Thank you for your help. Ann
Date: 10/19/98 at 18:24:38 From: Doctor Rick Subject: Re: "Year 0" Hello, Ann. Thanks for asking this question, it's a good one. To answer it, we need to look at the history of the calendar, and the history of math. BC dates were not used in the BC era. That's pretty obvious if you think about it. :-) As a matter of fact, AD and BC were not invented until around AD 525, by Dionysius Exiguus. Still, AD 525 is far enough in the past that people in Europe didn't have a clear idea about negative numbers. In fact, it wasn't until 1657 that a mathematician (John Hudde) used a single variable to represent either a positive or a negative number. For all those years until 1657, positive and negative numbers were handled as separate special cases. For instance, quadratic equations were solved by separate methods for 6 cases: ax^2 = bx, ax^2 = c, bx = c, ax^2 + bx = c, ax^2 + c = bx, and bx + c = ax^2 -- zero was a special case, too. (This was the approach of al-Khwarizmi in the Arabic book that gave algebra its name, about AD 830.) Let's get back to Dionysius. He identified the year 1 AD ("1 Anno Domini," the first year of the Lord) as the year that Christ was born (he was probably off by 4 to 6 years). The previous year was 1 BC, the first year "Before Christ." (I have not figured out why one abbreviation is in Latin while the other is in English.) Dionysius would not have thought of 1 BC as the year -1; he would not have thought of putting BC and AD together on a number line (time line). BC and AD were two separate cases. To find the time between two AD dates, you would take their difference; to find the time between an AD date and a BC date, you would add them and subtract 1. This would not be seen as a problem; it's just the way they solved quadratics - a set of special cases. It's a challenge to try to see the world as people saw it before key concepts were developed. It also gives perspective in dealing with students who are having trouble grasping concepts like negative numbers - we are asking them to lay hold of ideas that were missed by many generations of intelligent people! To answer your specific questions, it is incorrect to introduce negative numbers using a time line. If we had it to do over again, we would certainly make it so that a time line would work - but we are stuck with a year-numbering system that predates the integers, and we can't pretend otherwise. On the other hand, we sure have a great way to bring up the history of a key mathematical concept! ONLINE BIBLIOGRAPHY Here is an interesting Web page about the origin of the calendar (see the section "Century and Millennium"). http://ourworld.compuserve.com/homepages/Larry_Freeman/calendar.htm Here is another (see the section "The start of Anno Domini Dating"). http://ourworld.compuserve.com/homepages/khagen/Easter.html#AD Here is a Web page about the origin of negative numbers. http://www.seanet.com/~ksbrown/kmath298.htm This page is my reference for John Hudde. http://jeff560.tripod.com/variables.html And this is my reference for al-Khwarizmi. http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Al-Khwarizmi.html - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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