Dictionary:Legendre Theorem

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1. The potential caused by a disk at points away from its axis can be found in terms of the potential on the axis. The solution on the axis can be determined in closed mathematical form, while the solution away from the axis can be found in terms of a Legendre Series. 2. For a spherical triangle which is small compared with the spherical radius, the sides bear the same length relationship as a plane triangle whose corresponding angles are smaller by a third of the spherical excess (q.v.). This theorem is used in correcting plane surveying for Earth curvature. Named for Adrien Marie Legendre (1752–1833), French mathematician.