Many curves with interesting and unusual appearance can be easilygenerated using polar coordinates or parametric representation offunctions. The following curves are the results of a challenge given tomy students to find interesting curves.
| Spring 1996 | |||
| Student | Curve | Title | Image |
|---|---|---|---|
| Tripp Livingston | r=cos(10^cos(t)) | A Bug | Image |
| Melissa Finkle | r=(3t)/cos(t^2) | Conjunction | Image |
| Jason Barden | r=cos(t^3)+sin(t^3)+tan(t^3) | Look for Details | Image 1 Image 2 |
| Fall 1996 | |||
| Student | Curve | Title | Image |
| James Walton | r=sin( t^(1/2) ), theta=t^2, t in [0, Pi^2] | Repeating Spiral | Image 1 Image 2 |
| Bert Booker | r=tan(theta^2)-sec(theta^(1/2)) | Flights to Infinity | Image |
| Michelle Abney | x=sin(t)/(sin(t+w1)+s1), y=cos(t)/(cos(t+w2)+s2) | Deflated Balls | Image 1 Image 2 Image 3 |
| Spring 1997 | |||
| Student | Curve | Title | Image |
| Unknown | r=sin(4t)*sin(Pi*t) | Insect Wings | Image |
| Danny Bowen | x=sin(t)*|(cos(0.625t))^(1/2)|, y=sin(t)*|(sin(0.625t))^(1/2)| | Batman | Image |
| Paul Danker | r=Arcsin(cos(cos(sin(sin(3^(2-cos(t-1.6))))))) | Tiger Head | Image |
| Fall 2003 | |||
| Student | Curve | Title | Image |
| Saloua Bakkali, Nick Beasley, Cara Mulcahy, Dayna Rumfelt, Joe Steward | r=k tan(k t) | Crosses | Image 1 Image 2 |
| r=|log(ln(tan(cos^5(sin^2(t)))))|, t in [0,2pi] | Untitled | Image | |
| r=-1+t+cos(t)+cos(t^2)+cos(t^3), t in [0,3pi] | Aurora | Image | |
| x=sin(9t+8), y=cos^2(7t), t in [0,2pi] | Weave | Image | |
| r=Arctan(t^tan(t^Arctan(t))), t in [0,6.65] | Fan | Image | |
| Fall 2004 | |||
| Student | Curve | Title | Image |
| Heidi Armstrong | r=sin(9t), r=-2-sin(t) | Tomato | Image |
| Fall 2005 | |||
| Student | Curve | Title | Image |
| John Buckland | x=cos(3t/4)^3, y=-cos t, 2<t<10.5 | Heart | Image |
| x=2.9(sin(2t)+cos(8t)), y=(sin(8t)+cos(2t))^3 | Bird | Image | |
| Matt Gillman | r=sin(2cos(cosh(cos t))/(sinh(sin t)) | Funny Face | Image |
| Eric Ottosen | x=4.2cos t+0.2cos(2^(n+2) pi/0.2 t), y=4sin t+0.2sin(2^(n+2) pi/0.2 t), 0<t<2pi, n=-4,..,2 | Ring of Fire | Image |
| Spring 2011 | |||
| Student | Curve | Title | Image |
| Christopher Gardiner | r=tan(t/arctan(t))^(1/n), n in [1,infinity) | Ring of Fire 2 | Image |
| Jeremy Luchak | r=ąsin(cos(4/(t+Pi/2)^2))^2 | Vertical Yin Yang | Image |
| William Ruzicka | r=arctan(t)^2/77-cos(t)^2 | Infinifty Over the Finite | Image |
| Spring 2012 | |||
| Student | Curve | Title | Image |
| Cody McWilliams | r=1/2; r=1/2+4cos^6 t | Bowtie | Image |
| Janine Ray | r=sin^6(6t)+sin^5(5t)+sin^4(4t)+sin^3(3t)+sin^2(2t)+sin(t) | Moose | Image |
| Salome Hussein Scott | (tan(cos(3t)), tan(cos(3.1t)+sin(3t)) | Wings in Flight | Image |
