Mathematical Excursions

Mathematical Excursions: Side Trips along Paths Not Generally Traveled in Elementary Courses in Mathematics is a book on popular mathematics. It was written by Helen Abbot Merrill, published in 1933 by the Norwood Press,[1][2][3][4][5] and reprinted (posthumously) by Dover Publications in 1957.[6][7]

Topics

The book is devoted to mathematical puzzles and pastimes,[6] gathered from Merrill's experience as a teacher.[1][3] It has 15 chapters,[4] most on arithmetic and number theory but with one on geometry.[6]

Its topics include squared triangular numbers and other sums of powers,[5] Russian peasant multiplication,[2] binary numbers,[2][6] repeating decimals,[2] magic squares,[4] the irrationality of π,[2][5] mechanical linkages, linear Diophantine equations, the 15 puzzle,[6] perfect numbers,[7] and some unsolved problems in number theory.[2][5][6]

Audience and reception

The book is written for a general audience,[1] and is intended to spark the interest of high school students in mathematics.[4] In general, only high school levels of algebra and geometry are needed to appreciate the book and solve its problems.[1] It could be used as individual reading, or in mathematics clubs,[2] and also for mathematics teachers looking for examples and demonstrations for their classes.[5]

Of the original edition, reviewer David Eugene Smith wrote "the book ought to be in the hands of all teachers and on the shelves of all high schools and colleges".[3] By the time of the 1957 reprint, reviewer Samuel L. Greitzer complained about its obsolete notation, as well as its uneven level of exposition and non-uniform inclusion of solutions to problems,[6] and reviewer Roland Sprague noted that its treatment of perfect numbers was out of date.[7] Nevertheless, Greitzer suggested that it would be appropriate as "enrichment" for high-school students.[6]

References
  1. The Mathematics Teacher, 26 (5): 315, May 1933, JSTOR 27951594CS1 maint: untitled periodical (link)
  2. Wells, Mary E. (December 1933), The American Mathematical Monthly, 40 (10): 602–603, doi:10.2307/2301690, JSTOR 2301690CS1 maint: untitled periodical (link)
  3. Smith, David Eugene (December 1933), The Mathematics Teacher, 26 (8): 499–501, JSTOR 27951644CS1 maint: untitled periodical (link)
  4. P. W. L. C. (January 1934), The Marginal Fifty per Cent, Junior-Senior High School Clearing House, 8 (5): 319, JSTOR 30174218CS1 maint: untitled periodical (link)
  5. Inglis, Alex (February 1935), The Mathematical Gazette, 19 (232): 62, doi:10.2307/3606651, JSTOR 3606651CS1 maint: untitled periodical (link)
  6. Greitzer, Samuel L. (October 1958), The Mathematics Teacher, 51 (6): 481, JSTOR 27955732CS1 maint: untitled periodical (link)
  7. Sprague, R., zbMATH, Zbl 0080.00105CS1 maint: untitled periodical (link)
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