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, structure, space, models, and change. History On ...

specializing in

magic square In 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 diagonals are the same. The 'order' of the magic square is the number ...

s and

hypercube In geometry, a hypercube is an ''n''-dimensional analogue of a square () and a cube (). It is a closed, compact, convex figure whose 1- skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, ...

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 journals.

Early life 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, after Saskatoon, and is a commercial centre for southern Saskatchewan. As of the 2021 C ...

, 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 ...

British Columbia British Columbia (commonly abbreviated as BC) is the westernmost province of Canada, situated between the Pacific Ocean and the Rocky Mountains. It has a diverse geography, with rugged landscapes that include rocky coastlines, sandy beaches, ...

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 Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...

and graduated with a B.A. in mathematics. In the summer of 1951, he had just graduated from University, and was working in a fire-lookout tower near

Campbell River, British Columbia Campbell River, or Wiwek̓a̱m, is a city in British Columbia on the east coast of Vancouver Island at the south end of Discovery Passage, which lies along the 50th parallel north along the important Inside Passage shipping route. Campbell River ...

, when his tower was surrounded by the largest forest fire in Canada up to then, and he only narrowly managed to escape. He began his career as a

meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...

instructor in the

NATO The North Atlantic Treaty Organization (NATO, ; french: Organisation du traité de l'Atlantique nord, ), also called the North Atlantic Alliance, is an intergovernmental military alliance between 30 member states – 28 European and two No ...

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 province of Manitoba in Canada. It is centred on the confluence of the Red and Assiniboine rivers, near the longitudinal centre of North America. , Winnipeg had a city population of 749,6 ...

in 1984. Hendricks volunteered for groups including the

Monarchist League of Canada The Monarchist League of Canada (french: Ligue monarchiste du Canada) is a Canadian nonprofit monarchist advocacy organization.

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 In geometry, a cube is a three-dimensional space, three-dimensional solid object bounded by six square (geometry), square faces, Facet (geometry), facets or sides, with three meeting at each vertex (geometry), vertex. Viewed from a corner it i ...

. His interest in magic squares led to higher dimensions: magic cubes,

tesseracts In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eig ...

, 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 Canadian province of British Columbia, on the southern tip of Vancouver Island off Canada's Pacific coast. The city has a population of 91,867, and the Greater Victoria area has a population of 397,237. Th ...

. By this time, he was suffering from

Parkinson's disease Parkinson's disease (PD), or simply Parkinson's, is a long-term degenerative disorder of the central nervous system that mainly affects the motor system. The symptoms usually emerge slowly, and as the disease worsens, non-motor symptoms becom ...

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