A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (gōnía) 'angle' and μέτρον (métron) 'measure'. The first known description of a goniometer, based on the astrolabe, was by Gemma Frisius in 1538. Applications Surveying Prior to the invention of the theodolite, the goniometer was used in surveying. The application of triangulation to geodesy was described in the second (1533) edition of Cosmograficus liber by Petri Appiani as a 16-page appendix by Frisius entitled Libellus de locorum describendorum ratione. Communications The Bellini–Tosi direction finder was a type of radio direction finder that was widely used from World War I to World War II. It used the signals from two crossed antennas, or four individual antennas simulating two crossed ones, to re-create the radio signal in a small area between two loops of wire. The operator could then measure the angle to the target radio source by performing direction finding within this small area. The advantage to the Bellini–Tosi system is that the antennas do not move, allowing them to be built at any required size. The basic technique remains in use, although the equipment has changed dramatically. Goniometers are widely used for military and civil purposes, e.g. interception of satellite and naval communications on the French warship Dupuy de Lôme uses multiple goniometers. Crystallography In crystallography, goniometers are used for measuring angles between crystal faces. They are also used in X-ray diffraction to rotate the samples. The groundbreaking investigations of physicist Max von Laue and colleagues into the atomic structure of crystals in 1912 involved a goniometer. Light measurement Goniophotometers measure the spatial distribution of light visible to the human eye (often luminous intensity) at specific angular positions, usually covering all spherical angles. In medicine A goniometer is used to document initial and subsequent range of motion, at the visits for occupational injuries, and by disability evaluators to determine a permanent disability. This is to evaluate progress, and also for medico-legal purposes. It is a tool to evaluate Waddell's signs (findings that may indicate symptom magnification.) Rehabilitative therapy In physical therapy, occupational therapy, and athletic training, a goniometer measures range of motion of limbs and joints of the body. These measurements help accurately track progress in a rehabilitation program. When a patient has decreased range of motion, a therapist