John Robert Hendricks (September 4, 1929 – July 7, 2007) was a Canadian amateur

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

notable for his work in

magic square In mathematics, especially History of mathematics, historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diago ...

s and

hypercube In geometry, a hypercube is an ''n''-dimensional analogue of a square ( ) and a cube ( ); the special case for is known as a ''tesseract''. It is a closed, compact, convex figure whose 1- skeleton consists of groups of opposite parallel l ...

s. He published many articles in the

Journal of Recreational Mathematics The ''Journal of Recreational Mathematics'' was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue ...

as well as other mathematics-related journals.

Early life, education and career

Hendricks was born in

Regina, Saskatchewan Regina ( ) is the capital city of the Provinces and territories of Canada, Canadian province of Saskatchewan. The city is the second-largest in the province, and is a commercial centre for southern Saskatchewan. As of the 2021 Canadian census, ...

, in 1929, moving with his family to

Vancouver Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the cit ...

British Columbia British Columbia is the westernmost Provinces and territories of Canada, province of Canada. Situated in the Pacific Northwest between the Pacific Ocean and the Rocky Mountains, the province has a diverse geography, with rugged landscapes that ...

, at an early age. He attended the

University of British Columbia The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...

and graduated with a B.A. in mathematics. He began his career as a

meteorology Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agricultur ...

instructor in the

NATO The North Atlantic Treaty Organization (NATO ; , OTAN), also called the North Atlantic Alliance, is an intergovernmental organization, intergovernmental Transnationalism, transnational military alliance of 32 Member states of NATO, member s ...

flight training program, and was subsequently employed for 33 years by the Canadian Meteorological Service, until his retirement in

Winnipeg, Manitoba Winnipeg () is the capital and largest city of the Provinces and territories of Canada, Canadian province of Manitoba. It is centred on the confluence of the Red River of the North, Red and Assiniboine River, Assiniboine rivers. , Winnipeg h ...

, in 1984. Hendricks volunteered for groups including the

Monarchist League of Canada The Monarchist League of Canada () is a Canadian nonprofit monarchist advocacy organization."Who We Are"< ...

and the Manitoba Provincial Council, Duke of Edinburgh's Award in Canada. He received the Canada 125 medal for his volunteer work.

Amateur mathematician

When he was 13, Hendricks started collecting

s. As his interest in mathematics grew, so did his love of magic squares, and

cubes A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...

. His interest in magic squares led to higher dimensions: magic cubes, tesseracts, etc. He developed a new diagram for the four-dimensional tesseract. This was published in 1962 when he showed constructions of four-, five-, and six-dimensional magic hypercubes of order three. He later was the first to publish diagrams of all 58 magic tesseracts of order 3. Hendricks was also an authority on the design of inlaid magic squares and cubes (and in 1999, a magic tesseract). Following his retirement, he gave many public lectures on magic squares and cubes in schools and in-service teacher's conventions in Canada and the northern United States. He also developed a course on magic squares and cubes which he conducted for seven years at Acadia Junior High School in Winnipeg.

Later years

In April 1996, Hendricks and his wife Celia moved to

Victoria, British Columbia Victoria is the capital city of the Provinces and territories of Canada, Canadian province of British Columbia, on the southern tip of Vancouver Island off Canada's Pacific Ocean, Pacific coast. The city has a population of 91,867, and the Gre ...

. By this time, he was suffering from

Parkinson's disease Parkinson's disease (PD), or simply Parkinson's, is a neurodegenerative disease primarily of the central nervous system, affecting both motor system, motor and non-motor systems. Symptoms typically develop gradually and non-motor issues become ...

that meant he had difficulty walking or writing. He purchased a personal computer to help with his self-published work on magic hypercubes, which until this point he had carried out using only a programmable calculator. Despite his deteriorating health, Hendricks continued his work with magic hypercubes, achieving during this time: the first perfect magic tesseract (order 16), in April 1999; the first order 32 perfect magic tesseract; the first inlaid magic tesseract (order 6 with inlaid order 3) in October 1999; and the first bimagic cube (order 25), June 2000. In 2004, Hendricks was unable to continue with his mathematical work due to ill health. He died in Victoria in 2007, aged 77.

Self-published work after 1998

* ''Magic Squares to Tesseract by Computer'', 1998, 0-9684700-0-9 * ''Inlaid Magic Squares and Cubes'', 1999, 0-9684700-1-7 * ''Perfect n-Dimensional Magic Hypercubes of Order 2n'', 1999, 0-9684700-4-1 * ''All Third-Order Magic Tesseracts'', 1999, 0-9684700-2-5 * ''Bi-Magic Squares of Order 9'', 1999, 0-9684700-6-8 * ''Curves and Approximations'', 1999, 0-9684700-5-X ''An Inlaid Magic Tesseract'', 1999, as a 17" x 22" poster OR an 8-page self-cover booklet * ''Inlaid Magic Squares and Cubes'' (2nd edition), 2000, 0-9684700-3-3 * ''A Bimagic Cube of Order 25'', 2000, 0-9684700-7-6 * ''Magic Square Lexicon: Illustrated'' (co-author Harvey Heinz), HDH, 2000, 0-9687985-0-0 Through his life, Hendricks published 53 articles and papers on magic squares and cubes, 14 articles on statistics, 15 articles on meteorology, 14 miscellaneous articles and 12 books. A collection of his notes, a CD, and a copy of each of his books, has been added to the Strens Recreational Mathematics Collection at the University of Calgary, including all of the books above, which are now out-of-print.

References

External links