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The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius is 2 π . [ a ] Thus the circumference C is related to the radius r and diameter d by: C = 2 π r = π d . {\displaystyle C=2\pi r=\pi d.}
In the special cases of one of the diagonals or sides being a diameter of the circle, this theorem gives rise directly to the angle sum and difference trigonometric identities. [17] The relationship follows most easily when the circle is constructed to have a diameter of length one, as shown here.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown.. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them.
In many other European languages, the word for "inch" is the same as or derived from the word for "thumb", as a man's thumb is about an inch wide (and this was even sometimes used to define the inch [4]). In the Dutch language a term for inch is engelse duim (english thumb).
Following the so-called "quarter-girth formula" (the square of one quarter of the circumference in inches multiplied by 1 ⁄ 144 of the length in feet), the notional log is four feet in circumference, one inch of which yields the hoppus board foot, 1 foot yields the hoppus foot, and 50 feet yields a hoppus ton.
A metric ISO screw thread is designated by the letter M followed by the value of the nominal diameter D (the maximum thread diameter) and the pitch P, both expressed in millimetres and separated by a dash or sometimes the multiplication sign, × (e.g. M8-1.25 or M8×1.25). If the pitch is the normally used "coarse" pitch listed in ISO 261 or ...
For example, “.750-10 UNC-2A” is male (A) with a nominal major diameter of 0.750 inches, 10 threads per inch, and a class-2 fit; “.500-20 UNF-1B” would be female (B) with a 0.500-inch nominal major diameter, 20 threads per inch, and a class-1 fit. An arrow points from this designation to the surface in question. [19]