Plane Angle


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Related to Plane Angle: solid angle

plane angle

[′plān ‚aŋ·gəl]
(mathematics)
An angle between lines in the euclidean plane.

Angle, Plane

 

A plane angle, often called simply an angle, is a geometric figure formed by two rays that extend from a single point. The rays are known as the sides of the angle, and the point is called the vertex of the angle.

An angle with its vertex at the center O of a circle is referred to as a central angle. Such an angle determines on the circle an arc AB that is bounded by the points of intersection of the circle and the sides of the angle. This fact permits the measurement of angles to be reduced to the measurement of the corresponding arcs. Angles are commonly measured in degrees or radians.

Two angles such that each side of one is an extension, through the vertex, of a side of the other are said to be vertical angles. If two angles share a common side and their other sides lie on the same line, the angles are said to be adjacent supplementary angles.

In a number of practical problems it is desirable to treat an angle as a figure obtained by rotating a ray about its origin O to a specified position. In this case the angle is a measure of the rotation of the ray. Such an approach makes it possible to extend the concept of an angle. According to the direction of rotation, for example, a distinction can be made between positive and negative angles. We may speak of angles greater than 180° and angles equal to 0°. In trigonometry this approach permits the study of trigonometric functions for any value of the argument.

If two curves extend from a common point at which each curve has a definite tangent, the angle between the two tangents is taken as the angle between the two curves. The concept of a plane angle can be extended also to various objects considered in solid geometry. For example, the angle between a line and a plane is the smaller angle the line makes with its projection on the plane. The angle between two skew lines is the smaller angle formed by two lines that are parallel to the skew lines and share a common point. (See alsoDIHEDRAL ANGLE, POLYHEDRAL ANGLE, and SOLID ANGLE.)

References in periodicals archive ?
The inclination of upper incisors was evaluated using U1 to N-A (Angular), U1 to palatal plane angle and U1 to SN plane angle (Table 2).
Changing the bedding plane angles has a large impact on crack initiation and propagation.
Since the number of particles produced in heavy-ion collisions are finite, the calculated event plane angle [[PSI].sub.2] may not coincide with [[PSI].sub.r].
In the present study OSA children showed significantly steeper mandibular plane angle as compared to control.
It is clear from Figures 25(a) to 25(f) that an increase of the joint plane angle has significantly influenced the shape and size of damage zone.
The metal cutting theorist would like to help with this question but, along the way, might also like to predict shear plane angle, cutting forces, and temperatures, as well as estimating the likely tool life at any given speed.
The cephalometric measurements used to assess vertical control were: Y-axis, occlusal plane angle, FMA, PP.MP, SN.MP, SN.PP, Co-Go, AFH, PFH and FHI (Figure 3).
The goniometer provides a measurement of the frontal plane angle between the thigh and leg and did not account for lower extremity or knee positioning involving thigh or leg rotation.
Generally, there are several groups of plane angle measurement methods which could be implemented for the mentioned task [1].
It contains the indenter, which is diamond pyramid as per Vickers, with 136-degree plane angle to meet industry requirements.