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Curious Properties of an Iterative Process How could high school students present original mathematics research using Mathematica?

Ryohei Miyadera
Organization: Kwansei Gakuin High School
Department: Mathematics Department
Hiroaki Simoda
Hiroki Takebayashi
Naoya Urakawa
Kousuke Morimoto
Yoshiro Okamoto
Koichi Tukiyama
Yasuhumi Kotera
Horoshi Takimoto
Daisuke Minematu
Masahumi Matuda
Akihiko Obe

2004 International Mathematica Symposium
Conference location

Banff, Canada

We define a function by dsf[n] = a+ a+ ... + a where {a, a, ..., a} is the list of the digits of an integer n. Suppose we start with any positive integer n, and repeatedly apply the function dsf. We can then generate a sequence of integers a . This sequence will eventually enter into one of 8 kinds of loops. We could prove this fact using Mathematica. Many of ideas in this paper are proposed by students, and this research shows what High School students can achieve.

*Education > Precollege

iterative process, high school education, mathematics research
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*New Ideas in Symbolic Computation: Proceedings of the 6th International Mathematica Symposium   [in Books]