数学家传记
本杰明·富兰克林是一位美国科学家和外交家。他的数学兴趣包括幻方。
本杰明·富兰克林出生于波士顿,但一生大部分时间在费城度过(其间在伦敦和法国帕西居住)。他的正规教育不到两年,因此他主要是自学成才,得益于在印刷业学徒期间方便地获得书籍。
富兰克林在公众心目中最为人所知的是他的非科学追求:印刷工、美国革命者、大使,仅举他扮演的几个角色。他的科学声誉主要建立在他作为发明家和电学物理学的先驱理论家的成就上,但他的兴趣也涉及数学。他的幻方版本——现在称为富兰克林幻方的一种变体——受到米夏埃尔·施蒂费尔和Frénicle工作的启发,他们两人的幻方都属于更传统的类型。他还绘制了幻圆。
他首次发表的幻方和他唯一发表的幻圆出现在1767年的一本书中,该书还收录了托马斯·辛普森著作中不相关的摘录。两年后,富兰克林发表了这个幻方:
| 52 | 61 | 4 | 13 | 20 | 29 | 36 | 45 |
| 14 | 3 | 62 | 51 | 46 | 35 | 30 | 19 |
| 53 | 60 | 5 | 12 | 21 | 28 | 37 | 44 |
| 11 | 6 | 59 | 54 | 43 | 38 | 27 | 22 |
| 55 | 58 | 7 | 10 | 23 | 26 | 39 | 42 |
| 9 | 8 | 57 | 56 | 41 | 40 | 25 | 24 |
| 50 | 63 | 2 | 15 | 18 | 31 | 34 | 47 |
| 16 | 1 | 64 | 49 | 48 | 33 | 32 | 17 |
除了行和列的和为常数外,这个幻方还有许多其他“神奇”的性质。富兰克林幻方的更多例子直到他去世两个世纪后才得以发表,无疑还有许多已经失传。那些留存下来的相当令人印象深刻。
富兰克林与他那个时代的许多重要思想家,如休谟、普里斯特利、拉瓦锡和尼古拉·德·孔多塞,有着密切的个人和专业关系。他是许多国家学术团体的成员。其中包括皇家学会,该学会因他在电学方面的工作授予他著名的科普利奖章,以及美国哲学学会,他是该学会的创始人之一。他获得了几个荣誉学位,包括圣安德鲁斯的博士学位。
Benjamin Franklin was born in Boston, but spent most of his life in Philadelphia (punctuated by residences in London and Passy, France). His formal education lasted less than two years, and so he was mainly self-educated, aided by the convenient access to books provided by an apprenticeship in the printing business.
Franklin is best known in the popular imagination for his nonscientific pursuits: printer, American revolutionary, ambassador, to mention only a few roles he played. His scientific reputation rests mainly on his accomplishments as an inventor and as a pioneering theorist in the physics of electricity, but his interests were also mathematical. His version of magic square - a variant now termed the Franklin magic square - was inspired by the work of Stifel and Frénicle, both of whose magic squares were of a more traditional variety. He also drew magic circles.
His first published magic square and his only published magic circle appeared in a 1767 book which also included unrelated excerpts from work by Thomas Simpson. Two years later, Franklin published this square:
| 52 | 61 | 4 | 13 | 20 | 29 | 36 | 45 |
| 14 | 3 | 62 | 51 | 46 | 35 | 30 | 19 |
| 53 | 60 | 5 | 12 | 21 | 28 | 37 | 44 |
| 11 | 6 | 59 | 54 | 43 | 38 | 27 | 22 |
| 55 | 58 | 7 | 10 | 23 | 26 | 39 | 42 |
| 9 | 8 | 57 | 56 | 41 | 40 | 25 | 24 |
| 50 | 63 | 2 | 15 | 18 | 31 | 34 | 47 |
| 16 | 1 | 64 | 49 | 48 | 33 | 32 | 17 |
Aside from the row and column sums being constant, this square also has many other "magical" properties. Further examples of Franklin's magic squares would not be published until two centuries after his death, and doubtless many more were lost. Those which do survive are quite impressive.
Franklin enjoyed close personal and professional relationships with quite a few of the important thinkers of his day, such as Hume, Priestley, Lavoisier and Condorcet. He was a member of the learned societies of many nations. Among these were the Royal Society, which awarded him its prestigious Copley medal for his work in electricity, and the American Philosophical Society, of which he was a founder. He received several honorary degrees, including a doctorate from St. Andrews.
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