#### Presentation Title

Hyperbolic Numbers

#### 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.

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.