The bullet curve has three double points in the real projective plane, at x = 0 and y = 0, x = 0 and z = 0, and y = 0 and z = 0, and is therefore a unicursal (rational) curve of genus zero.
If
then
are the two branches of the bullet curve at the origin.
References
J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 128–130. ISBN0-486-60288-5.
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bullet, nose, curve, mathematics, bullet, nose, curve, unicursal, quartic, curve, with, three, inflection, points, given, equation, with, displaystyle, bullet, curve, three, double, points, real, projective, plane, therefore, unicursal, rational, curve, genus,. In mathematics a bullet nose curve is a unicursal quartic curve with three inflection points given by the equationBullet nose curve with a 1 and b 1 a 2 y 2 b 2 x 2 x 2 y 2 displaystyle a 2 y 2 b 2 x 2 x 2 y 2 The bullet curve has three double points in the real projective plane at x 0 and y 0 x 0 and z 0 and y 0 and z 0 and is therefore a unicursal rational curve of genus zero If f z n 0 2 n n z 2 n 1 z 2 z 3 6 z 5 20 z 7 displaystyle f z sum n 0 infty 2n choose n z 2n 1 z 2z 3 6z 5 20z 7 cdots then y f x 2 a 2 b displaystyle y f left frac x 2a right pm 2b are the two branches of the bullet curve at the origin References EditJ Dennis Lawrence 1972 A catalog of special plane curves Dover Publications pp 128 130 ISBN 0 486 60288 5 This algebraic geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Bullet nose curve amp oldid 1124927296, wikipedia, wiki, book, books, library,