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Bullet Nose

\begin{figure}\begin{center}\BoxedEPSF{bullet_nose.epsf scaled 600}\end{center}\end{figure}

A plane curve with implicit equation

{a^2\over x^2}-{b^2\over y^2}=1.
\end{displaymath} (1)

In parametric form,
$\displaystyle x$ $\textstyle =$ $\displaystyle a\cos t$ (2)
$\displaystyle y$ $\textstyle =$ $\displaystyle b\cot t.$ (3)

The Curvature is
\kappa={3ab\cot t\csc t\over (b^2\csc^4 t+a^2\sin^2 t)^{3/2}}
\end{displaymath} (4)

and the Tangential Angle is
\phi=\tan^{-1}\left({b\csc^3 t\over a}\right).
\end{displaymath} (5)


Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 127-129, 1972.

© 1996-9 Eric W. Weisstein