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1—10 of 19 matching pages
1: 4.42 Solution of Triangles
2: 22.18 Mathematical Applications
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§22.18(i) Lengths and Parametrization of Plane Curves
►Ellipse
… ►The arc length in the first quadrant, measured from , is … ►Lemniscate
… ►The arc length , measured from , is …3: 19.30 Lengths of Plane Curves
§19.30 Lengths of Plane Curves
►§19.30(i) Ellipse
… ►The length of the ellipse is … ►§19.30(ii) Hyperbola
… ►The perimeter length of the lemniscate is given by …4: 32.14 Combinatorics
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►With , is said to be an increasing
subsequence of of length
when .
Let be the length of the longest increasing subsequence of .
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32.14.1
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5: 23.23 Tables
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►The values are tabulated on the real and imaginary -axes, mostly ranging from 0 to 1 or in steps of length 0.
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6: 26.13 Permutations: Cycle Notation
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►Cycles of length one are fixed points.
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►An element of with fixed points, cycles of length
cycles of length
, where , is said to have cycle type
.
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►A transposition is a permutation that consists of a single cycle of length two.
…A permutation that consists of a single cycle of length
can be written as the composition of two-cycles (read from right to left):
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7: 27.16 Cryptography
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►To code a message by this method, we replace each letter by two digits, say , , , , and divide the message into pieces of convenient length smaller than the public value .
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8: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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is the number of permutations of with cycles of length 1, cycles of length 2, , and cycles of length
:
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9: 3.1 Arithmetics and Error Measures
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►Computer algebra systems use exact rational arithmetic with rational numbers , where and are multi-length integers.
During the calculations common divisors are removed from the rational numbers, and the final results can be converted to decimal representations of arbitrary length.
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10: 7.20 Mathematical Applications
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►Then the arc length between the origin and equals , and is directly proportional to the curvature at , which equals .
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