Title

On the Existence of Perfect Cuboids

Presenter Information

Seth Kitchen

Department

Mechanical and Aerospace Engineering

Major

Aerospace Engineering

Research Advisor

Insall, Matt

Advisor's Department

Mathematics and Statistics

Abstract

An Euler brick is a rectangular prism with integer sides and integer face diagonals. A perfect cuboid is an Euler brick with an integer space diagonal. An infinite amount of Euler bricks exist, but before this research, it was an unanswered whether a perfect cuboid existed. We show an exponential and logarithmic equation which could be used to prove the existence or nonexistence of a perfect cuboid (PC). We then continue the computer search for a PC and finish a proof of nonexistence.

Biography

Seth Kitchen is a first year sophomore at Missouri S&T. He was born and raised in Saint Peters, Missouri and graduated from Fort Zumwalt South High School in 2014. At Missouri University of Science and Technology, Seth is involved with the cross country and track teams, AAVG design team, business incubator, and is an advanced mathematics tutor for Project MEGSSS. He is currently managing the thermocouple bay for the electronics subgroup of the campus rocket team. He has also worked on a high school senior research project, The Determination of an Effective Parafoil for Human-Powered Bicycle Aircraft, with a mentor from Boeing. Seth was captain of the Missouri team at the US Department of Energy National Science Bowl in 2014.

Research Category

Sciences

Presentation Type

Poster Presentation

Document Type

Poster

Award

Sciences poster session, First place

Location

Upper Atrium/Hall

Presentation Date

15 Apr 2015, 9:00 am - 11:45 am

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Apr 15th, 9:00 AM Apr 15th, 11:45 AM

On the Existence of Perfect Cuboids

Upper Atrium/Hall

An Euler brick is a rectangular prism with integer sides and integer face diagonals. A perfect cuboid is an Euler brick with an integer space diagonal. An infinite amount of Euler bricks exist, but before this research, it was an unanswered whether a perfect cuboid existed. We show an exponential and logarithmic equation which could be used to prove the existence or nonexistence of a perfect cuboid (PC). We then continue the computer search for a PC and finish a proof of nonexistence.