A Look into the Missing Square Puzzle — Presentation Detail — Celebration of Scholars

Instructions

Student presentations must have a faculty sponsor.

Abstracts must include a title and a description of the research, scholarship, or creative work. The description should be 150-225 words in length and constructed in a format or style appropriate for the presenter’s discipline.

The following points should be addressed within the selected format or style for the abstract:

A clear statement of the problem or question you pursued, or the scholarly goal or creative theme achieved in your work.
A brief comment about the significance or uniqueness of the work.
A clear description of the methods used to achieve the purpose or goals for the work.
A statement of the conclusions, results, outcomes, or recommendations, or if the work is still in progress, the results you expect to report at the event.

Presenter photographs should be head and shoulder shots comparable to passport photos.

Additional Information

More information is available at carthage.edu/celebration-scholars/. The following are members of the Research, Scholarship, and Creativity Committee who are eager to listen to ideas and answer questions:

Jun Wang
Kim Instenes
John Kirk
Nora Nickels
Andrew Pustina
James Ripley

A Look into the Missing Square Puzzle

Name: Alexandria Wheeler
Major: Mathematics
Hometown: Kenosha
Faculty Sponsor: Erlan Wheeler
Other Sponsors:
Type of research: Independent research
Funding: N/A

Abstract

In this paper we will be discussing the famous missing square puzzle invented by Paul Curry in 1953. In this problem a triangle is split up into many pieces and seemingly reassembled into another triangle of the same dimensions but missing one square of its area. The purpose of this problem is to teach young math students not to rely on mathematical figures when solving problems, but instead work the problem out. We will show how this puzzle works and delve deeper into the math behind it, including looking into the fact that the Fibonacci numbers appear frequently. We will also show how to make an infinite number of missing square puzzles of different sizes by using the right Fibonacci numbers, and explain why this works. We prove this is true by working through a mathematical proof by induction and relating it back to the missing square puzzle.