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| CentralAngle(central angle) |
| appearance as argument number 1 |
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| (instance CentralAngle TwoDimensionalAngle) | Mid-level-ontology.kif 5869-5869 | Central angle is an instance of two dimensional angle |
| (documentation CentralAngle EnglishLanguage "A CentralAngle is an angle whose apex (vertex) is the center of a Circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arcLength is the central angle of a circle of radius one (measured in Radians).The central angle is also known as the arc's angular distance.[Wikipedia]") | Mid-level-ontology.kif 5870-5874 | Central angle is an instance of two dimensional angle |
| (relatedInternalConcept CentralAngle CenterOfCircleFn) | Mid-level-ontology.kif 5876-5876 | Central angle is internally related to center of circle |
| appearance as argument number 2 |
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| (termFormat EnglishLanguage CentralAngle "central angle") | Mid-level-ontology.kif 5875-5875 |
| antecedent |
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| (=> (instance ?A CentralAngle) (exists (?L ?L2 ?C ?R) (and (equal ?L ClosedLineSegment) (sideOfFigure ?L ?A) (equal ?L2 ClosedLineSegment) (sideOfFigure ?L2 ?A) (equal ?C Circle) (geometricPart ?A ?C) (pointOfIntersection ?L ?L2 (CenterOfCircleFn ?C)) (lineMeasure ?L ?R) (lineMeasure ?L2 ?R) (radius ?C ?R)))) |
Mid-level-ontology.kif 5894-5908 | If X is an instance of central angle, then All of the following hold: (1) there exist Y, Z,, , W (2) V such that equal Y (3) closed line segment (4) the size of X is Y (5) equal Z (6) closed line segment (7) the size of X is Z (8) equal W (9) circle (10) W is a geometric part of X (11) Y is point of intersection Z for the center of circle of W (12) V is a line measure of Y (13) V is a line measure of Z (14) the radius of W is V |
| (=> (and (equal ?S CircleSector) (equal ?A CentralAngle) (angleOfFigure ?A ?S) (equal ?L ClosedLineSegment) (sideOfFigure ?L ?A) (sideOfIntersection ?A ?S ?L) (lineMeasure ?L ?R)) (exists (?AC) (and (equal ?AC CircularArc) (sideOfFigure ?AC ?S) (arcLength ?AC ?R) (angularMeasure ?A (MeasureFn 1 Radian))))) |
Mid-level-ontology.kif 5910-5924 | If All of the following hold: (1) equal X and circle sector (2) equal Y and central angle (3) Y is the angle found in X (4) equal Z and closed line segment (5) the size of Y is Z (6) Z is the intersection Y and X (7) W is a line measure of Z, then there exists V such that equal V and circular arc and the size of X is V and W is the LengthMeasure of V and 1 radian(s) is an angular measure of Y |
| (=> (and (instance ?A CentralAngle) (angleOfFigure ?A ?C) (equal ?C Circle)) (angularMeasure ?A (MeasureFn 360 AngularDegree))) |
Mid-level-ontology.kif 5926-5931 | If X is an instance of central angle, X is the angle found in Y, and equal Y and circle, then 360 angular degree(s) is an angular measure of X |
| consequent |
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| (=> (equal ?S CircleSector) (exists (?A ?AC) (and (equal ?A CentralAngle) (angleOfFigure ?A ?S) (equal ?AC CircularArc) (sideOfFigure ?AC ?S)))) |
Mid-level-ontology.kif 5774-5781 | If equal X and circle sector, then All of the following hold: (1) there exist Y (2) Z such that equal Y (3) central angle (4) Y is the angle found in X (5) equal Z (6) circular arc (7) the size of X is Z |
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