Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti
Authors / Editors
Research Areas
Publication Details
Output type: Journal article
Author list: Euler L, Keppler J
Publisher: Elsevier
Publication year: 2008
Journal: Research Policy (0048-7333)
Volume number: 2
Issue number: 3
ISSN: 0048-7333
URL: http://www.url.com
Abstract
The beautiful Euler spiral, defined by the linear relationship between curvature and arclength, was
first proposed as a problem of elasticity by James Bernoulli, then solved accurately by Leonhard Euler.
Since then, it has been independently reinvented twice, first by Augustin Fresnel to compute diffraction
of light through a slit, and again by Arthur Talbot to produce an ideal shape for a railway transition
curve connecting a straight section with a section of given curvature. Though it has gathered many
names throughout its history, the curve retains its aesthetic and mathematical beauty as Euler had
clearly visualized. Its equation is related to the Gamma function, the Gauss error function (erf), and is
a special case of the confluent hypergeometric function.
Keywords
No matching items found.
