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US hat size is the circumference of the head, measured in inches, divided by pi, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter. [1] Diameter at breast height is the circumference of tree trunk, measured at height of 4.5 feet, divided by pi. This corresponds to the 1D mean diameter.
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 ...
Dimensionless quantities, or quantities of dimension one, [1] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [2] [3] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units.
The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m −1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus
The zero-dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ∞ if the set is infinite. Likewise, the one-dimensional Hausdorff measure of a simple curve in R n {\displaystyle \mathbb {R} ^{n}} is equal to the length of the curve, and the two-dimensional Hausdorff measure of a Lebesgue-measurable subset ...
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A basic dimension of zero is assumed where axes, center planes, or surfaces are shown coincident on a drawing, and the relationship between features is defined by geometric tolerances. Dimensions and tolerances are valid at 20 °C (68 °F) and 101.3 kPa (14.69 psi) unless stated otherwise.