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# Mathematics and Primary Sources: In Search of the Perfect Calendar

This post is by Michael Apfeldorf of the Library of Congress.

Sometimes analyzing primary sources can help us reflect on commonplace aspects of our culture that we take for granted, illustrating how arbitrary they are, or how they change over time.

Joseph Collins’ 1939 “Proposed Utopian Calendar” provides one such example – an attempt by Collins to reform the Gregorian calendar, which had been in place for more than 350 years and which we still use today. The proposed calendar offers students the opportunity to practice historical, mathematical, and scientific reasoning to reflect on how humans have historically sought to organize our activities.

Start by asking students to make observations, reflections, and questions related to the first page of the document. Focus questions might include:

• How is the Collins’ calendar similar to the one we use today? how does it differ?
• Why do you think Collins wanted to design a new calendar?
• What are advantages and disadvantages to his proposed system?

Students will likely notice the consistent 28 day months, causing each numerical date to fall on the same day of the week each year. They may also notice that the proposed calendar uses 13 months and has eliminated leap years. But the mathematically savvy might also reason that 13 months x 28 days/month equals 364 days, and wonder how this calculation is reconciled with the actual time it takes for the Earth to revolve around the sun.

The two sets of rings surrounding the square calendar offer more opportunities for analysis. The inner ring represents the Gregorian calendar we use today; the outer represents the Proposed Utopian Calendar; together they serve as a conversion tool to help make the switch.

Next, direct students to examine Collins’ commentary on the following page for a summary of his changes, his rationale, and for directions on how people can find their “real” birthday. Students may note that Collins will mail the calendar anywhere in the world for 25 cents!

Using this commentary, challenge students to work out Collins’ mathematics to see if it works – or doesn’t – with the 13 month, 28 day calendar on the previous page. Do the numbers add up if you still assume a 24 hour day with no leap days? If not, can you think of a way to make it work?

The tricky mathematics involved underscores the problems that face anyone attempting to devise a calendar that not only aligns with astronomical cycles but also provides people with stable, easy-to-use increments with which to organize their activities.

Analyzing this calendar also might lead to additional student investigations, such as:

Students might even be challenged to create their own “perfect calendar.”  Let us know what creative insights your students come up with!
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