2025 Summer Undergraduate Research Program (SURP) symposium
Location
Dr. Ken Budke Family Auditorium, Schindler Education Center, University of Nothern Iowa
Presentation Type
Open Access Poster Presentation
Document Type
poster
Abstract
A quaternion is number which is hyper-complex, it has the form,
Where a₁, a₂, a₃, and a₄ are real “scalars”. Then i, j, and k are imaginary numbers which have the following properties:
q = a1 +a2i + a3j + a3k
Relevant operations on these quaternions include taking the conjugate and the norm (or commonly described as the distance).
The norm of q is equal to:
(a1)2 + (a2)2 + (a3)2 + (a4)2
The conjugate of q is:
¯q = a1 - a2i - a3j - a4k
Note that quaternions are non-abelian, so generally pq ≠ qp.
Start Date
1-8-2025 11:00 AM
End Date
1-8-2025 1:30 PM
Event Host
Summer Undergraduate Research Program, University of Northern Iowa
Faculty Advisor
Theron Hitchman
Department
Department of Mathematics
Copyright
©2025 Parker Sjomeling
File Format
application/pdf
Recommended Citation
Sjomeling, Parker, "Duality of Quadrilaterals via Quaternions" (2025). Summer Undergraduate Research Program (SURP) Symposium. 13.
https://scholarworks.uni.edu/surp/2025/all/13
Duality of Quadrilaterals via Quaternions
Dr. Ken Budke Family Auditorium, Schindler Education Center, University of Nothern Iowa
A quaternion is number which is hyper-complex, it has the form,
Where a₁, a₂, a₃, and a₄ are real “scalars”. Then i, j, and k are imaginary numbers which have the following properties:
q = a1 +a2i + a3j + a3k
Relevant operations on these quaternions include taking the conjugate and the norm (or commonly described as the distance).
The norm of q is equal to:
(a1)2 + (a2)2 + (a3)2 + (a4)2
The conjugate of q is:
¯q = a1 - a2i - a3j - a4k
Note that quaternions are non-abelian, so generally pq ≠ qp.
