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For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...
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 .Given the perimeter of a non-circular object P, one can calculate its perimeter-equivalent radius by setting
A circle circumference and radius are proportional. The area enclosed and the square of its radius are proportional. The constants of proportionality are 2 π and π respectively. The circle that is centred at the origin with radius 1 is called the unit circle. Thought of as a great circle of the unit sphere, it becomes the Riemannian circle.
If is held constant, and the radius is allowed to vary, then we have = As the central angle approaches π, the area of the segment is converging to the area of a semicircle, π R 2 2 {\displaystyle {\tfrac {\pi R^{2}}{2}}} , so a good approximation is a delta offset from the latter area:
If R is a regular polygon's radius and n is the number of its sides, then its perimeter is 2 n R sin ( 180 ∘ n ) . {\displaystyle 2nR\sin \left({\frac {180^{\circ }}{n}}\right).} A splitter of a triangle is a cevian (a segment from a vertex to the opposite side) that divides the perimeter into two equal lengths, this common length being ...
a = the radius of the base circle h = the height of the paboloid from the base cicle's center to the edge Solid ellipsoid: a, b, c = the principal semi-axes of the ...
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
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. If the area of the circle is not equal to that of the triangle, then it must be either greater or less.