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Richard Dedekind gave at least two proofs of Fermat's theorem on sums of two squares, both using the arithmetical properties of the Gaussian integers, which are numbers of the form a + bi, where a and b are integers, and i is the square root of −1. One appears in section 27 of his exposition of ideals published in 1877; the second appeared in ...
If exponentiation is considered as a multivalued function then the possible values of (−1 ⋅ −1) 1/2 are {1, −1}. The identity holds, but saying {1} = {(−1 ⋅ −1) 1/2 } is incorrect. The identity ( e x ) y = e xy holds for real numbers x and y , but assuming its truth for complex numbers leads to the following paradox , discovered ...
As a theme and as a subject in the arts, the anti-intellectual slogan 2 + 2 = 5 pre-dates Orwell and has produced literature, such as Deux et deux font cinq (Two and Two Make Five), written in 1895 by Alphonse Allais, which is a collection of absurdist short stories; [1] and the 1920 imagist art manifesto 2 × 2 = 5 by the poet Vadim Shershenevich.
2.4:1 = 12:5 ~ 21:9 Rounded notation of 2.39:1 also known as 2.40:1. All film releases may use 800 lines of the 1920×800 resolution resulting in the 2.40:1 aspect ratio of Blu-ray Disc. 2.55:1 = 51:20 Original aspect ratio of CinemaScope before optical sound was added to the film in 1954. This was also the aspect ratio of CinemaScope 55. 2 ...
Current M-series sensors are effectively full-frame (crop factor 1.0). 548 mm 2 area Canon's APS-H format for high-speed pro-level DSLRs (crop factor 1.3). Current 1D/5D-series sensors are effectively full-frame (crop factor 1.0). 548 mm 2 area APS-H format for the high-end mirrorless SD Quattro H from Sigma (crop factor 1.35)
In the first international game, Scotland against England on 30 November 1872, England played with seven or eight forwards in a 1–1–8 or 1–2–7 formation, and Scotland with six, in a 2–2–6 formation. For England, one player would remain in defence, picking up loose balls, and one or two players would roam the midfield and kick the ...
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