Miscellaneous Curves
 

The ceva trisectrix

This subpage contains pairs of constructions for many different curves instead of being dedicated to only one curve.  It’s not because this array of curves is less important or less interesting than those commanding an entire subpage; it’s because I don’t have enough material on any specific one of them to make it worthwhile for an entire page.  Additionally, most of the constructions will not be 100% geometric; I’m able to use the plotting and graphing capability of my Dynamic Geometry tool, so in many cases, the construction is based on an algebraic interpretation of the curve.  As with all of the previous subpages, the first of the pair is a construction that introduces the curve.  The second of the pair is my artistic rendering based on the first of the pair, but with all of the mathematical information hidden.

 

The Cowboy's Hat

The Cowboy's Hat Art

A Bowditch Curve by Compass Only

A Bowditch Curve by Compass Only Art

The Osculating Circle of a Bowditch Curve 

The Osculating Circle of a Bowditch Curve Art

A Bowditch Curve Tangent

A Bowditch Curve Tangent Art

The Bowditch Family of Curves

The Bowditch Family of Curves Art

The Lemniscate of Gerono and Osculating Circle

The Lemniscate of Gerono and Osculating Circle Art

The Noah Curve 

The Noah Curve Art

Two curves by Parametric Equation

Two curves by Parametric Equation Art

Valentine's Day Curve by Parametric Equation

Valentine's Day Curve by Parametric Equation Art

The Lemniscate of Gerono Made Easy

The Lemniscate of Gerono Made Easy Art

A 5 Cusped Hypocycloid

A 5 Cusped Hypocycloid Art

The Scyphoid by Parametric Equation

The Scyphoid by Parametric Equation Art

The Bicorn Curve by Parametric Equation

The Bicorn Curve by Parametric Equation Art

The Ceva Trisectrix

The Ceva Trisectrix Art