2023 Summer Undergraduate Research Program (SURP) Symposium
Location
ScholarSpace, Rod Library, University of Northern Iowa
Presentation Type
Open Access Poster Presentation
Document Type
poster
Abstract
p-Circles are a generalization of the usual circle satisfying the equation |x|p + |y|p = 1. The 1-circle is the square with vertices (1,0),(0,1),(-1,0),(0,-1). As p goes to infinity the p-circle equation becomes max(|x|, |y|) = 1. So the ∞-circle is the square with vertices (1,1),(-1,1),(-1,-1),(1,-1). From 1≤p≤2 the p-circle smoothly transforms from a square to a circle, and from 2≤p≤∞ the p-circle smoothly transforms from a circle to a square.
Start Date
28-7-2023 11:00 AM
End Date
28-7-2023 1:30 PM
Event Host
Summer Undergraduate Research Program, University of Northern Iowa
Faculty Advisor
Bill Wood
Department
Department of Mathematics
Copyright
©2023 Isaiah Dempsey and Dr. Bill Wood
File Format
application/pdf
Recommended Citation
Dempsey, Isaiah and Wood, Bill, "Geometric Curves from p-Circles" (2023). Summer Undergraduate Research Program (SURP) Symposium. 2.
https://scholarworks.uni.edu/surp/2023/all/2
Geometric Curves from p-Circles
ScholarSpace, Rod Library, University of Northern Iowa
p-Circles are a generalization of the usual circle satisfying the equation |x|p + |y|p = 1. The 1-circle is the square with vertices (1,0),(0,1),(-1,0),(0,-1). As p goes to infinity the p-circle equation becomes max(|x|, |y|) = 1. So the ∞-circle is the square with vertices (1,1),(-1,1),(-1,-1),(1,-1). From 1≤p≤2 the p-circle smoothly transforms from a square to a circle, and from 2≤p≤∞ the p-circle smoothly transforms from a circle to a square.
