Radian Comparison Table

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Radian comparison table

Subject is an instance of documentation is a kind of be second domain of be first domain of have axiom

PlaneAngleMeasure A ConstantQuantity is a PhysicalQuantity which has a constant value, e.g. 3 meters and 5 hours. The magnitude (see MagnitudeFn) of every ConstantQuantity is a RealNumber. ConstantQuantities are distinguished from FunctionQuantities, which map ConstantQuantities to other ConstantQuantities. All ConstantQuantites are expressed with the BinaryFunction MeasureFn, which takes a Number and a UnitOfMeasure as arguments. For example, 3 Meters can be expressed as (MeasureFn 3 Meter). ConstantQuantities form a partial order (see PartialOrderingRelation) with the lessThan relation, since lessThan is a RelationExtendedToQuantities and lessThan is defined over the RealNumbers. The lessThan relation is not a total order (see TotalOrderingRelation) over the class ConstantQuantity since elements of some subclasses of ConstantQuantity (such as length quantities) are incomparable to elements of other subclasses of ConstantQuantity (such as mass quantities) ConstantQuantity measure TangentFn
(=>
(instance ?FUNCTION UnaryConstantFunctionQuantity)
(and
(domain ?FUNCTION 1 ConstantQuantity)
(range ?FUNCTION ConstantQuantity)))

SystemeInternationalUnit The Class of Systeme International (SI) units UnitOfMeasure MeasureFn SubtractionFn
(=>
(and
(instance ?REL RelationExtendedToQuantities)
(instance ?REL BinaryRelation)
(instance ?NUMBER1 RealNumber)
(instance ?NUMBER2 RealNumber)
(holds ?REL ?NUMBER1 ?NUMBER2))
(forall (?UNIT)
(=>
(instance ?UNIT UnitOfMeasure)
(holds ?REL (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)))))

Radian SystemeInternationalUnit SI PlaneAngleMeasure. Symbol: rad. It is the angle of a circle subtended by an arc equal in length to the circle's radius. Another definition is: the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius. Radian = m/m = 1 MeasureFn TangentFn
(equal
(MeasureFn ?NUMBER AngularDegree)
(MeasureFn (MultiplicationFn ?NUMBER (DivisionFn Pi 180)) Radian))

Subject	is an instance of	documentation	is a kind of	be second domain of	be first domain of	have axiom
PlaneAngleMeasure		A ConstantQuantity is a PhysicalQuantity which has a constant value, e.g. 3 meters and 5 hours. The magnitude (see MagnitudeFn) of every ConstantQuantity is a RealNumber. ConstantQuantities are distinguished from FunctionQuantities, which map ConstantQuantities to other ConstantQuantities. All ConstantQuantites are expressed with the BinaryFunction MeasureFn, which takes a Number and a UnitOfMeasure as arguments. For example, 3 Meters can be expressed as (MeasureFn 3 Meter). ConstantQuantities form a partial order (see PartialOrderingRelation) with the lessThan relation, since lessThan is a RelationExtendedToQuantities and lessThan is defined over the RealNumbers. The lessThan relation is not a total order (see TotalOrderingRelation) over the class ConstantQuantity since elements of some subclasses of ConstantQuantity (such as length quantities) are incomparable to elements of other subclasses of ConstantQuantity (such as mass quantities)	ConstantQuantity	measure	TangentFn	(=> (instance ?FUNCTION UnaryConstantFunctionQuantity) (and (domain ?FUNCTION 1 ConstantQuantity) (range ?FUNCTION ConstantQuantity)))
SystemeInternationalUnit		The Class of Systeme International (SI) units	UnitOfMeasure	MeasureFn	SubtractionFn	(=> (and (instance ?REL RelationExtendedToQuantities) (instance ?REL BinaryRelation) (instance ?NUMBER1 RealNumber) (instance ?NUMBER2 RealNumber) (holds ?REL ?NUMBER1 ?NUMBER2)) (forall (?UNIT) (=> (instance ?UNIT UnitOfMeasure) (holds ?REL (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)))))
Radian	SystemeInternationalUnit	SI PlaneAngleMeasure. Symbol: rad. It is the angle of a circle subtended by an arc equal in length to the circle's radius. Another definition is: the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius. Radian = m/m = 1		MeasureFn	TangentFn	(equal (MeasureFn ?NUMBER AngularDegree) (MeasureFn (MultiplicationFn ?NUMBER (DivisionFn Pi 180)) Radian))

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