#### Presentation Title

When is the Volume of a Hexahedron Equal to the Fourth Root of the Product of its Surface Areas?

#### Presentation Type

Oral Presentation

#### School

School of Sciences and Social Sciences

#### Discipline

Mathematics

#### Mentor

Vincent Ferlini

#### Date & Time

April 9th at 2 PM - 3 PM

#### Location

David F. Putnam Science Center, Room 102

#### Abstract

A recent mathematical result gives the conditions needed to ensure that a quadrilateral will have an area that is equal to the square root of the product of its sides. This research project looks at a similar question in three dimensions. Does a polyhedron with six sides, called a hexahedron, exist with the property that its volume is equal to the fourth root of the product of the areas of its sides? This talk will classify the types of hexahedra that exist and show that there exists at least one of each satisfying the given property.

When is the Volume of a Hexahedron Equal to the Fourth Root of the Product of its Surface Areas?

David F. Putnam Science Center, Room 102

A recent mathematical result gives the conditions needed to ensure that a quadrilateral will have an area that is equal to the square root of the product of its sides. This research project looks at a similar question in three dimensions. Does a polyhedron with six sides, called a hexahedron, exist with the property that its volume is equal to the fourth root of the product of the areas of its sides? This talk will classify the types of hexahedra that exist and show that there exists at least one of each satisfying the given property.