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Cuello is a Maya archaeological site in northern Belize. The site is that of a farming village with a long occupational history. It was originally dated to 2000 BC, but these dates have now been corrected and updated to around 1200 BC. [1] [2] Its inhabitants lived in pole-and-thatch houses that were built on top of low plaster-coated platforms ...
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. [1] [2] The exponents p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89. [3]
Thus, the smallest candidate for the next double Mersenne prime is , or 2 2305843009213693951 − 1. Being approximately 1.695 × 10 694127911065419641, this number is far too large for any currently known primality test. It has no prime factor below 1 × 10 36. [2]
The black dot shows the point with coordinates x = 2, y = 3, and z = 4, or (2, 3, 4). A Cartesian coordinate system for a three-dimensional space consists of an ordered triplet of lines (the axes ) that go through a common point (the origin ), and are pair-wise perpendicular; an orientation for each axis; and a single unit of length for all ...
[2] Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational symmetry about the longitudinal axis, such as water flow in a straight pipe with round cross-section, heat distribution in a metal cylinder , electromagnetic fields produced by an electric current in a long, straight wire, accretion disks ...
These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.