Bring's curve

In mathematics, Bring's curve is the curve given by the equations

$v+w+x+y+z=v^2+w^2+x^2+y^2+z^2=v^3+w^3+x^3+y^3+z^3=0.$

It was named by Klein (2003, p.157) after Erland Samuel Bring who studied a similar construction in 1786 in Promotionschrift submitted to the University of Lund.

References

• Bring, Erland Samuel; Sommelius, Sven Gustaf (1786), Meletemata quædam mathematica circa transformationem æquationem algebraicarum, Promotionschrift, University of Lund
• Edge, W. L. (1978), "Bring's curve", Journal of the London Mathematical Society 18 (3): 539–545, doi:10.1112/jlms/s2-18.3.539, ISSN 0024-6107, MR 518240
• Klein, Felix (2003) [1884], Lectures on the icosahedron and the solution of equations of the fifth degree, Dover Phoenix Editions, New York: Dover Publications, ISBN 978-0-486-49528-6, MR 0080930