Mathematical Recreations

One of my main interests for many years has been in mathematical recreations, as will be evidenced by my Mayhematics pages, although I've not done much original work lately. However, I would like to get back to doing some.

Recently I have been receiving emails from various people active in mathematical recreations, who are furthering some of the subjects that have particularly interested me in the past. I give here some links to websites showing their work.

The following are investigating magic knight's tours on three dimensional boards, among much else: Aale de Winkel, Awani Kumar, Harvey Heinz and Francis Gaspalou.

I have also heard from Vaclav Kotesovec who is studying leaper and hopper tours, revisiting work done by myself and T. H. Willcocks in my magazine Chessics as far back as 1976. In particular he has constructed a 64-cell closed grasshopper-over-knight tour. It begins with Grasshopper a1 and Knight f6 and ends with the Grasshopper back at a1 and the Knight at b1.

Green Shoots of Spring

Another photo of the tree opposite my front door shows the green shoots of spring appearing at last. There are also road works going on, but these seem to be all year round.

Some of the seagulls are acting crazy, shouting and dancing in the road, but I've not been able to get a photo of them so far. From my windows I also see a lot of pigeons of variegated colours. I put a query about this on the Dawkins Forum. Apparently this is because they are feral pigeons, descended from domesticated pigeons, whose colours have been selected by pigeon breeders.

Monday night I went to the Hastings Writers' Group. It was submission day for a Mystery story of not more than 2000 words. We read extracts from what we had written, up to a cliff-hanging point where others could start to guess what the solution to the mystery would be. My own story was about the missing portraits of Robert Hooke, the 17th century scientist.

Astronomy Picture of the Day

The Astronomy Picture of the Day site is one I often look at. Here are two recent and two older images that I particularly recall.

Melk Abbey manuscript c.1490 showing the Ptolemaic view of the universe, pre-Copernicus.

M101 pinwheel galaxy everyone's idea of a galaxy.

In the Shadow of Saturn a view of Saturn's rings, looking back towards Earth, which is just a tiny dot.

Cat's eye Nebula like a flower in the sky.

Lazybones

Tuesday last week (31 March), I took a walk along the front to Bexhill and back. It was a lovely sunny day with a blue sky and calm sea. Unfortunately I forgot to take my camera. It's much as I remember it from ten years ago, though many more rocks have been put in place to keep the sea at bay from the adjacent railway line. If or when the expected sea-level rise occurs, as a result of global warming, the line will be the first thing cut off.

This Easter weekend, as often lately, I have been spending time listening to the countdown of favourite music on Classic FM, and doing the crossword and number puzzles in the Guardian. The Easter crossword puzzle which as usual is by my favourite composer "Araucaria" was really enjoyable, though I had to look in the dictionary a good deal for words I'd never heard of. His clues are always very fair however, if you have the right answer it is always clear that it is the right answer.

I feel rather guilty at times that I ought to be doing more creative things. But with puzzles you always know that there is a solution. Whereas with more recondite problems you can spend hours and days and months and even years and get nowhere. Perhaps I don't have sufficient incentive, such as desire for fame and fortune, or perhaps I'm just lazy. What would incentivise me to get back to serious work I wonder?

Kepler's Lenten Pretzel

A 400th Anniversary. One of the figures in the book by Owen Gingerich reviewed last time is Johannes Kepler's diagram, from his Astronomia Nova (1609) which he likened to a "panis quadragesimalis" or Lenten Pretzel. It shows the path, relative to the Earth, taken by the planet Mars during the years 1580 to 1596, based on the observations of the astronomer Tycho Brahe. "Mars repeatedly approaches the Earth, makes a backward loop, only to recede and repeat the process roughly two years later at a spot in the zodiac about fifty degrees to the east of the previous loop. The loops themselves trace round the entire sky in approximately seventeen years during which time Mars itself circumnavigates the sky eight times." Ptolemy and Copernicus (relying on less accurate data) had tried to explain this convoluted orbit as a combination of circular motions in various ways. Kepler resolved the problem by showing that the answer was to use elliptical orbits.