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 ?
Another study reported a decrease (improvement) of the mandibular plane angle of OSA children at the 5-year follow-up after adenotonsillectomy and attributed this to the greater posterior face height growth that was affected by the improved level of growth hormone after adenotonsillectomy.
Analysis of the measurements for the vertical component shows that there is no statistically significant difference between the pre- and posttreatment values of the occlusal plane angle (-0.
Pkf = Peak vertical ground reaction force, BW = body weight, KFlexCon = Knee flexion angle at initial contact, FPmax = Frontal plane knee angle at maximum knee flexion, FP30 = Maximum frontal plane angle at 30 degrees of knee flexion, FProm30 = Knee range of motion in the frontal plane from 0 degrees of knee flexion to 30 degrees of knee flexion, FPrommax = Knee range of motion in the frontal plane from 0 degrees of knee flexion to maximum knee flexion, VL = vastus lateralis muscle, VM = vastus medialis muscle, MH = medial hamstring muscles, LH = lateral hamstring muscle, GA = gastrocnemius muscle (Lateral head), * = RMS was normalized to a percent of the greatest RMS value, for that muscle, during the pre-fatigue condition.
The real angle made by two lines, if they are straight, is simply the plane angle made by them; if they are curved, it may be equated with the plane angle made by the two lines tangent to the curves at their point of intersection and lying in the same planes as the curves.
In growing patients with skeletal class II malocclusion combined with high mandibular plane angle, the traditional and most widely used treatment approach ranges from the use of high-pull headgear to the use of mandibular anterior jumping appliance, or combination of both, with or without extraction of permanent teeth.
For the mandibular arch, there was statistically significant correlation between the mandibular plane angle and mandibular inter-canine widths.
The mandibular plane angle Gonial and PP-GoGn angle are larger in persons with AOB.
As noted, the mean pre-treatment maxillary-mandibular plane angle value was 33o, showing a tendency to- wards an associated high angle or increased anterior lower facial height.
As noted, the mean pre-treatment maxillary-mandibular plane angle value was 33o, show- ing a tendency towards an associated high angle or increased anterior lower facial height.
The aim of the present study was to assess whether, vertical parameters such as Maxillary to Mandibular plane angle and Lower facial height play a significant role in the development of lower incisor crowding.
The angular measurements used from Tweed triangle were incisor mandibular plane angle (IMPA) 900+50, Frankfort mandibular plane angle (FMA) 250+50 and Frankfort mandibular incisor angle (FMIA) 650+50 (Fig 1).