Assertion: circle's area | /r/HasProperty | proportional
Facets:
value: to the square of its diameter
type: OTHER
value: to its radius
type: LOCATION
value: always
type: DEGREE
value: to its angle
type: OTHER
value: to the arc length
type: OTHER
Source sentences:
text: (The areas are proportional.)
text: Eudoxus of Cnidus in the fifth century B.C. had found that the area of a disk is proportional to its radius squared.
text: Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.
text: 2π (because the area of the sector is proportional to its angle, and 2π is the angle for the whole circle, in radians):
text: In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk (the region enclosed by a circle) is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.
text: Eudoxus of Cnidus, also in the 5th century BCE, also found that the area of a disk is proportional to its radius squared.
text: The area of sector is always proportional to the arc length.