Order 30 SPSS
Order 30 Simple Perfect Squared Squares have been divided into 5
separate menus accessible at left.
Order 30 is also provided as
spsso30.pdf(30M) for download, and a postscript file with 20 SPSSs per page, o30spss-20pp.ps (3.5M).
The smallest SPSS of of order 30 has a side of 201, the largest has a side of 2710.
- In 1979, P. J. Federico produced a table (Table II) in his 'Squaring Rectangles and Squares, A Historical Review with Annotated Bibliography' which stated there were no known SPSSs of order 30 as at 1977.
- In December 1994, in 'Album of Simple Perfect Squared Squares of order 26' by C.J. Bouwkamp and A.J.W. Duijvestijn, Bouwkamp wrote, " as of March 1, 1993 we know almost 700 SPSS of orders 27 through 30, of course a small fraction of the
possible ones. By the way, the total number of SPSS of order 30 could be something about one-hundred-thousand." This turned out to be a 5-fold over estimation.
- In 'Simple Perfect Squared Squares of order 27', published June 1998, C.J.Bouwkamp states there are 243 known SPSSs of order 30.
- By 2003, J. D. Skinner, using software provided by Duijvestijn which he, Skinner, adapted, had discovered 4311 order 30 SPSSs (about 21% of the total number) .
- In 2011 October 2011, Stephen Johnson announced he had discovered over 500+ SPSSs from order 30 to order 36. Included were 70 new SPSSs of order 30.
- In April 2012, Lorenz Milla completed searches of the 13 and 14 vertex, 31 edge polyhedral graph classes, using Stuart Anderson's noddy (node analysis on electrical nets) software and found 61 new SPSSs of order 30 (there are all up 75 SPSSs derived from the 31 edge, 14 vertex graphs, and none from the 31 edge, 13 vertex graphs).
- In January and February of 2013 James Williams wrote a program which he ran for 6 weeks which produced over 15 million SPSSs from orders 21 to 44. The software was not exhaustive, it did not find all SPSSs in a given order, the goal was to find as many perfect squares as possible in a practical amount of time. James Williams found 9189 SPSSs of order 30 (about 45% of the total of this order).
- In March and April 2013, Lorenz Milla and Stuart Anderson enumerated simple squared squares of order 30. Lorenz used plantri (McKay/Brinkmann) to generate graphs, and Stuart Anderson's sqfind to find squared squares and his sqt to encode the dissections. Lorenz ran the programs on 17 dual core computers over the Easter school holidays. Some 6756 new SPSSs were found, combined with the known SPSSs of order 30, there are exactly 20566 order 30 SPSSs in total.
- Other discoverers of order 30 SPSSs include A.J. Duijvestijn (168 SPSSs), C.J. Bouwkamp (10 SPSSs), and one SPSS by Ian Gambini.