XV

Fifteen years! 15 years, that’s 5479 days, including 4 days for leap years, that’s 328,740 minutes, or 19,724,400 incredible seconds the Renaissance Mathematicus has polluted the Internet. I am more than a little flabbergasted, I really do have to repeat what I have said on more than one occasion, when I started this blog I didn’t think I would last more than six weeks. Now 1211 blog posts and more than 11,000 comments later, fifteen years have passed and I wonder where they have gone.  I have led a life that was full of change, different jobs, different countries, different courses of study, without finishing any of them and one thing I realised writing this, being a #histsci blogger for fifteen years is the longest period I have stuck to anything in my whole life. I think I might just have found my niche in life.

Fifteen is not a particularly interesting number. It is the product of three and five the first two uneven primes and that’s about it. A fifteen sided polygon is a pentadecagon and an internal angle of 156°, which is constructible with compass and straight edge. Because it has so many edges and vertices it has quite a lot of symmetries.

The symmetries of a regular pentadecagon as shown with colours on edges and vertices. Lines of reflections are blue. Gyrations are given as numbers in the centre. Vertices are coloured by their symmetry positions.(Wikipedia)

It also has three regular star polygons: {15/2}, {15/4}, {15/7}, and three regular star figures: {15/3}, {15/5}, {15/6}

{15/2} Interior angle 132°

{15/3} Interior angle 108°

{15/4} Interior angle 84°

{15/5} Interior angle 60°

{15/6} Interior angle 36°

{15/7} Interior angle 12° All diagrams Wikimedia Commons

The regular pentadecagon is the Petrie polygon for some higher-dimensional polytopes, projected in a skew orthogonal projection

14-Simplex 14D
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions The simplex is so-named because it represents the simplest possible polytope in any given dimension.

Fifteen years, one and a half decades, is called a “quindecennium” or a “quindecade.” More interesting for a blog that often pokes around in the Middle Ages, it is also known as an indiction. An indiction was a fiscal period of fifteen years, instituted by Constantine in 313 CE (but counting from 1st September 312), used throughout the Middle Ages as a way of dating events, documents etc.

Bible chronologist, Joseph Justus Scaliger (1540–1609) used the indiction in his Julian period, which he used to determine the date of creation, to quote myself:

Scaliger defined something he called the Julian Period of 7980 years, which was a product of three different dating cycles: The 19-year Meton cycle used in lunar-solar calendars, such as the Jewish one, the 28-year solar cycle, which is the number of years it takes for days of the week to repeat in the Julian calendar and the 15-year indiction cycle used for dating medieval manuscripts. Working backwards 4731 BCE is the last time that all three cycles were in their respective first years. Scaliger chose this date because it preceded his own calculated date for creation, 3949 BCE. With a unified scale Scaliger could give a Julian year number to any historical event within his research, thus making cross-cultural comparisons possible.

Indictions seem to have played a role in my life. I was fifteen years and five days old, when my mother died under, for me, traumatic circumstances, as I’ve documented elsewhere. I celebrated my second indiction, my thirtieth birthday, here in Franconia, a couple of weeks after I had decided to stay and settle down here, at least for the foreseeable future, on the holiday trip that originally brought me here. On my sixtieth birthday, the end of my fourth indiction I acquired my first iPad, my birthday present from my siblings. I have another two and a half years till the end of my fifth indiction, I wonder what that will bring. 

As is my wont at the end of my bog’s annual journey around the sun, I thank all of those who have engaged with my humble efforts, those who have simply read them, those who have commented, and especially those who have dared to contradict, from whom I often learn something new. Learning is what keeps me focused and stops me going insane.