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In geometry, the area enclosed by a circle of radius r is πr 2.Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that ( 2 r − x ) x = ( y / 2) 2 .
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes' twin circles. If the arbelos is normed such that the diameter of its outer (largest) half circle has a length of 1 and r denotes the radius of any of the inner half circles, then the radius ρ of such an Archimedean ...
In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [8] The longest diameter is called the ...
Consider a circle in with center at the origin and radius . Gauss's circle problem asks how many points there are inside this circle of the form ( m , n ) {\displaystyle (m,n)} where m {\displaystyle m} and n {\displaystyle n} are both integers.
Measurement of tree circumference, the tape calibrated to show diameter, at breast height. The tape assumes a circular shape. The perimeter of a circle of radius R is 2 π R {\displaystyle 2\pi R} .
Draw the diameter of the circle by joining points and with a straight line ¯. Draw the Mohr Circle . The centre O {\displaystyle O} of the circle is the midpoint of the diameter line A B ¯ {\displaystyle {\overline {AB}}} , which corresponds to the intersection of this line with the σ n {\displaystyle \sigma _{\mathrm {n} }} axis.