Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey (Hardcover)

~ (Author)
Key Phrases: parallel bent rows, excentric circles, magic sum, Poor Richard, New York, Benjamin Franklin (more...)

Editorial Reviews

From Publishers Weekly

Pasles, an associate professor of mathematics at Villanova, speculates gleefully on the oft-denied mathematical genius of Benjamin Franklin. The author focuses on magic squares, a type of matrix that Franklin dismissed (inaccurately) as incapable of any useful application but enjoyed playing with for almost 50 years. Not content with matrices where columns, rows and diagonals all have equal sums, Franklin created magic squares where bent diagonals and other groupings have special properties and then went on to develop even more complex magic circles, outclassing not only his contemporaries but also many modern mathematicians Drawing on Franklin's letters and journals as well as modern-day reconstructions of his library, Pasles touches on Franklin's fondness for magazines of mathematical diversions; publication of arithmetic problems in Poor Richard's Almanac; startlingly accurate projections of population growth and cost-benefit arguments against slavery. Going further afield, he suggests that only a man comfortable with numbers would refer to electrical poles as positive and negative and wonders what might have transpired had a young Franklin been introduced to Isaac Newton by a mutual acquaintance. Historians may quail at the textbook-style problems that illustrate various topics, but mathematicians will enjoy them and share Pasles's pleasure at restoring Franklin's tarnished numerological reputation. Color and b&w illus. (Nov.)
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Review

"It was Franklin's electrical work, viewed in the light of Maxwell's equations that gave us genuine mathematical magic." -- Jared Wunsch, Nature

"This book provides plenty of background to help the reader admire his interest." -- Justin Mullins, New Scientist

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Product Details

• Hardcover: 266 pages
• Publisher: Princeton University Press (October 15, 2007)
• Language: English
• ISBN-10: 0691129568
• ISBN-13: 978-0691129563
• Product Dimensions: 9.3 x 6.3 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #150,779 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

5.0 out of 5 stars Franklin's Genius on the Square, February 24, 2008

By	R. Hardy "Rob Hardy" (Columbus, Mississippi USA) - See all my reviews (TOP 50 REVIEWER)    (REAL NAME)

If I could sit down with anyone from the past, my choice would be easy: Benjamin Franklin. Franklin would have been easy to talk to, even if he might have been a little pedantic. But he was funny, and sociable, and what a résumé he has: diplomat, printer, businessman, scientist, inventor, musician, expert chess player, essayist, autobiographer. It is hard to think of any aspect of this myriad-minded man that has not been covered by previous biographers, but they have always tended to leave out his discoveries in mathematics. Paul C. Pasles, an associate professor of mathematical sciences, has now paid tribute to those discoveries, and has uncovered more of them than any previous biographer has known. _Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey_ will be a delight for Franklin fans like me, and it will provide those who are interested in number puzzles, simple to complex, with much to play with. Pasles has included puzzles in every chapter, and, don't worry, has put all the answers and explanations in an appendix. Franklin's mathematical achievements are chiefly his discoveries in magic squares, and readers will come away not only with an appreciation of his mathematical cleverness, but of the beauty of the remarkable objects he discovered.

Franklin didn't do well in math at his school, but became adept at using numbers for his printing business, and had to be able to calculate for some of the tables in his famous almanacs. He used numbers for predictions of population statistics, but the magic square was his mathematical delight. A magic square is an arrangement of numbers in a square grid, generally starting from one and using each successive number in its box on the grid, so that the rows, columns, diagonals, and other patterns add up to the same sum. Franklin did his initial work on the squares around 1736, when he was bored by debates in the Pennsylvania Assembly, for which he was clerk. His attitude expressed in a letter sounds just like the one he had toward all his endeavors: "Not being content with these [regular properties of magic squares], which I looked on as common and easy things, I had imposed on myself more difficult tasks, and succeeded in making other magic squares, with a variety of properties, and much more curious." There are many of his eight-by-eight squares given here, some with elaborate keys; one shows that not only the rows and bent diagonals sum up properly to 260, but so do bent diagonals parallel to the corner-to-corner version, as do the four corner squares added to the four central squares, as do "knight's move" diagonals; and any 2-by-2 inner block of cells adds up to half of 260. Then there are the 16-by-16 monsters. And then there are the magic circles he invented, with radii and concentric circles adding up to a specific number, as do what Franklin called the "excentric" circles spiraling around the circular pattern.

Franklin knew that some of his magic square inventions were better than any that had ever been made. Of one, he wrote, "...for I make no question you will readily allow this square of 16 to be the most magically magical of any magic square ever made by any magician." And yet they represented Franklin at play, and he remained modest about his magic square efforts, writing later in life that he had amused himself at making magic squares because he had the leisure, leisure which "I still think I might have employed more usefully". Franklin was eventually disappointed in his studies in electricity because (when electrical storage was still primitive) it could not be made practical and beneficial, and maybe he would have felt this way about his magic squares as well. Utility, Pasles reminds us, is not the measure of good mathematics, however. "Our object," he writes, "is not to show that Franklin would have identified himself as a mathematician, only that he was adept at the systematic and creative ways of thinking about numbers, arrangements, and relationships that characterize mathematical thought." Pasles has included many of Franklin's squares, and printed many in colors that show the complicated weave of patterns within them. It is a wonderful introduction to an entirely new way of admiring a great thinker.

1 of 1 people found the following review helpful:

5.0 out of 5 stars An original and quick read, March 25, 2008

By	Antonio Cangiano (Toronto, Canada) - See all my reviews

Most geeks admire Ben Franklin, and not only for patriotic reasons. He was a brilliant, vibrant mind who made contributions to several fields. There isn't a lack of biographies about the man. Or even good ones at that. What this short (and sweet) book does though, is to cover Franklin as a mathematician, a side of the genius that is often hidden or disputed. This hardcover focuses on Magic Squares and Franklin's contribution to this field, even though he wrongly considered them as enjoyable, but useless in practice. Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey is filled with mathematical puzzles and will be a pleasure to read for those who can appreciate small challenges and the historical importance of Pasles' research.

5.0 out of 5 stars Ben"s Genius, July 9, 2008

By	Ely J. Titley "ejt" (ct.usa) - See all my reviews (REAL NAME)

Benjamin Franklin's Numbers is very facinating, I never knew he more than a founding father. This is a great book for anyone who loves numbers and has a math background, something you won't learn in school.