In this section, we propose some ideas for bringing the history of the misseri-calendar to the classroom.
For instance, an interesting question for students to consider is why the use of the misseri-calendar survived for as long as it did. Some possible answers to this question include the following:
It had been in use for two centuries before the introduction of the Christian calendar.
It was maintained as a secular calendar by law, contained in the oldest collection of laws, Grágás [16], registered in a mid-thirteenth-century manuscript Konungsbók. It is thus rooted in the medieval literary heritage which was studied in Iceland through the centuries.
In northern latitudes such as in Iceland, the difference between darkness in winter and brightness in summer is extreme. Celebrating midwinter and First Summer Day and counting the weeks in-between is a tribute to the light and is intimately related to life in northern Nature.
The habit of counting the years in whole weeks and the need to insert the Summer’s Extra Week every fifth or sixth year, may also interest students. They might, for example, work out the number of days during a 40-year period, called the Solar Cycle, in the misseri-calendar, and compare it to the number of days in 40 years using the regular Roman calendar.
Modeling the track of the Sun using the graph of a cosine function with the aid of graphical software, such as GeoGebra, offers a variety of options. Students might draw graphs of the Sun track at their particular latitude at different times of the year. They could then compare the actual times of sunrise and sunset to their models after taking the geographical environment into account. They could also compare their results to those for Iceland or Rome. The formula that is used in this paper is adjusted to northern latitudes: \[f(x) =\, – (90\, –\mbox{latitude})\cos\left (\frac{2\pi}{360}x \right).\] At summer and winter solstices, this formula becomes, respectively, \[f(x) =\, – (90\, –\mbox{latitude})\cos\left (\left (\frac{2\pi}{360}+23.44 \right)x \right)\] and \[f(x) =\, – (90\, –\mbox{latitude})\cos\left (\left (\frac{2\pi}{360} -23.44 \right)x \right).\] These formulas can easily be adapted to southern latitudes. A more advanced student project would be to determine the accuracy of these simulated paths in comparison to the sun’s actual path using formulas from spherical trigonometry.
E. G. Richards [17] recounted many calendars used at various times and places around the world. For instance, he described a prehistoric calendar from the Neolithic age (4500–2200 BC) that was postulated by Alexander Thom based on alignments found in megalith structures in various parts of Britain [18]. In particular, sunrise alignments within a megalith could be used to identify the solstices, as well as two particular days surrounding each solstice, one occurring about 23 days before a solstice and the second about 23 days after it. Accordingly, the re-constructed calendar divided the year into 16 months of about 23 days each, but not all of equal length. After being given this information, students could be asked to determine possible divisions of the year that would correspond to such a calendar. Decisions to be made would include deciding when the year would begin (i.e., when "Month 1" begins relative to our current calendar), where the solstices and equinoxes would fall, and which particular months would be shorter (or longer) than 23 days in order to give the entire solar year [19]. As an extension, students might also be asked to consider the problem of ensuring their calendar was constructed in such a way that a reasonable approximation to the average of 365.2422 days in a solar year was reached in an acceptable number of years, possibly by inserting a month at a regular interval, or regularly adding a day to one of the months.
Teachers might also wish to discuss with their students the history of calendars and timekeeping more generally, and the misseri-calendar in particular. For instance, students could research the origins of English words, phrases, and proverbs related to various systems of timekeeping.
Figure 8. The famous megalith Stonehenge at sunrise on July 30, 2007.
[16] Grágás. Konungsbók. Laws of early Iceland: Grágás, the Codex Regius of Grágás, with material from other manuscripts. 1980–2000. Translated by A. Dennis, P. Foote, R. Perkins. Winnipeg: University of Manitoba Press.
[17] Richards, E. G. 1998. Mapping Time. The Calendar and its History, p. 141-144. Oxford: Oxford University Press 1998.
[18] Thom, Alexander, Megalithic sites in Britain, Clarendon Press, Oxford, 1967.
[19] Richards, p. 142, provides a table illustrating Thom’s hypothetical division of the year.