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Figure 1 is used for multiples of 1, 3, 7, and 9. Figure 2 is used for the multiples of 2, 4, 6, and 8. These patterns can be used to memorize the multiples of any number from 0 to 10, except 5.
The Rhind Mathematical Papyrus, [1] [2] an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/n into Egyptian fractions (sums of distinct unit fractions), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers.
The following table shows a Relay and Bye Stand Mitchell for eight tables with Table 2 and Table 3 sharing one group of boards and the bye stand between Table 6 and Table 7 (which, with eight tables, are directly opposite Table 2 and Table 3, respectively, in the rotation).
From the Bernegger table: sin (75° 10′) = 0.9666746 sin (75° 9′) = 0.9666001. The difference between these values is 0.0000745. Since there are 60 seconds in a minute of arc, we multiply the difference by 50/60 to get a correction of (50/60)*0.0000745 ≈ 0.0000621; and then add that correction to sin (75° 9′) to get :
Likewise, in the same column we find that the probability that y=1 given that x=0 is 2/9 ÷ 6/9 = 2/6. In the same way, we can also find the conditional probabilities for y equalling 0 or 1 given that x=1. Combining these pieces of information gives us this table of conditional probabilities for y:
The "Left" and "Right" halves of the table show which bits from the input key form the left and right sections of the key schedule state. Note that only 56 bits of the 64 bits of the input are selected; the remaining eight (8, 16, 24, 32, 40, 48, 56, 64) were specified for use as parity bits.
The word 'tables' is derived from the Latin tabula which primarily meant 'board' or 'plank', but also referred to this genre of game. From its plural form, tabulae, come the names in other languages for this family of games including the Anglo-Saxon toefel, German [wurf]zabel, Greek tavli, Italian tavoli, Scandinavian tafl, Spanish tablas and, of course, English and French tables.
This is an injective relation: each combination of the values of the headers row (row 0, for lack of a better term) and the headers column (column 0 for lack of a better term) is related to a unique cell in the table: Column 1 and row 1 will only correspond to cell (1,1); Column 1 and row 2 will only correspond to cell (2,1) etc.