anglemathematics
Main
Aspects of this topic are discussed in the following places at Britannica.
role in
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history of geometry
( in geometry: Trisecting the angle )
The Egyptians told time at night by the rising of 12 asterisms (constellations), each requiring on average two hours to rise. In order to obtain more convenient intervals, the Egyptians subdivided each of their asterisms into three parts, or decans. That presented the problem of trisection. It is not known whether the second celebrated problem of archaic Greek geometry, the trisection of any...
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trigonometry ( in trigonometry: Trigonometric functions
)
A somewhat more general concept of angle is required for trigonometry than for geometry. An angle A with vertex at V, the initial side of which is VP and the terminal side of which is VQ, is indicated in the figure by the solid circular arc. This angle is generated by the continuous counterclockwise rotation of a line segment about the point V...
in trigonometry )the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure....
Citations
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role in
-
history of geometry geometry
The Egyptians told time at night by the rising of 12 asterisms (constellations), each requiring on average two hours to rise. In order to obtain more convenient intervals, the Egyptians subdivided each of their asterisms into three parts, or decans. That presented the problem of trisection. It is not known whether the second celebrated problem of archaic Greek geometry, the trisection of any...
-
trigonometry ( in trigonometry: Trigonometric functions
)
A somewhat more general concept of angle is required for trigonometry than for geometry. An angle A with vertex at V, the initial side of which is VP and the terminal side of which is VQ, is indicated in the figure by the solid circular arc. This angle is generated by the continuous counterclockwise rotation of a line segment about the point V...
in trigonometry )the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure....
Student Encyclopædia Britannica articles specifically written for elementary and high school students.
- Online Math Applications -...
member of a Germanic people, which, together with the Jutes, Saxons, and probably the Frisians, invaded England in the 5th century ad. The Angles gave their name to England, as well as to the word Englisc, used even by Saxon writers to denote their vernacular tongue. The Angles are first mentioned by Tacitus (1st century ad) as worshipers of the deity Nerthus. According to the Venerable Bede in the Ecclesiastical History of the English People, their continental homeland was centred in Angulus, traditionally identified as the Angeln district in Schleswig between the Schlei inlet and the Flensburger Förde, which they appear to have abandoned at the time of their invasion of Britain. They settled in large numbers during the 5th and 6th centuries in the kingdoms of Mercia, Northumbria, and East and Middle Anglia.
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etymology of name English language
The Jutes, Angles, and Saxons lived in Jutland, Schleswig, and Holstein, respectively, before settling in Britain. According to the Venerable Bede, the first historian of the English people, the first Jutes, Hengist and Horsa, landed at Ebbsfleet in the Isle of Thanet in 449; and the Jutes later settled in Kent, southern Hampshire, and the Isle of Wight. The Saxons occupied the rest of England...
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Germanic peoples Germanic peoples
...Havel and the Spree rivers, were a Suebic people, as were the Langobardi (Lombards), who lived northwest of the Semnones. Among the seven peoples who worshiped the goddess Nerthus were the Angli (Angles), centred on the peninsula of Angeln in eastern Schleswig. As for the Danubian frontier of the Roman Empire, the Hermunduri extended from the neighbourhood of Regensburg northward through...
history of
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England ancient Rome
...in Sapaudia (Savoy), and established the Alani in Orléans. The other provinces were lost: Britain,...
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use in trigonometry trigonometry
Numerical values can be assigned to angles by selecting a unit of measure. The most common units are the degree and the radian. There are 360° in a complete revolution, with each degree further divided into 60′ (minutes) and each minute divided into 60″ (seconds). In theoretical work, the radian is the most convenient unit. It is the angle at the centre of a circle that...
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hydrocarbons hydrocarbon
...requires the C−C−C angles to be 60°. This 60° angle is much smaller than the normal tetrahedral bond angle of 109.5° and imposes considerable strain (called angle strain) on cyclopropane. Cyclopropane is further destabilized by the torsional strain that results from having three eclipsed C−H bonds above the plane of the ring and three...
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Euclidean geometry Euclidean geometry
...theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. Following this, there are corresponding angle-side-angle (ASA) and side-side-side (SSS) theorems.
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