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Wednesday, 4 February 2015

Trigonometry

Trigonometry


Trigonometry (from the greek Trigonon (τρίγωνον, triangle) and Metron (μέτρον, measure): resolution of the triangle) is the part of mathematics that studies triangles starting from their corners. The main task of trigonometry, as well as reveals the etymology of the name, is to calculate the measures that characterize the elements of a triangle (the sides, corners, medians, etc.) starting from other measures already known (at least three, of which at least a length), by means of special functions. 

This task is referred to as the resolution of the triangle. You can also make use of trigonometric calculations in solving problems related to more complex geometric shapes, such as polygons or solid geometrical figures, and in many other branches of mathematics.

Trigonometric functions (the most important of which are the sine and cosine), introduced in this area, are also used independently from the geometry, appearing in other fields of mathematics and its applications, for example in connection with the function exponential or with vector operations.


For many centuries, trigonometry had his progress almost exclusively the work of great astronomers and geographers. In fact, the foundation of this science is due to Hipparchus and Ptolemy, both astronomers and geographers that most mathematicians. Significant contributions were made to this science by the Arabs, from the French Gersonides and later by Copernicus and Tycho Brahe, aims to describe and predict ever more precisely the celestial phenomena, also for a more accurate and convenient calculation of longitudes and latitudes.

The Optical Mirror

The Optical Mirror


Telescopes and other sophisticated tools are used mirrors to aluminizing front, ie where the metal layer is applied by the reflective side of the glass. This eliminates the double reflections and increases to 90-95% the proportion of reflected light (mirror new), but at the same time requires attention in handling the delicate object. Sometimes it is used the silver but more often the aluminum, which better reflects at shorter wavelengths, which are applied in vacuum chambers.

 Often also is deposited a protective layer over the reflective to prevent oxidation and corrosion. The coating needs to be redone periodically to maintain high performance, for this astronomical possibly have laboratories aluminizing. The reflectivity of a mirror is measured with the reflectometer, and is a function of the wavelength used and the metal. Sometimes we talk about it with mirrors hot or cold. The cold mirror reflects visible light but is transparent to infrared light, while the hot mirror does exactly the opposite, reflecting the infrared rays. In the halogen-type dichroic cold mirror reflector reflects visible light in a useful beam, while the infrared rays unnecessary through the reflector and are dispersed on the back of the lamp.

For particular scientific applications, for example in lasers, dielectric mirrors are often used, in which on the glass or more often other materials, is deposited a layer of dielectric material. by appropriately selecting the material and its thickness, can predetermine reflected light spectrum and reflectivity. The best mirrors of this type come to reflect the 99,999% of the incident light (in a limited range of wavelengths).