P J Federico

Pasquale Joseph Federico (March 25, 1902 – January 2, 1982) was a lifelong mathematician and longtime head of the United States Patent Office. Pat was born March 25, 1902 (Easter time, "Pasqua" Italian for Easter, hence Pasquale), in Monessen, Pennsylvania, a town twenty miles or so south of Pittsburgh. About 1910 the family moved for improved job opportunity to Cleveland, Ohio, where he grew up and got his initial schooling, ending with a B.S. in physics at Case Institute of Technology in June 1923. Federico also studied mathematics and was offered a teaching position, but the following September he entered the United States Patent Office and was assigned to Division 43.

P J Federico

Pasquale Joseph Federico

He was instrumental in several major changes to how patents were issued and how intellectual property is treated. Federico also served for many years as the Patent Office's unofficial historian and editor of the "Journal of the Patent Office Society". Some of his most well known contributions to the field of mathematics focused on the study of perfect squared squares and the history and enumeration of polyhedra.

in 1963 P.J. Federico published [10] 'note on some low-order perfect squared squares' a paper in which he provided a detailed account of CPSS construction methods. Federico gave a new general empirical method, by means of which 24 perfect squares of order below 29 were constructed. The CPSSs he gave in his paper included two new CPSSs of order 25, one with a side of 235 and the other with a side of 344, a new CPSS of order 26, with side 384, 8 new CPSSs of order 27 with sides 325, 408, 600, 618, 645, 648, 825 and 849, and 13 new CPSSs of order 28 with sides 374, 714, 732, 741, 765, 765, 824, 1071, 1089, 1113, 1137, 1166 and 1166. He did this when computer methods were only able to extend up to order 19.

Federico defined the term 'low order' to mean the squared squares below order 29, he stated "this limit was chosen to avoid too long a list", and he also noted "twenty-nine perfect squares of order 29 were collected without attempting to apply fully the methods to this and higher orders", but only gave one example of a particular order 29 CPSS, size 468, indicative of the methods being illustrated in the list at the end of the paper. However in the paper itself he indicated how 7 new order 29 CPSSs were found, and gave sufficient information to work out their sizes, which were; 704, 724, 1341, 1377, 1412, 1457 and 1516. He also listed a number of CPSSs in order 30's and above.

In 1964 P.J. Federico, with T. H. Willcocks, pioneered a variety of techniques in squared square construction known as 'transforms'. In 1967 Willcocks wrote [2], "In 1964, P. J. Federico, in a personal communication, explained to the writer how, after discarding two opposite corner squares of Brooks' square, he had been able to divide the remaining figure into two blocks which could be repositioned with respect to each other so that, with the addition of three further squares, a new simple perfect square of order 39 and side 6121 emerged. This interesting observation implied that a similar transformation could be applied to a whole class of squared (but not necessarily perfect) squares. By seeking in the first instance suitable trivially imperfect squares (containing either a single trivial imperfection involving a corner square or two trivial imperfections involving opposite corner squares) and then applying Federico's transformation, a number of simple perfect squares of order n less than 37 have been obtained, the imperfections being eliminated in the process."

Detailed accounts of transforms are given by T.H. Willcocks in 1967[2], by Federico himself in 1978[6], by C.W. Bouwkamp[8] and are fully illustrated in J.D. Skinners book "Squared Squares, Who's Who and What's What"[9].

Federico wrote an extensive history of the squaring of rectangles and squares[6]. This is still the most detailed historical article on the subject in print. It was produced on the occasion of Prefessor W.T. Tutte's sixieth birthday, and coincided with Duijvestijn's discovery of the lowest order simple perfect squared square 21: 112

Federico followed Duijvestijn and Bouwkamp's computer work closely, making extensive use of their squared rectangle catalogues to produce many squared squares. He also took a mathematical interest in the graph theoretical aspects of that work. With Duijvestijn he produced a paper The Number of Polyhedral (3-Connected Planar) Graphs[4], which used Tutte's theoretical work on the enumeration of polyhedra, and Duijvestijn's computer generation of c-nets (graphs corresponding to polyhedral nets) to enumerate convex polyhedra, and show the equivalence of theory and computer experiment in this area of combinatorics.

In 1982, his final paper, with Duijvestijn and Leeuw[7], "Compound Perfect Squares", proved Willcocks order 24 : 175 the lowest order and only perfect compound square of that order. The paper used computer methods of Leeuw and Duijvestijn applied to Willcocks and Federico's earlier manual methods and was not improved upon until the turn of the century.

Federico is credited for providing the quotation underlying the scope of patentable subject matter under United States law when he testified before a House subcommittee in 1951 that "under section 101 a person may have invented a machine or manufacture, which may include anything under the sun that is made by man." This testimony was later quoted by the United States Supreme Court when the Court held in 1980 that living organisms were proper subject matter for patents.

This quote has been the subject of much legal argument. One view[xii] is that "The enactment of section 103 in 1952 was a reaction to a line of Supreme Court cases in which U.S. patents were held to be invalid because they lacked ‘‘invention.’’ In one celebrated case, Justice William O. Douglas went so far as to state that for a device to be patentable, it ‘‘must reveal the flash of creative genius.’’ The Supreme Court’s anti-patent bias during the period leading up to 1952 was so pronounced that Justice Robert H. Jackson in a dissent complained ‘‘that the only patent that is valid is one which this Court has not been able to get its hands on.’’ In his Commentary on the New Patent Act, Mr. P. J. Federico, a senior official of the U.S. Patent Office and one of the principal authors of the 1952 Act, stated as follows:

There has been some discussion as to whether section 103 modifies the so-called standard of invention (which itself is an unmeasurable quantity having different meanings for different persons) in the courts and it may be correct to state that the printed record does not show an explicit positive command to the courts. While it is not believed that Congress intended any radical change in the level of invention or patentable novelty, nevertheless, it is believed that some modification was intended in the direction of moderating the extreme degrees of strictness exhibited by a number of judicial opinions over the past dozen or more years; that is, that some change of attitude more favorable to patents was hoped for. This is indicated by the language used in section 103 as well as by the general tenor of remarks of the Committees in the reports and particular comments."

Many others hold the opposite view that the Supreme Court went too far in the other direction in allowing the patenting of genes. No doubt Federico himself would have sought the best outcome for all parties.

" Pat Federico was the ideal public servant. Politicians may come and politicians may go and in the process get most of the publicity in governmental affairs, but it is people like Pat who make government work. It was my privilege and greatly to my benefit to come to know Pat some thirty-four years ago, to have worked with him on a couple of lengthy legislative projects, and to have remained in touch with him throughout the rest of his fruitful life." [xi]
Hon. Giles S. Rich



  1. Vector Differential Geometry of Curves, By Pasquale Joseph Federico, Published by George Washington University, 1925
  2. "Some Squared Squares and Rectangles", T. H. Willcocks, Journal of Combinatorial Theory 3, 54-56 (1967)
  3. "Descartes on polyhedra: a study of the De solidorum elementis," By Pasquale Joseph Federico. Edition: illustrated, Published by Springer, 1982
  4. The Number of Polyhedral (3-Connected Planar) Graphs By A. J. W. Duijvestijn and P. J. Federico
  5. Origins of Graph Theory by P.J. Federico, an extensive unpublished manuscript , referred to in Chapter 17 of History of Topology by Robin J. Wilson
  6. Squaring Rectangles and Squares, A Historical Review with Annotated Bibliography by P. J. Federico, in Graph theory and Related Topics: proceedings of the conference held in honour of Professor W. T. Tutte on the occasion of his sixtieth birthday, University of Waterloo, July 5-9, 1977
  7. A. J. W. Duijvestijn, P. J. Federico, and P. Leeuw, "Compound Perfect Squares", Amer. Math. Monthly 89 (1982) pp 15-32
  8. On Some New Simple Perfect Squared Squares 1992, C. W. Bouwkamp, Discrete Mathematics 106/107 (1992) pp67-75
  9. "Squared Squares, Who's Who and What's What". JD Skinner II, 1993, pp 9, 51, T1-T27
  10. P. J. Federico, Note on some low-order perfect squared squares, Canad. J. Math., 15. pp 350-363"(1963)

Patent Office

  1. "The First Patent Act," By Pasquale Joseph Federico, Journal of the Patent Office Society 14:237-252 (April 1932)
  2. "Statutory Disclaimers in Patent Law," By Pasquale Joseph Federico, Published by P. Pearlman, 1935
  3. "Operation of the Patent Act of 1790," By Pasquale Joseph Federico, Journal of the Patent Office Society 18:237-251 (April 1936)
  4. "A Fragment of Texas History", By P.J. Federico and J.R. Nunn, Journal of the Patent Office Society 18:407-410 (1936)
  5. "Outline of the History of the United States Patent Office," By P.J. Federico, Volume 18, Journal of the Patent Office Society, 251 (1936).
  6. "Treaties Between the United States and Other Countries Relating to Trademarks," By Pasquale Joseph Federico, Published 1949
  7. "Distribution of Patents Issued to Corporations (1939-55): Study of the Subcommittee on Patents, Trademarks, and Copyrights of the Committee on the Judiciary, United States Senate, Eighty-fourth Congress, Second Session, Pursuant to S. Res. 167," By Pasquale Joseph Federico, United States Congress. Senate. Committee on the Judiciary. Subcommittee on Patents, Trademarks, and Copyrights, United States Patent Office, Published by U. S. Govt. Print. Off., 1957
  8. "Opposition and Revocation Proceedings in Patent Cases: Study of the Subcommittee on Patents, Trademarks, and Copyrights of the Committee on the Judiciary, United States Senate, Eighty-fourth Congress, Second Session, Pursuant to S. Res. 167," By Pasquale Joseph Federico, United States Congress. Senate. Committee on the Judiciary. Subcommittee on Patents, Trademarks, and Copyrights, Published by U.S. Govt. Print. Off., 1957
  9. Two notebooks: One is marked "Patent Office" and contains materials 1789-1841, relating to the Patent Office's early years and copies of official reports to the Congress. The second notebook is marked "Elliot" and consists mainly of the Elliot controversies. P.J. Federico worked at the Patent Office for many years and was also its unofficial historian and editor of the "Journal of the Patent Office Society." The papers in the two notebooks relate to the early history of the Patent Office and charges of misfinance against superintendents of the office by William Elliot and his son William Parker Elliot. Mr. and Mrs. Federico Collection, 1789-1936, Archives Center, National Museum of American History.
  10. "Renewal Fees and Other Patent Fees in Foreign Countries: Study of the Committee on the Judiciary, United States Senate, Eighty-fifth Congress, Second Session, Pursuant to S. Res. 236," By Pasquale Joseph Federico, United States Congress. Senate. Committee on the Judiciary. Subcommittee on Patents, Trademarks, and Copyrights, Published by U.S. Govt. Printing Office, 1958
  11. Rich, Giles S. (1982). "P.J. (Pat) Federico and His Works". Journal of the Patent Office Society 64 (1). ISSN 0096-3577.
  12. "The Evolution of Gene Patents Viewed from the United States Patent Office", Hon. Gerald J. Mossinghoff; Senior Counsel, Oblon, Spivak, McClelland, Maier & Neustadt (2003)