Kōji Husimi (June 29, 1909 – May 8, 2008, ) was a Japanese

theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

who served as the president of the

Science Council of Japan The Science Council of Japan (SCJ) is a representative organization of Japanese scholars and scientists in all fields of sciences, including humanities, social sciences, life sciences, natural sciences, and engineering. , president of Toyohashi ...

.. Husimi trees in

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

, the Husimi Q representation in

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

, and Husimi's theorem in the

mathematics of paper folding The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened without damaging it), and the use of paper ...

are named after him.

Education and career

Husimi studied at the

University of Tokyo The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

, graduating in 1933. He spent a year there as an assistant, and then moved to

Osaka University The , abbreviated as UOsaka or , is a List of national universities in Japan, national research university in Osaka, Japan. The university traces its roots back to Edo period, Edo-era institutions Tekijuku (1838) and Kaitokudō, Kaitokudo (1724), ...

in 1934, where he soon began working with

Seishi Kikuchi was a Japanese physicist, known for his explanation of the Kikuchi lines that show up in diffraction patterns of diffusely scattered electrons. Kikuchi's research was recorded in the official Nobel Prize selection meeting minutes of the 1930s. ...

. At Osaka, he became Dean of the Faculty of Science. He moved to

Nagoya University , abbreviated to or NU, is a Japanese national research university located in Chikusa-ku, Nagoya. It was established in 1939 as the last of the nine Imperial Universities in the then Empire of Japan, and is now a Designated National Universit ...

in 1961, and directed the plasma institute there. He retired in 1973, and became a

professor emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". ...

of both Nagoya and Osaka.

Contributions

Physics

A 1940 paper by Husimi introduced the Husimi Q representation in

. Husimi also gave the name to the

kagome lattice In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. See in particular Theorem 2.1.3, p. 59 (classification of uniform tilings); Figure 2.1.5, p.63 (illustration of this tiling), Theorem 2. ...

, frequently used in statistical mechanics.

Graph theory

In the mathematical area of

, the name "Husimi tree" has come to refer to two different kinds of graphs:

cactus graph In graph theory, a cactus (sometimes called a cactus tree) is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently, it is a connected graph in which every edge belongs to at most one simple cycle, or ...

s (the graphs in which each edge belongs to at most one cycle) and

block graph Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96. ...

s (the graphs in which, for every cycle, all diagonals of the cycle are edges). Husimi studied cactus graphs in a 1950 paper, and the name "Husimi trees" was given to these graphs in a later paper by

Frank Harary Frank Harary (March 11, 1921 – January 4, 2005) was an American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together with ...

and

George Eugene Uhlenbeck George Eugene Uhlenbeck (December 6, 1900 – October 31, 1988) was a Dutch-American theoretical physicist, known for his significant contributions to quantum mechanics and statistical mechanics. He co-developed the concept of electron spin, a ...

. Due to an error by later researchers, the name came to be applied to block graphs as well, causing it to become ambiguous and fall into disuse.

Pacifism and world affairs

Husimi was an early member of the Science Council of Japan, joining it in 1949, and it was largely through his efforts that the Science Council in 1954 issued a statement proposing principles for the peaceful use of

nuclear power Nuclear power is the use of nuclear reactions to produce electricity. Nuclear power can be obtained from nuclear fission, nuclear decay and nuclear fusion reactions. Presently, the vast majority of electricity from nuclear power is produced by ...

and opposing the continued existence of

nuclear weapon A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission or atomic bomb) or a combination of fission and fusion reactions (thermonuclear weapon), producing a nuclear exp ...

s. This statement, in turn, led to the Japanese law outlawing military uses of nuclear technology. Later, he served as president of the Science Council of Japan from 1977 to 1982. He was also a frequent participant in the

Pugwash Conferences on Science and World Affairs The Pugwash Conferences on Science and World Affairs is an international organization that brings together scholars and public figures to work toward reducing the danger of armed conflict and to seek solutions to global security threats. It was fo ...

and a leader of the Committee of Seven for World Peace.

Recreational mathematics

Husimi's recreational interests included

origami ) is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a ...

; he designed several variations of the traditional orizuru (paper crane), folded on paper shaped as a

rhombus In plane Euclidean geometry, a rhombus (: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhom ...

instead of the usual square, and studied the properties of the bird base that allow it to be varied within a continuous family of deformations. With his wife, Mitsue Husimi, he wrote a book on the mathematics of origami,. 2nd ed., 1984, . which included a theorem characterizing the folding patterns with four folds meeting at a single vertex that may be folded flat. The generalization of this theorem to arbitrary numbers of folds at a single vertex is sometimes called Husimi's theorem..