Added an algorithm that approximates line lengths

maths/line_length.py

@@ -0,0 +1,62 @@
+from typing import Callable, Union
+import math as m
+
+def line_length(fnc: Callable[[Union[int, float]], Union[int, float]],
+                x_start: Union[int, float],
+                x_end: Union[int, float],
+                steps: int = 100) -> float:
+
+    """
+    Approximates the arc length of a line segment by treating the curve as a
+    sequence of linear lines and summing their lengths
+    :param fnc: a function which defines a curve
+    :param x_start: left end point to indicate the start of line segment
+    :param x_end: right end point to indicate end of line segment
+    :param steps: an accuracy gauge; more steps increases accuracy
+    :return: a float representing the length of the curve
+
+    >>> def f(x):
+    ...    return x
+    >>> '%.6f' % line_length(f, 0, 1, 10)
+    '1.414214'
+
+    >>> def f(x):
+    ...    return 1
+    >>> '%.6f' % line_length(f, -5.5, 4.5, 100)
+    '10.000000'
+
+    >>> def f(x):
+    ...    return m.sin(5 * x) + m.cos(10 * x) + x * x/10
+    >>> '%.6f' % line_length(f, 0.0, 10.0, 10000)
+    '69.534930'
+    """
+
+    x1 = x_start
+    fx1 = fnc(x_start)
+    length = 0.0
+
+    for i in range(steps):
+
+        # Approximates curve as a sequence of linear lines and sums their length
+        x2 = (x_end - x_start) / steps + x1
+        fx2 = fnc(x2)
+        length += m.hypot(x2 - x1, fx2 - fx1)
+
+        # Increment step
+        x1 = x2
+        fx1 = fx2
+
+    return length
+
+if __name__ == "__main__":
+
+    def f(x):
+        return m.sin(10*x)
+
+    print("f(x) = sin(10 * x)")
+    print("The length of the curve from x = -10 to x = 10 is:")
+    i = 10
+    while i <= 100000:
+        length = line_length(f, -10, 10, i)
+        print("With {} steps: {}".format(i, length))
+        i *= 10