- 30 Jul '05 11:24 / 1 editAssuming O is the center of the movement (where the pendulum is attached), A and C are the extremes, B is in the middle, and O is the intersection of AC and OB, I get (approximately):

a) 30 cm

b) 200 cm² (199.5...)

c) 300 cm²

d) 100 cm² (100.5..)

e) 5.4 cm

miscalcs are very realistic though. - 01 Aug '05 17:47

wow, that brings back memories, learned that one when I was in*Originally posted by ilywrin***Check this**

http://www.bbc.co.uk/dna/h2g2/A827453

grade school at the First Lutheran School in El Monte California.

Wonder how you would do it for cube roots? can this method be

generalized for Nth roots? - 01 Aug '05 18:27

Well i just did a little googling and found this generalization*Originally posted by sonhouse***wow, that brings back memories, learned that one when I was in**

grade school at the First Lutheran School in El Monte California.

Wonder how you would do it for cube roots? can this method be

generalized for Nth roots?

http://en.wikipedia.org/wiki/Shifting_nth-root_algorithm

- 02 Aug '05 03:03

For square root, I recommend using the "Divide and Average" algorithm. It has quadratic convergence (ie, it smokes), and it can be generalized for nth root. From what I see in the algorithms presented here, they seem to have linear convergence (ie, they're slow).*Originally posted by LittleBear*

my rec.

If only I could remember how to get the square root of a number using only paper and pencil... :'(

Here's Divide and Average.

Say you want to find the square root of the number k.

Set X(0) to be a guess of the square root of k.

Now, set X(n+1) = (1/2)*(X(n)+(k/(X(n))).

Another good thing about Divide and Average is that if you make a mistake, your mistake gets smaller, and smaller with every iteration. With linear convergence methods, if you make a mistake, your results are worthless, regardless of how far you carry the calculation after your mistake. With Divide and Average, you can make a mistake at every step, and each mistake gets damped more and more, as you iterate, so you always approach the answer you are interested in.