Mathematical Rebuses

Humanistic Mathematics Network Journal Volume 1 | Issue 14

Article 11

11-1-1996

Mathematical Rebuses Florentin Smarandache Pima Community College

Follow this and additional works at: http://scholarship.claremont.edu/hmnj Part of the Mathematics Commons Recommended Citation Smarandache, Florentin (1996) "Mathematical Rebuses," Humanistic Mathematics Network Journal: Vol. 1: Iss. 14, Article 11.

Available at: http://scholarship.claremont.edu/hmnj/vol1/iss14/11

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tiful as it does music. Rothstein backs up this premise and truth. Rothstein de scribe s mathematical proof as with quotes such as this from Hermann Weyl: "My ritual and uses a quote from G. H . Hardy to support work always tried to unite truth with the beautiful; his contention: "If we were to push it to its extreme, bu t when I had to choose one or the other, I usua lly we should be led to rather a paradoxical conclusion: chose the beautiful." The Cantor set, formulae involv - that there is, st rictly, no such thing as mathematical ing pi, and severa l pa ges on the Golden Ratio are in- proof; that we can, in the last analysis, do nothing but clude d as examp les of beau ty in mathe matics. point; that proofs are ... ga s, rhetorical flourishes de signed to affect psycholog y. " In Chapter 5, "Fugue: The Making of Truth," the aesthetic/religiou s natures of mathematics an d music are We are finally prepared for the point: The mathema tidescribed to show wha t the author consi de rs the re- cian, the mu sician, the poet, all imitate "Na tur e at ally impor tant connections of these subjects. We are work, reproducing in their creations the emblem s that Nature had bodied forth in he rs .. . A mathe matician will spin out a new theory or a composer create a miniature sonic universe; a poet will turn an experience "My work always tried to unite truth with the beautiful; a scene into a source of illumina tion. into metaphor, but when I hadto choose one or the other, I usually And each creator will, 'mid circumstances awful and chose the beautiful." sublime,' be as astonished by the result as w as Keple r or Bach." reminded that both mathematics and m usic ha ve been closely associated with religious ritual. How do math- The book is really a wonderful w ork which glorifies ematics and music seem so "othe r world ly" yet im- two subjects of great importance to any civilization. pact our lives daily? This question is not about the It would be excellent as a required or ancill ary readinternal w or kings of the subjects bu t about how they ing in a Libera l Arts Mat hematics course. "map into" the world - it is a que stion about meaning

Mathematical Rebuses Florentin Smarandache Pima Community College Tucson, AZ85709

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mathematical algorithm involving the Fibonacci sequence and the concept of modularity to compose a musical piece. we were rather unexpectedly led to a result in number theory.

lishing Company, Boston (1976).

[31M. Gogins, Iterated Functions Systems Music, Computer Music Journal, 15, (1991) 40-48.

REFERENCES [41 G. Hlooley (ed.), Larousse Em;yclopedia 01 Music, Hamlyn [1 1R. Bidlack, Chaotic Systems as Simple (butComplex) Com- Publishing Group, Lordon. 1971. positional Algorithms, ComputerMusicJoumal, 16, (1992) 33-47.

15JJ. Pressing, Non-linearMaps as Generators of Musical De[21 D. Burton, ElementaryNumber Theory, Allyn and Bacon Pub-

Sign, Computer MusicJoumal, 12, (1988) 35-46.

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REFERENCES

[1] Young, Cindy and Wendy Maulding, "Mathematicsand Mother Goose", Teaching Children Mathematics, 1:1 (September 1994),

[10JShirley, Lawrence H., "Activities fromAfrican Calendar and Time Customs", Mathematics Teaching in the Middle School I :8 (January- February 19961, 616-620_

36-38_ [1 11Berken, Bernadette A., "Multicultural Mathematical Ideas: a [2] Hopkins, Lindy, "Popping Up Numbel Sense", Teaching Chit- New Course", Humanistic Mathematices Network Journal #13 dren Mathematics, 2:2 (October 19951, 82-86.

(May 1996), 34-35_

[3} Schwartz, David M., tf You Make aMittion, New York: Lathrop, Lee and Shepherd Books, 1989.

{1 2] Elkin, Benjamin, Six Foolish Fishermen, Eau Claire,Wisconsin: E.M. Hale and Company.

[4] Oppedal, Diane Cradick, "Mathematicsis Something Good!", Teaching Children Mathmatics, 2:1 (September 19951, 36-40.

[13] Ginsberg, Mirra, Two Greedy Bears, New York : Macmillan,

1976.

15] Munsch,Robert,Motra's Birthday, Toronto :Annick Press, 1987_ (1 4] Nahmad, H_M, "The Ape and the TwoCats",in The Peasant and the Donkey, london: Oxford University Press, 1967.

[6] Bogart, Jo Ellen, Ten forDinner, New York:Scholastic Books , [15] Bulatkin, I. F., "Molla Nasreddinand his Donkey", in Eurasian Fotk and Fairy Tales , New York: Criterion, 1965, 64-68.

1989.

[7} Modesitt, Jeanne, The Story of l , Saxonvilte, Massachusetts:Picture Book Studios, 1990.

[16] Ausubel, Nathan, "Rabbinical ArithmetiC' , in A Treasury 01 JewishFolklore, New York: Crown Publishers, 1948, 93-94.

[8] Myller, Roll, How Big ts a Foot?, New York: Dell PUblishing,

1980.

[17J Walker, Barbara, Watermelons, Walnuts, and the Wisdom of Allah, New York: Parents' MagaZine Press, 1967.

[9] Sullivan, Emilie P. and William Nielsen, "Fictional literaturein Mathematics", Mathematics Teaching in the Middle School 1:8 (January-February 1996), 646-647.

[18] Curcio, Frances R. and MyraZarnowski,"Revisiting the Powers of 2", Teaching Children Mathmatics, 2:5(January 19961, 304.

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