# Question: I have a collection of National Geographic magazines. The very first issue was released in October of 1888. Every month, a new issue is released. National Geographic uses volumes and...

**Question:** I have a collection of National Geographic magazines. The very first issue was released in October of 1888. Every month, a new issue is released. National Geographic uses volumes and "issue numbers" to categorize their magazines. Every six months. (every 6 magazines) represents one volume. Each year is two volumes. For example, the October 1888 issue is volume 1, "issue" number 1. November 1888 January -- June is Volume 2, Numbers 1 - 6. November 1888, July -- December is Volume 3, Numbers 7 - 12.

**What I need to do:** I want to create an equation that, given the month of publication, and year of publication, can determine the Volume number and "issue number".

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### 1 Answer

The information you have is only partially correct.

From 1888 to 1913 each year was assigned a volume and the issues ran from 1 to 12, indicating the month number. Thus June 1907 was volume 17 issue 6 while November 1907 was volume 17 issue 11.

Starting in 1914 each year was split into 2 volumes; each volume was numbered from 1 to 6. So May 1914 is volume 25 issue 5 while November 1914 is volume 26 issue 5.

The formula you will need is a piecewise function given in the attachment.

Given the year y=xxxx and the month m; if y is less than or equal to 1913 then the volume is y-1889 and the issue is the month.

If y>1913, then if m less than or equal to 6 the volume is 2y-3803 while if m>6 the volume is 2y-3802.

If m is less than or equal to 6 the issue is m; if m>6 the issue is 12-m.

Thus for October 1988, the volume is 2(1988)-3802=174 and the issue is 4.

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**For the problem as stated**: Assume that each year has two volumes. The first volume is numbered 1-6 while the second volume is numbered 7-12.

Now suppose you are given the year in the form y=xxxx and the month m as a number from 1-12.

The issue number would be the month number.

The volume number could be found as 2(y-1888)+|_ m/6 _| where the symbols around the m/6 indicate the floor function. The floor function (or greatest integer function) returns the largest integer that is smaller than the given value. So is m=5, gif(5/6)=0 while if m=7, gif(7/6)=1.

So for May 1890, the volume is 2(1890-1888)+0=4 and the issue is 5.

For November 1890, the volume is 2(1890-188)+1=5 and the issue is 5.

Again, this is incorrect for the actual numbering system.