Why does math.sqrt result in ValueError: math domain error?

Question

What causes the problem?

from math import sqrt
print "a : "
a = float(raw_input())
print "b : "
b = float(raw_input())
print "c : "
c = float(raw_input())
d = (a + b + c)/2
s = sqrt(d*(d-a)*(d-b)*(d-c))
print("a+b+c =", a, b, c)
print("Distr. =", d*2, "Area =", s)

Error:

Traceback (most recent call last):
   File "C:/Python27/fájlok/háromszög terület2.py", line 11, in <module>
       s = sqrt(d*(d-a)*(d-b)*(d-c))
ValueError: math domain error

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_{See also: Why does math.log result in ValueError: math domain error? for the equivalent problem using math.log; Python math domain error using math.acos function for the equivalent problem using math.acos.}

Answer 1

The problem is that the Heron's formula holds good only when the sum of the two numbers are greater than the third. You need to check that explicitly.

A better way as you are using a code to do that is by using Exception handling

try:
    s = sqrt(d*(d-a)*(d-b)*(d-c))
    print "a+b+c =", a, b, c
    print "Distr. =", d*2, "Area =", s
except ValueError:
    print "Please enter 3 valid sides"

If you want to do it without try block you can do it as

delta = (d*(d-a)*(d-b)*(d-c))
if delta>0:
    s = sqrt(delta)
    print "a+b+c =", a, b, c
    print "Distr. =", d*2, "Area =", s
else:
    print "Please enter 3 valid sides"