Johann Carl Friedrich Gauss – ein Geburtstagsgruß – A Birthday Tessellation for April 30th.

According to Wikepedia, Chapter m Verse n among the mathematical achievements of Carl Friedrich Gauss was the calculation of his own birthdate, by a process akin to calculating the date of Easter for a given year, which process many of us tried out to while away the time when small enough to consult the back of the Anglican Book of Common Prayer unseen by the vicar sermonising from the pulpit. Gauss calculated that a Wednesday, eight days before the Feast of the Ascension must be  30th April 1777.

Gauss was born in Braunschweig, by the way, which must be an important historical city because, as with Köln, München, Nürnberg and Regensburg, English speakers have coined their own version of its name; Brunswick.

No doubt there were many, probably an infinity, of other solutions to the equations determining the birthdate of Gauss all but one of which he rejected on dubious axiomatic grounds, certainly dismissing  those solutions still in the future. However mathematicians even in Gauss’s day had grown to allow variables to take on values once thought nonsensical – negative, irrational, imaginary, infinitesimal, transfinite – so we  should  keep a lookout for mathematical prodigies born on any Wednesday 3oth. April eight days before the feast of the Ascension.

Here is a tessellation, Trefoil Lattice Labyrinth (30,4) dedicated to the memory (i.e. the works) of Carl Friedrich Gauss and to anyone else born on April 30th. irrespective of the day of the week on which they first saw the light and its relation to the date of Easter, and also without regard to their ability as a Wrangler.

Trefoil (30,4) Gauss Birthday Final

Just six supertiles of the infinitely extendable tessellation are shown above; they are in two orientations at 180° to each other. Appropriately, the supertile of this lattice labyrinth is more branched than any oither I have yet constructed. It is made up of 30² + 30×4 + 4² that is 1036 equilateral triangles. To slightly anticipate the Find the Factors blog, this number = 37 x 7 x 2².

Here are some links to the inexpensive how-to-do-it  Lattice Labyrinths workbook which is available from the publisher or you-know-who , or from a good independent bookshop or via Google.


About davescarthin

After terminating academic and local government careers, long an independent bookseller/publisher at Scarthin Books, Cromford, Derbyshire, UK. An antiquarian bookseller in two senses, I now have more time to be an annuated independent post-doc, developing the long dormant topic of lattice labyrinth tessellations - both a mathematical recreation and a source of compelling practical tiling and textile designs. Presenting a paper and experiencing so many others at Bridges Seoul 2014 Mathart conference was a great treat, as were the spirited MathsJam Annual Conferences in November 2016 and 2017. I'm building up to a more academic journal paper and trying hard to find practical outlets in graphic design and landscape architecture. I submitted 8 ft square tiling designs to the Wirksworth Festival Art and Architecture Trail in 2016 and 2017. I love giving illustrated talks, tailored to the audience. Get in touch to commission or to collaborate.
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3 Responses to Johann Carl Friedrich Gauss – ein Geburtstagsgruß – A Birthday Tessellation for April 30th.

  1. ivasallay says:

    Gauss certainly deserves a lattice labyrinth that is more branched than any other you have constructed! It’s very nice looking as well. It will take a while before I get to 1036 on my blog, but isn’t 30² + 30×2 + 2² = 964, not 1036?


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