The squares
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Tema: Strategies for deducing reasonable conclusions from a mathematical model.
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España > Matemáticas > 2º ESO > Sentido algebraico
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Enunciado
Julia Bowman (1919-1985), prestigious American mathematician. She was the first female member of the Mathematics Division of the United States National Academy of Sciences, and the first female president of the American Mathematical Society.
She dedicated part of her scientific work to game theory, which is a branch of mathematics with applications in very different disciplines (sociology, psychology, economics, business management, military strategy, biology, artificial intelligence, etc.) that analyses the interactions between individuals who make decisions. In fact, Julia managed to prove a convergence theorem that is considered the most important one in elementary game theory.
The following game is proposed: The squares
It is a well-known Asian strategy game, intended to be played on a blackboard, although it can also be played with a pencil and a sheet of paper.
How to play and rules
Two people play. 16 letters are written in rows of 4. The game consists of forming squares whose sides are lines that join two letters. It is played alternately and every time you get a square you have the right to make another line. The person who gets the most squares wins.
A B C D
E F K L
I J K L
M N O P
The following picture is very illustrative. One of the Chinese girls (who would be the first player) writes sixteen different letters in four rows as shown in the picture. Join two of the letters with a straight line, for example, A and B, pass the board to your opponent, who will have to connect two other letters, for example, E with A, thus making lines joining the letters two by two. If the first player were to connect E and F now, the other player would connect B with F and win a square, which would entitle her to play one more time. Whoever manages to close the most squares wins. Each one will mark their squares to identify them, for example, with an X or with a •
http://acanomas.com/images/ingenio/image065.jpg (16/04/2022)
Observaciones y contexto
- The 9-dot square board is easy to analyse, but the 16-dot board in this exercise is complex enough to be a real challenge.
- It can be played on square or rectangular boards of various shapes and sizes as long as they contain an odd number of squares.
- The game can be expanded and more people can play.
- Julia Bowman had a difficult childhood: her mother died when she was 2 years old; at the age of 10 she contracted rheumatic fever, which forced her to spend a year isolated from others, missing two years of schooling; and her father committed suicide after losing all their savings as a result of the Great Depression, when she was 18 years old.
- Despite missing two years of schooling, when she returned to school, she studied mathematics and physics, being the only woman to attend these classes. She graduated in 1936 with honours in science and was awarded the Bausch-Lomb Honorary Medal for excellent results in mathematics and science.
- She had great family support, in particular from her sister Constance and her adoptive mother, Edenia, who always encouraged her to continue her studies.
- She died in 1985 as a result of leukaemia. Her husband, Raphael Mitchel Robinson, established the Julia Bowman Robinson Scholarship Fund for graduate students in mathematics in Berkeley in 1986.
- Julia Bowman's predecessors are Theano of Crotone (6th century BC) mathematician and philosopher; Hypatia of Alexandria (360-415), mathematician and philosopher; Elena Lucrezia Cornaro Piscopia (1646-1684), mathematician and philosopher; Émilie du Châtelet (1706-1749), mathematician, physicist and philosopher; Laura Maria Catharina Bassi (1711-1778), scientist, poetess and philosopher; Maria Gaetana Agnesi (1718-1799), mathematician, linguist and philosopher; Sophie Germain (1776-1831), mathematician; and Maria Skłodowska-Curie (1867-1934), physicist, mathematician and chemist.
- Her contemporaries were the mathematicians Jacqueline Ferrand (1918-2014), Katherine Johnson (1918-2020), Paulette Libermann (1919-2007), Vera Nikolaevna Kublanovskaya (1920-2012) and Kateryna Yushchenko (1919-2001), mathematician and computer scientist.
- Other important female scientists of the early 20th century are Barbara McClintock (1902-1992), biologist; Rosalind Franklin (1920-1958), chemist; Inge Lehmann (1888-1993) geologist and seismologist; Dorothy Crowfoot Hodgkin (1910-1994), chemist; Mary Leakey (1913-1996), anthropologist; Marie Tharp (1920-2006), geologist and cartographer; Hedy Lamarr (1914-2000), inventor; and Grace Murray Hopper (1906-1992), computer scientist and admiral, among others.
Descripción
The squares game is an abstract strategy game, which is intended to be played on a blackboard (although it can also be played with pencil and paper). It has a mathematical structure and it is part of game theory.