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
Keywords
Quaternions; Quadrilaterals;
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.
