In [1]:

```
%pylab
%matplotlib inline
```

A continuous functions $f$ which changes its sign in an interval $[a,b]$, i.e. $f(a)f(b)< 0$, has at least one root in this interval. Such a root can be found by the *bisection method*.

This method starts from the given interval. Then it investigates the sign changes in the subintervals $[a,\frac{a+b}{2}]$ and $[\frac{a+b}{2},b]$. If the sign changes in the first subinterval $ b$ is redefined to be $b:=\frac{a+b}{2}$ otherwise $a$ is redefined in the same manner to $a:=\frac{a+b}{2}$, and the process is repeated until the $b-a$ is less than a given tolerance.

In [ ]:

```
def bisect(f, a, b):
return 0
# implement this!
```

Implement the function `bisect`

above until the following does not complain:

In [ ]:

```
assert allclose(bisect(sin, 3., 4.), pi)
```