line_length.py

from __future__ importannotations

importmath
fromcollections.abcimportCallable


defline_length(
fnc: Callable[[float], float],
x_start: float,
x_end: 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
 >>> f"{line_length(f, 0, 1, 10):.6f}"
 '1.414214'

 >>> def f(x):
 ... return 1
 >>> f"{line_length(f, -5.5, 4.5):.6f}"
 '10.000000'

 >>> def f(x):
 ... return math.sin(5 * x) + math.cos(10 * x) + x * x/10
 >>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
 '69.534930'
 """

x1=x_start
fx1=fnc(x_start)
length=0.0

for_inrange(steps):
# Approximates curve as a sequence of linear lines and sums their length
x2= (x_end-x_start) /steps+x1
fx2=fnc(x2)
length+=math.hypot(x2-x1, fx2-fx1)

# Increment step
x1=x2
fx1=fx2

returnlength


if__name__=="__main__":

deff(x):
returnmath.sin(10*x)

print("f(x) = sin(10 * x)")
print("The length of the curve from x = -10 to x = 10 is:")
i=10
whilei<=100000:
print(f"With {i} steps: {line_length(f, -10, 10, i)}")
i*=10