On square-dance numbers and mirror multiplication

• Main Author: Chua, Chandice R.
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Programming (Mathematics); Number theory; Multiplication
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16437
• Institution: De La Salle University

Numbers that are seemingly uninteresting at first glance possesses certain features that are unknown to us. Such is the case of the square-dance numbers and mirror multipliers. These two special numbers are the kind of numbers that have unique properties and characteristics. Based on two articles Square-Dance Numbers by J. Schwartzman and H.S. Schultz (1989), and Mirror Multiplication by J. H. Manheim (1979), these numbers are fascinating enough to deserve a more in-depth study. Square-Dance Numbers are even numbers n, having the property that the set (1,2,3,..., n) can be partitioned into pairs so that the sum of each pair is a square. On the other hand, Mirror Multiplication is about searching for products such that when the digits are reversed, the answer remains the same. Several theorems, based from some observed properties possessed by these special numbers, are established to help generate such numbers systematically. However, certain square-dance numbers that cannot be generated by these theorems need to employ the trial and error method. A computer program is included in this study to further expedite the generation of these special numbers, and to present other unique pairings for some square-dance numbers.