Updates to Chapter 14, "Maltese Crosses",
in Dissections: Plane & Fancy, by Greg N. Frederickson

Wild Conjecture about A. E. Hill

An enduring mystery has been who was A. E. Hill, the creator of that lovely 7-piece dissection of a Maltese Cross to a square. A search of various biographical databases has turned up no obvious candidates. So please indulge me as I make a wild conjecture.
Perhaps the handwriting on the correspondence was so unclear that the first initial is wrong, and the person Dudeney called "A. E. Hill" was actually "Rev. E. Hill", with the "R" mistaken for an "A". (Note the topological similarity between these two characters.) This leads us then to Rev. Edwin Hill, born in 1843, matriculating at St. John's College, Cambridge in 1862. He earned a B.A. in 1866, with the distinction of "5th Wrangler" in mathematics. He earned an M.A. in 1869, was a Fellow 1867-1890, and a Tutor 1875-1889. Ordained as a deacon in 1867 and a priest in 1868, he served as rector of Cockfield, Suffolk 1889-1929. He died in 1933 at the age of 90.
Hill started out in mathematics and later turned to geology. From 1868 to 1876 he published at least five articles in Messenger of Mathematics. From 1872 to 1897 he published at least 30 articles in the field of geology. He also published at least seven questions in Mathematical Questions and Solutions, from the "Education Times" during the period 1891-1897.
The position that Hill held at Cockfield was controlled by St. John's College, so that he still maintained some connection with Cambridge University. Thus he could well have enjoyed contact with geometers at Cambridge such as Geoffrey Bennett, William Macaulay, and Henry Martyn Taylor, who were all involved with geometric dissections. Bennett was a mathematics student at St. Johns, graduating in 1890, and a fellow at Emmanuel College from 1893 to 1943, who had sent Henry Dudeney the 5-piece dissection of an octagon to a square in 1926. Macaulay had received an M.A. from King's College, Cambridge, in 1884, and was employed by the university from 1884 until 1926. He published five articles on geometric dissections between 1914 and 1922. Taylor earned a B.A. at Trinity College, Cambridge, in 1865, and an M.A. in 1868, and was employed at Trinity as a tutor from 1869 to 1894. He published an article on geometric dissections in 1905 and was resident in Cambridge until he died in 1927.
The origin of the 7-piece dissection of the Maltese Cross was sometime between 1920 and 1926. This would have placed Hill somewhere between 77 and 83 years of age, which could explain why his name might have been only semi-legible. Note that Dudeney was not always perfect with names, as evidenced by having "M'Elroy" rather than "McElroy" in one comment in his 1907 book The Canterbury Puzzles.
Any additional information, either in support of, or in contradiction to, this conjecture would be most welcome.

More on "P. Gerwien"

In June 2007, Douglas Rogers forwarded to me a message from Lars-Holger Thümmler, a specialist in Prussian military history during the time of Napolean and an archivist with the administrative archives in Berlin and a project manager at the university library of Humboldt University. In his message, Thümmler responded to a query by Douglas asking for information regarding a "P. Gerwien" who was in the Prussian 22nd infantry regiment. Thümmler identified a Karl Ludwig Gerwien as the only Gerwien in the Prussian 22nd infantry regiment. Details:
Karl Ludwig Gerwien was born in 1799 in Landsberg in East Prussia. He entered the Garde-Ulanen-Regiment in 1815, then climbed the military ladder: becoming a second lieutenant in 22nd infantry regiment in 1818, a first lieutenant in 1829, a captain and company commander in 1835, then major in 1843, lieutenant colonel in 1851, colonel in 1852, major general in 1857. He died in Münster, Westfalen, in 1858.
Gerwien commanded a general war school 1820-1823, was a teacher in the division school of the 12th division 1823-26, was a teacher at the cadet institute in 1826-1833, shifted to the general staff in 1849, and became commander of the 26th infantry brigade in 1856.
I contacted Thümmler to ask a few follow-up questions. In particular, I asked him whether the "P." in "P. Gerwien" might be an abbreviation for "Premierlieutenant", Gerwien's rank at the time that he published his articles in Crelle's journal as well as his two-volume work with von Holleben. In reply, Thümmler affirmed that there was only one Gerwien in the whole regiment history of the 22nd infantry regiment, and none in the 21st, which was von Holleben's regiment. By the same token, Thümmler stated that using "P" as an abbreviation for "Premierlieutenant" was not normal practice. Karl Ludwig Gerwien may or may not have followed normal practice, but his dates and positions are so close a match that he is almost certainly the author listed as "P. Gerwien" in Crelle's Journal.
The sources consulted by Lars-Holger Thümmler are:

Yet more on "P. Gerwien"

In March 2009, Darrah Chavey informed me of a passage in the book by Otto Julius Bernhard von Corvin-Wiersbitzki (1812-1886), A Life of Adventure, an Autobiography, London: Richard Bentley, 1871. (See the Wikipedia entry on von Corvin's fascinating life.) In volume 1 (of 3 volumes) von Corvin wrote about his time as a cadet at the Prussian cadet institute, including a tidbit of information about our Lieutenant Gerwien. The following events happened, according to the author's memory, in 1824:
"I was amusing myself once in the hospital with oil-painting, when the major of the second company, von Schehha, visited some of his cadets. He became interested in my endeavours, and was so friendly as to offer that I should take part in the private lessons which were given to the eldest Prince Byron of Curland, by a landscape-painter, Mr. W. Bruck, of Berlin.
"The prince wore the uniform of the cadets, but had his own room, and was placed under the especial direction of the major. In a similar relation to the Cadet House stood a Prince Solms-Braunfels, who was related to the royal family, and already wore the uniform of an officer. However, he generally attended at lessons in citizens' dress, but whenever not quite sure of his mathematics, he put on his uniform, with the badge of the Order of the Guelphs, because, although Lieutenant Gerwien, who was very strict, had not the least regard for a princely sluggard, he respected an officer's epaulettes so much, that he dared not scold their wearer."
Thanks, Darrah, for that tidbit of military life!

More and more crosses

In 1998, Bernard Lemaire continued to work on a wide variety of different crosses, including Maltese crosses. He collaborated with Gavin Theobald on the following two manuscripts:
"Geometric dissections of a family of forky Maltese Crosses: Mn", 3rd version, December 1998.
"Geometric dissections: twenty-two crosses squared", December 1998.
These are almost exclusively dissections of crosses to squares.

Copyright 1999-2009, Greg N. Frederickson.
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Last updated April 4, 2009.