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To construct a diameter parallel to a given line, choose the chord to be perpendicular to the line. The circle having a given line segment as its diameter can be constructed by straightedge and compass, by finding the midpoint of the segment and then drawing the circle centered at the midpoint through one of the ends of the line segment.
The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle ... The formula for the unit circle ...
Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.141359. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides
The arc length, from the familiar geometry of a circle, is s = θ R {\displaystyle s={\theta }R} The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of θ {\displaystyle \theta } ):
A page from Archimedes' Measurement of a Circle. Measurement of a Circle or Dimension of the Circle (Greek: Κύκλου μέτρησις, Kuklou metrēsis) [1] is a treatise that consists of three propositions, probably made by Archimedes, ca. 250 BCE. [2] [3] The treatise is only a fraction of what was a longer work. [4] [5]
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.
The equivalent diameter (or mean diameter) ... the equivalent diameter is the "diameter of a circle with an equal ... The formula for a rotational ellipsoid is ...
When a circle's diameter is 1, its circumference is ... The above formula can be rearranged to solve for the circumference: = ...