In this video I'd like to show how to
calculate the Cube root of a number
using an old mechanical calculator.

 

Since this isn't directly supported by the machine, I use an
interval-based approximation method.

 

The interval is gradually reduced further and further,
until we get a good approximation for the result.

 

I'd like to show this for the
third root of 3.5375
as an example.

 

For the
initial interval
we need a number, that is smaller than the result we're looking for
and one that is greater.

 

1 to the power of 3 is 1
which is smaller than 3.5375

2 to the power of 3 is 8
which is greater.

 

The number we are looking for is therefore
in the interval from one to two.

 

We now halve the interval and as a first approximation we get
1.5
which is the mean value of the interval limits