Tractrix has Cusp on Axis
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Theorem
Let $\TT$ be a tractrix embedded in a Cartesian plane whose axis is the $y$-axis and whose asymptote is the $x$-axis.
The point $\paren {0, a}$ is a single cusp of $\TT$ of the first kind.
Proof
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Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): tractrix
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): tractrix