Bonnie Madison Stewart (July 10, 1914 – April 15, 1994) was a professor of mathematics at

Michigan State University Michigan State University (Michigan State, MSU) is a public university, public Land-grant university, land-grant research university in East Lansing, Michigan. It was founded in 1855 as the Agricultural College of the State of Michigan, the fi ...

from 1940 to 1980. He earned his Ph.D. from the

University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...

in 1941, under the supervision of

Cyrus Colton MacDuffee Cyrus Colton MacDuffee (June 29, 1895 – August 21, 1961) from Oneida, New York was a professor of mathematics at University of Wisconsin. He wrote a number of influential research papers in abstract algebra. MacDuffee served on the Council of the ...

Contributions

Number theory

In 1952, the first edition of his book, ''Theory of Numbers'', was published.Review of ''Theory of Numbers'' by H. Bergström, . Stewart's contributions to number theory also include a complete characterization of the

practical number In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 ...

s in terms of their factorizations, which he published in 1954, a year before

Wacław Sierpiński Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a Polish mathematician. He was known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions, and to ...

's independent discovery of the same result.

Geometry

In 1970 he published a book, '' Adventures among the toroids. A study of orientable polyhedra with regular faces'', in which he discussed what are now called

Stewart toroid In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a -holed torus), having a topological genus () of 1 or greater. Notable examples include the Császár and Szilassi polyhedra. Variations in definition Toroidal polyhedr ...

s. The book was handwritten in

calligraphy Calligraphy (from el, link=y, καλλιγραφία) is a visual art related to writing. It is the design and execution of lettering with a pen, ink brush, or other writing instrument. Contemporary calligraphic practice can be defined as "t ...

with many formulas and illustrations. Like the

Platonic solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...

Archimedean solid In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed ...

s, and

Johnson solid In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...

s, the Stewart polyhedra have

regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either convex p ...

s as faces. The first three categories are all convex, whereas Stewart toroids have polygonal-faced tunnels."Bonnie Stewarts Hohlkörper"
by Christoph Pöppe, Spektrumdirekt (website of the German edition of

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

Selected publications

* B. M. Stewart, ''Theory of Numbers'', Macmillan, 1952. 2nd ed., Macmillan, 1964. *. * B. M. Stewart, '' Adventures Among the Toroids'' (1970) This 5"x13" edition was self-published by the author (printed by The John Henry Company) and has no ISBN. * B. M. Stewart, ''Adventures Among the Toroids'', Revised Second Edition (1980) 11"x8.5". , converted much later to

References

External links

Stewart Toroids (Toroidal Solids with Regular Polygon Faces)

Stewart toroids
{{DEFAULTSORT:Stewart, Bonnie 1914 births 1994 deaths 20th-century American mathematicians University of Wisconsin–Madison alumni Michigan State University faculty