J. R. Hendricks
Encyclopedia
John Robert Hendricks was a mathematician
specializing in magic square
s and hypercube
s. He has published many articles in the Journal of Recreational Mathematics
as well as other Journals.
, but moved with his family to Vancouver, British Columbia at an early age.
He attended the University of British Columbia
and graduated with a B.A. in mathematics. He started his career as a meteorology instructor in the N.A.T.O. flight training program. Then for 33 years he was employed by the Canadian Meteorological Service until his retirement in Winnipeg, Manitoba in 1984.
.
He liked this job because it gave him lots of free time to indulge in his magic hypercube studies. Suddenly his tower was surrounded by the largest forest fire in Canada up to that time, and he barely managed to escape. He was relieved when he return after the fire to find that his precious notes had also survived.
His interest in magic squares had quickly advanced to higher dimensions: magic cubes, tesseracts, etc. He developed a new diagram for the 4-dimension tesseract. This was published in 1962 when he showed constructions of four, five, and six-dimensional magic hypercubes of order three [1]. He later was the first to publish diagrams of all 58 magic tesseracts of order 3.
He is also an authority on the design of inlaid magic squares and cubes (and in 1999, a magic tesseract). Following his retirement, he gave any 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.
. By this time, he was suffering from Parkinson's disease
and it had progressed to the stage that he had difficulty walking or writing because of his shaky hands.
He purchased his first personal computer to help with his self-publishing work on magic hypercubes. It is astounding that up to this time, the only aid for his work on magic hypercubes was a programmable calculator. Despite his deteriorating health, John continued to make advances in magic hypercube knowledge. Some of his accomplishments were:
After 1998, he self-published:
Unfortunately, all of his books are now out-of-print. Some are available for downloading in PDF format from his website (see "Links"). All are available at the University of Calgary
, Strens Recreational Mathematics Collection.
In total, 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 (above).
A collection of his notes, a CD, and a copy of each of his books, has been accepted for inclusion in The University of Calgary, Strens Recreational Mathematics Collection.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
specializing in magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
s and hypercube
Magic hypercube
In mathematics, a magic hypercube is the k-dimensional generalization of magic squares, magic cubes and magic tesseracts; that is, a number of integers arranged in an n × n × n × .....
s. He has published many articles in the Journal of Recreational Mathematics
Journal of Recreational Mathematics
The Journal of Recreational Mathematics is an American journal dedicated to recreational mathematics, started in 1968. It is published quarterly by the Baywood Publishing Company....
as well as other Journals.
Early years
John Robert Hendricks was born in Regina, SaskatchewanRegina, Saskatchewan
Regina is the capital city of the Canadian province of Saskatchewan. The city is the second-largest in the province and a cultural and commercial centre for southern Saskatchewan. It is governed by Regina City Council. Regina is the cathedral city of the Roman Catholic and Romanian Orthodox...
, but moved with his family to Vancouver, British Columbia at an early age.
He attended the University of British Columbia
University of British Columbia
The University of British Columbia is a public research university. UBC’s two main campuses are situated in Vancouver and in Kelowna in the Okanagan Valley...
and graduated with a B.A. in mathematics. He started his career as a meteorology instructor in the N.A.T.O. flight training program. Then for 33 years he was employed by the Canadian Meteorological Service until his retirement in Winnipeg, Manitoba in 1984.
Volunteer work
During his working years, he spent many hours in volunteer work in service groups. These included The Monarchist League of Canada and the Manitoba Provincial Council, Duke of Edinburgh’s Award in Canada. He was a recipient of the Canada 125 medal for his volunteer work.Hobby
When he was 13 years old, he started collecting magic squares. As his interest in mathematics grew, so did his love of magic squares, and cubes. In the summer of 1951, he had just graduated from University, and was working in a fire-lookout tower near Campbell River, British ColumbiaCampbell River, British Columbia
Campbell River is a coastal city in British Columbia on the east coast of Vancouver Island at the south end of Discovery Passage, which lies along the important coastal Inside Passage shipping route...
.
He liked this job because it gave him lots of free time to indulge in his magic hypercube studies. Suddenly his tower was surrounded by the largest forest fire in Canada up to that time, and he barely managed to escape. He was relieved when he return after the fire to find that his precious notes had also survived.
His interest in magic squares had quickly advanced to higher dimensions: magic cubes, tesseracts, etc. He developed a new diagram for the 4-dimension tesseract. This was published in 1962 when he showed constructions of four, five, and six-dimensional magic hypercubes of order three [1]. He later was the first to publish diagrams of all 58 magic tesseracts of order 3.
He is also an authority on the design of inlaid magic squares and cubes (and in 1999, a magic tesseract). Following his retirement, he gave any 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.
His move west
In April 1996, John and his wife Celia moved to Victoria, British ColumbiaVictoria, British Columbia
Victoria is the capital city of British Columbia, Canada and is located on the southern tip of Vancouver Island off Canada's Pacific coast. The city has a population of about 78,000 within the metropolitan area of Greater Victoria, which has a population of 360,063, the 15th most populous Canadian...
. By this time, he was suffering from Parkinson's disease
Parkinson's disease
Parkinson's disease is a degenerative disorder of the central nervous system...
and it had progressed to the stage that he had difficulty walking or writing because of his shaky hands.
He purchased his first personal computer to help with his self-publishing work on magic hypercubes. It is astounding that up to this time, the only aid for his work on magic hypercubes was a programmable calculator. Despite his deteriorating health, John continued to make advances in magic hypercube knowledge. Some of his accomplishments were:
- The first perfect magic tesseract (order-16), April 1999
- The first order-32 perfect magic tesseract
- The first inlaid magic tesseract (order-6 with inlaid order-3) in October 1999
- The first bimagic cube (order-25), June 2000.
After 1998, he self-published:
- 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
Unfortunately, all of his books are now out-of-print. Some are available for downloading in PDF format from his website (see "Links"). All are available at the University of Calgary
University of Calgary
The University of Calgary is a public research university located in Calgary, Alberta, Canada. Founded in 1966 the U of C is composed of 14 faculties and more than 85 research institutes and centres.More than 25,000 undergraduate and 5,500 graduate students are currently...
, Strens Recreational Mathematics Collection.
In total, 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 (above).
Last years
By 2004, his health had failed to the extent that he was unable to carry on. He was hospitalized several times and died in Victoria, aged 77.A collection of his notes, a CD, and a copy of each of his books, has been accepted for inclusion in The University of Calgary, Strens Recreational Mathematics Collection.
Sources
- The Five and Six-Dimensional Magic Hypercubes of Order 3, Canadian Mathematical Bulletin, 5:2:1962:171-190
- Hendricks, John R., All Third-Order Magic Tesseracts, 1999, 0-9684700-2-5.
- In Memoriam: John Robert Hendricks:September 4, 1929 - July 7, 2007, Journal of Recreational Mathematics, Vol. 34, No. 1, 2005–2006, page 80
See also
- Magic cube class
- magic tesseractMagic tesseractIn mathematics, a magic tesseract is the 4-dimensional counterpart of a magic square and magic cube, that is, a number of integers arranged in an n × n × n × n pattern such that the sum of the numbers on each pillar as well as the main space diagonals is equal to a single number,...
- Magic hypercubes
- Perfect magic cubePerfect magic cubeIn mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant....
External links
- Hendricks material compiled and posted before his death
- page about J. R. Hendricks
- http://cboyer.club.fr/multimagie/English/Hendricks.htm (possibly the same dead link)