Presentation Title

Four Dimensional Geometry

Presentation Type

Oral Presentation

School

School of Sciences and Social Sciences

Discipline

Mathematics

Mentor

Vincent Ferlini, Ockle Johnson

Abstract

: We live in what we think of as a three-dimensional world. We justify this by noting that if a point is selected as the origin and three mutually perpendicular real number lines are drawn through the origin, then each point in space can be represented by a unique ordered triple of real numbers. If a fourth dimension exists, then there must be a fourth real line through the origin that is perpendicular to the other three. As yet, nobody has demonstrated physical evidence of that fourth dimension. This does not stop us from thinking about it and trying to imagine what objects look like in four dimensions. Using geometric models and computer programs, we will explore ways of understanding four-dimensional space through similarities with the second and third dimensions. We will also present objects that exist in four dimensions but not three.

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Four Dimensional Geometry

: We live in what we think of as a three-dimensional world. We justify this by noting that if a point is selected as the origin and three mutually perpendicular real number lines are drawn through the origin, then each point in space can be represented by a unique ordered triple of real numbers. If a fourth dimension exists, then there must be a fourth real line through the origin that is perpendicular to the other three. As yet, nobody has demonstrated physical evidence of that fourth dimension. This does not stop us from thinking about it and trying to imagine what objects look like in four dimensions. Using geometric models and computer programs, we will explore ways of understanding four-dimensional space through similarities with the second and third dimensions. We will also present objects that exist in four dimensions but not three.