All Science Fair Projects

Title: What Patterns Are Formed When Number Sequences Are Translated
into Different Base Systems and Interpreted in Base-10?

Objectives/Goals

The goal of my project was to find and study patterns formed through the
translation of the first thirty
terms of figurate number sequences into bases-2 through 20 when the results of
these translations are
interpreted in base-10. I hypothesized that I would find patterns related to the
original sequences.

Methods/Materials

An iMac AppleWorks spreadsheet application's base translator, pencil, and paper
were used. The
sequences were entered into the spreadsheet, creating a chart for each sequence
and its translations from
base-2 through 20. For each sequence studied, the chart was scanned for patterns
formed across many or
all of the base systems.

Results

Overall twenty different patterns were found that demonstrated connections
between bases. Most of the
patterns created were related to the sequences that created them. Many patterns
were related to each other
even when the sequences that created them were different.

Conclusions/Discussion

This study demonstrates the relationship between the laws of place value in base
number systems and the
functions that produce the sequences. Many of the patterns are explainable in
mathematical terms, as
discussed further in this study. Future investigation may involve translation of
longer or more complex
sequences into higher bases and/or the use of a computer program to search for
patterns.

Summary Statement

This project explores the mathematical relationships between number sequences
and patterns formed by
their translation into multiple base systems.

Help Received

Mother and Father helped edit report and display.