Steiner's Hat: a Constant-Area Deltoid Associated with the Ellipse
Ronaldo Garcia, Dan Reznik, Hellmuth Stachel, Mark Helman
TL;DR
This paper explores the properties of the Negative Pedal Curve of an ellipse, revealing its affine relation to the Steiner Deltoid and its invariant area across all boundary points.
Contribution
It introduces the concept of the Negative Pedal Curve of an ellipse and its affine connection to the Steiner Deltoid, highlighting invariant area properties.
Findings
Negative Pedal Curve of an ellipse is a 3-cusp closed curve.
This curve is an affine image of the Steiner Deltoid.
The family of these curves has invariant area.
Abstract
The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary point M is a 3-cusp closed-curve which is the affine image of the Steiner Deltoid. Over all M the family has invariant area and displays an array of interesting properties.
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