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117 lines
3.6 KiB
Text
117 lines
3.6 KiB
Text
\Module \Math provides methods for basic trigonometric,
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logarithmic, and transcendental functions, and for extracting roots.
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You can write its constants and method calls thus:
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Math::PI # => 3.141592653589793
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Math::E # => 2.718281828459045
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Math.sin(0.0) # => 0.0
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Math.cos(0.0) # => 1.0
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If you include module \Math, you can write simpler forms:
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include Math
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PI # => 3.141592653589793
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E # => 2.718281828459045
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sin(0.0) # => 0.0
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cos(0.0) # => 1.0
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For simplicity, the examples here assume:
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include Math
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INFINITY = Float::INFINITY
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The domains and ranges for the methods
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are denoted by open or closed intervals,
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using, respectively, parentheses or square brackets:
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- An open interval does not include the endpoints:
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(-INFINITY, INFINITY)
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- A closed interval includes the endpoints:
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[-1.0, 1.0]
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- A half-open interval includes one endpoint, but not the other:
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[1.0, INFINITY)
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Many values returned by \Math methods are numerical approximations.
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This is because many such values are, in mathematics,
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of infinite precision, while in numerical computation
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the precision is finite.
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Thus, in mathematics, <i>cos(π/2)</i> is exactly zero,
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but in our computation <tt>cos(PI/2)</tt> is a number very close to zero:
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cos(PI/2) # => 6.123031769111886e-17
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For very large and very small returned values,
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we have added formatted numbers for clarity:
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tan(PI/2) # => 1.633123935319537e+16 # 16331239353195370.0
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tan(PI) # => -1.2246467991473532e-16 # -0.0000000000000001
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See class Float for the constants
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that affect Ruby's floating-point arithmetic.
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=== What's Here
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==== Trigonometric Functions
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- ::cos: Returns the cosine of the given argument.
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- ::sin: Returns the sine of the given argument.
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- ::tan: Returns the tangent of the given argument.
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==== Inverse Trigonometric Functions
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- ::acos: Returns the arc cosine of the given argument.
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- ::asin: Returns the arc sine of the given argument.
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- ::atan: Returns the arc tangent of the given argument.
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- ::atan2: Returns the arg tangent of two given arguments.
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==== Hyperbolic Trigonometric Functions
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- ::cosh: Returns the hyperbolic cosine of the given argument.
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- ::sinh: Returns the hyperbolic sine of the given argument.
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- ::tanh: Returns the hyperbolic tangent of the given argument.
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==== Inverse Hyperbolic Trigonometric Functions
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- ::acosh: Returns the inverse hyperbolic cosine of the given argument.
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- ::asinh: Returns the inverse hyperbolic sine of the given argument.
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- ::atanh: Returns the inverse hyperbolic tangent of the given argument.
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==== Exponentiation and Logarithmic Functions
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- ::exp: Returns the value of a given value raised to a given power.
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- ::log: Returns the logarithm of a given value in a given base.
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- ::log10: Returns the base 10 logarithm of the given argument.
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- ::log2: Returns the base 2 logarithm of the given argument.
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==== Fraction and Exponent Functions
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- ::frexp: Returns the fraction and exponent of the given argument.
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- ::ldexp: Returns the value for a given fraction and exponent.
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==== Root Functions
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- ::cbrt: Returns the cube root of the given argument.
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- ::sqrt: Returns the square root of the given argument.
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==== Error Functions
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- ::erf: Returns the value of the Gauss error function for the given argument.
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- ::erfc: Returns the value of the complementary error function
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for the given argument.
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==== Gamma Functions
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- ::gamma: Returns the value of the gamma function for the given argument.
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- ::lgamma: Returns the value of the logarithmic gamma function
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for the given argument.
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==== Hypotenuse Function
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- ::hypot: Returns <tt>sqrt(a**2 + b**2)</tt> for the given +a+ and +b+.
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