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By the Pythagorean theorem, the plane located units above the "equator" intersects the sphere in a circle of radius and area (). The area of the plane's intersection with the part of the cylinder that is outside of the cone is also π ( r 2 − y 2 ) {\displaystyle \pi \left(r^{2}-y^{2}\right)} .
Hipparchus could have constructed his chord table using the Pythagorean theorem and a theorem known to Archimedes. He also might have used the relationship between sides and diagonals of a cyclic quadrilateral , today called Ptolemy's theorem because its earliest extant source is a proof in the Almagest (I.10).
The law of iterated logarithms operates "in between" the law of large numbers and the central limit theorem.There are two versions of the law of large numbers — the weak and the strong — and they both state that the sums S n, scaled by n −1, converge to zero, respectively in probability and almost surely:
The split form, EVIII (or E 8(8)), which has maximal compact subgroup Spin(16)/(Z/2Z), fundamental group of order 2 (implying that it has a double cover, which is a simply connected Lie real group but is not algebraic, see below) and has trivial outer automorphism group.
In mathematics, the Bony–Brezis theorem, due to the French mathematicians Jean-Michel Bony and Haïm Brezis, gives necessary and sufficient conditions for a closed subset of a manifold to be invariant under the flow defined by a vector field, namely at each point of the closed set the vector field must have non-positive inner product with any exterior normal vector to the set.
By Landau's theorem and the observation about the range of H in the proof of the Little Picard Theorem, there is a constant C > 0 such that |H′(w)| ≤ C / Re(w). Thus, for all real numbers x ≥ 2 and 0 ≤ y ≤ 2π,
This is an accepted version of this page This is the latest accepted revision, reviewed on 28 December 2024. Equitable transfer of the risk of a loss, from one entity to another in exchange for payment "Insure" redirects here. Not to be confused with Ensure. For other uses, see Insurance (disambiguation). An advertisement for a fire insurance company Norwich Union, showing the amount of assets ...
The outbreak of the COVID-19 pandemic in 2020 has reduced the growth of every economy in the world, including every sector like banking, insurance and services. [14] Other sectors such as tourism, are also facing challenges and the GDP per capita is expected to drop by 4.2% this period.