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Reinhardt's conjecture: the smoothed octagon has the lowest maximum packing density of all centrally-symmetric convex plane sets [48] Sphere packing problems, including the density of the densest packing in dimensions other than 1, 2, 3, 8 and 24, and its asymptotic behavior for high dimensions.
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.
Each fraction / (in lowest terms) has a circle tangent to the line at the point (/,) with curvature . Three of these curvatures, together with the zero curvature of the axis, meet the conditions of Descartes' theorem whenever the denominators of two of the corresponding fractions sum to the denominator of the third.
Alternately, one may use a continued fraction, whose construction is based on the Euclidean algorithm. The continued fraction for 1024 ⁄ 15625 (0.065536 exactly) is [;15,3,1,6,2,1, 3]; [18] its convergent terminated after the repetend is 313 ⁄ 4776, giving us x 0 =–4776 and y 0 =313.
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
In 1991, Levitov proposed that lowest energy configurations of repulsive particles in cylindrical geometries reproduce the spirals of botanical phyllotaxis. [17] More recently, Nisoli et al. (2009) showed that to be true by constructing a "magnetic cactus" made of magnetic dipoles mounted on bearings stacked along a "stem".
2. (of a fold) The imaginary central line or plane dividing the limbs of the fold as symmetrically as possible; the crest from which strata dip downward and away in an anticline, or the lowest depth of the trough from which strata rise in opposite directions in a syncline. [4] 3.