## 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.