Search results
Results from the WOW.Com Content Network
In the special case of λ, μ and ν real, with 0 ≤ λ,μ,ν < 1 then the s-maps are conformal maps of the upper half-plane H to triangles on the Riemann sphere, bounded by circular arcs. This mapping is a generalization of the Schwarz–Christoffel mapping to triangles with circular arcs. The singular points 0,1 and ∞ are sent to the ...
Wallis derived this infinite product using interpolation, though his method is not regarded as rigorous. A modern derivation can be found by examining ∫ 0 π sin n x d x {\displaystyle \int _{0}^{\pi }\sin ^{n}x\,dx} for even and odd values of n {\displaystyle n} , and noting that for large n {\displaystyle n} , increasing n ...
John Wallis (26 December 1650 – 14 March 1717), [7] MP for Wallingford 1690–1695, married Elizabeth Harris (d. 1693) on 1 February 1682, with issue: one son and two daughters Elizabeth Wallis (1658–1703 [ 8 ] ), married William Benson (1649–1691) of Towcester, died with no issue
Spatial extract, transform, load (spatial ETL), also known as geospatial transformation and load (GTL), is a process for managing and manipulating geospatial data, for example map data. It is a type of extract, transform, load (ETL) process, with software tools and libraries specialised for geographical information.
In hyperbolic geometry (where Wallis's postulate is false) similar triangles are congruent. In the axiomatic treatment of Euclidean geometry given by George David Birkhoff (see Birkhoff's axioms ) the SAS similarity criterion given above was used to replace both Euclid's parallel postulate and the SAS axiom which enabled the dramatic shortening ...
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
The first, Fast Johnson Lindenstrauss Transform (FJLT), [11] was introduced by Ailon and Chazelle in 2006. This method allows the computation of the matrix vector product in just d log d + k 2 + γ {\displaystyle d\log d+k^{2+\gamma }} for any constant γ > 0 {\displaystyle \gamma >0} .
In Arnold's native Russian, the map is known as "okroshka (cold soup) from a cat" (Russian: окрошка из кошки), in reference to the map's mixing properties, and which forms a play on words. Arnold later wrote that he found the name "Arnold's Cat" by which the map is known in English and other languages to be "strange". [2]