Albert Harry Wheeler (18 January 1873,

Leominster, Massachusetts Leominster ( ) is a city in Worcester County, Massachusetts, United States. It is the second-largest city in Worcester County, with a population of 43,222 at the 2023 census. Leominster is located north of Worcester and northwest of Boston. Bo ...

– 1950) was an American mathematician, inventor, and mathematics teacher, known for physical construction (usually in paper) of polyhedral models and teaching this art to students.

Education and career

A. Harry Wheeler received in 1894 his Bachelor of Science degree from

Worcester Polytechnic Institute The Worcester Polytechnic Institute (WPI) is a Private university, private research university in Worcester, Massachusetts, United States. Founded in 1865, WPI was one of the United States' first engineering and technology universities and now h ...

. He taught high school in

Worcester, Massachusetts Worcester ( , ) is the List of municipalities in Massachusetts, second-most populous city in the U.S. state of Massachusetts and the list of United States cities by population, 113th most populous city in the United States. Named after Worcester ...

from 1894 to 1896 and then was a graduate student in mathematics from 1896 to 1899 at Clark University, but left without a degree. He taught high school mathematics in Worcester from 1899 to 1920. His

textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...

s are ''First Course in Algebra'' (1907) and ''Examples in Algebra'' (1914). At age 47, returned in 1920 to graduate study in mathematics at

Clark University Clark University is a private research university in Worcester, Massachusetts, United States. Founded in 1887 with a large endowment from its namesake Jonas Gilman Clark, a prominent businessman, Clark was one of the first modern research uni ...

, receiving a master's degree in 1921. Wheeler was an Invited Speaker of the

ICM ICM may refer to: Organizations * Irish Church Missions, an Anglican mission * Institut du Cerveau, the Paris Brain Institute, a research center * Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw * Interna ...

in 1924 at Toronto.Wheeler, Albert Harry (1924
"Certain forms of the icosahedron and a method for deriving and designating higher polyhedra."
In ''Proceedings of the International Mathematical Congress'', Toronto, vol. 1, pp. 701–708. In 1924 he began part-time teaching (in addition to his high school teaching) as an adjunct instructor of geometry, first at

Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...

and then at

Wellesley College Wellesley College is a Private university, private Women's colleges in the United States, historically women's Liberal arts colleges in the United States, liberal arts college in Wellesley, Massachusetts, United States. Founded in 1870 by Henr ...

; however, his college-level adjunct teaching ended by the early 1930s. Wheeler and H. S. M. Coxeter planned to be coauthors (with two other mathematicians) of a short book, which was eventually named ''

The Fifty-Nine Icosahedra ''The Fifty-Nine Icosahedra'' is a book written and illustrated by Harold Scott MacDonald Coxeter, H. S. M. Coxeter, Patrick du Val, P. Du Val, H. T. Flather and J. F. Petrie. It enumerates certain stellations of the regular convex or Platonic re ...

'' and became a minor classic of mathematical literature. However, in 1938 Wheeler objected to Coxeter's expository style so that Coxeter replaced Wheeler's name on the book's title page by another author, although Wheeler is briefly mentioned in the text. Extending work of

Max Brückner Johannes Max Brückner (5 August 1860 – 1 November 1934) was a German geometer, known for his collection of polyhedral models. Education and career Brückner was born in Hartau, in the Kingdom of Saxony, a town that is now part of Zitta ...

, Wheeler actually constructed previously unknown polyhedra. In particular, he produced new

stellation In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific ...

s of the

icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical tha ...

. This achievement impressed Coxeter, who noted Wheeler's achievement in the text.

Wheeler continued teaching high school mathematics in Worcester until his retirement. His models continued to attract attention. In 1950 he received an invitation to exhibit part of his model collection at the 1950 ICM in

Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. It is a suburb in the Greater Boston metropolitan area, located directly across the Charles River from Boston. The city's population as of the 2020 United States census, ...

from 30 August to September 6. However, serious illness prevented him from attending the conference, and he died in December 1950.

Selected works

Books

* *

Patents

Blower for peas or the like. US Patent 921,764, 1909

Playing-cards. US Patent 931,977, 1909
* with Albert A. Wheeler and Martin V. Haskins

Puzzle. US Patent 959,903, 1910

Mathematical model. US Patent 1,192,483, 1916

Blank for forming hollow polyhedrons. US Patent 1,292,188, 1919

References

{{DEFAULTSORT:Wheeler, Albert Harry 1873 births 1950 deaths American mathematics educators American geometers 19th-century American mathematicians 20th-century American mathematicians Worcester Polytechnic Institute alumni Clark University alumni