Assertion: circle's area | /r/HasProperty | enclosed by circle
Facets:
value: to a right triangle
type: TRANSITIVE-OBJECT
Source sentences:
text: As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to π multiplied by the radius squared:
text: Suppose that the area enclosed by the circle is less than the area T of the triangle.
text: Therefore, the area of a disk is the more precise phrase for the area enclosed by a circle.
text: Following Archimedes' argument in The Measurement of a Circle (c. 260 BCE), compare the area enclosed by a circle to a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius.
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: The formula for the area of a circle (more properly called the area enclosed by a circle or the area of a disk) is based on a similar method.
text: Therefore, it must be the case that the area enclosed by the circle is precisely the same as the area of the triangle.