Presentation Title

Hyperbolic Numbers

Presenter Information

Kegan LandfairFollow

Presentation Type

Oral Presentation

School

School of Sciences and Social Sciences

Discipline

Mathematics

Mentor

Vincent Ferlini

Date & Time

April 9th at 10:15 AM - 11:15 AM

Location

David F. Putnam Science Center, Room 102

Abstract

Abstract: The algebraic equation x^2 = 1 has two solutions x = -1, 1. We assume the existence of a new number u, called the unipotent, which has the property that u does not equal -1 or 1 and that u^2 = 1. The hyperbolic numbers then are of the form a + bu where a and b are real numbers. These are similar to complex numbers which are of the form a + bi where i^2 = -1. This talk will present the basic properties of hyperbolic numbers and emphasize the similarity with complex numbers. In addition, the Lorentz equations that relate the times and positions of an event as measured by two observers in relative motion in Einstein’s Theory of Relativity will be derived using hyperbolic numbers.

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Apr 9th, 10:15 AM

Hyperbolic Numbers

David F. Putnam Science Center, Room 102

Abstract: The algebraic equation x^2 = 1 has two solutions x = -1, 1. We assume the existence of a new number u, called the unipotent, which has the property that u does not equal -1 or 1 and that u^2 = 1. The hyperbolic numbers then are of the form a + bu where a and b are real numbers. These are similar to complex numbers which are of the form a + bi where i^2 = -1. This talk will present the basic properties of hyperbolic numbers and emphasize the similarity with complex numbers. In addition, the Lorentz equations that relate the times and positions of an event as measured by two observers in relative motion in Einstein’s Theory of Relativity will be derived using hyperbolic numbers.