Question

Can someone explain the babylonian method to me

Answer 1

method for what ....

Answer 2

for estamating squaroots

Answer 3

oh, well tell me what your thoughts about it are, or where it loses you at. in the mean time ill refresh my history of math memorys and chime in

Answer 4

im on square 1

Answer 5

basically nothing

Answer 6

you got a specific sqrt you want to determine?

Answer 7

lets see 130

Answer 8

sqrt(130) ... now take a guess

Answer 9

10

Answer 10

ok

now take the average of 10 and 130/10

Answer 11

add them together and divide by 2?

Answer 12

yep .. in the mean time ill try to math some evidence for it

Answer 13

\[\sqrt{n}=g+E\]
\[n=g^2+2gE+E^2\]
\[\frac{n}{g}=g+2E+\frac{E^2}{g}\]
\[g+\frac{n}{g}=2g+2E+\frac{E^2}{g}\]
\[\frac{g+\frac{n}{g}}{2}=g+E+\frac{E^2}{2g}\]
when the error is small enough, g is a good approximation

in fact if E=0, our guess is exact

Answer 14

so you plug you estamtion in g

Answer 15

you plug your 'guess' in for g yes

Answer 16

and E?

Answer 17

the formula creates a new 'guess' that can be refined even further

E is just some error, since we are not exact then g+E = n for some Error E

the smaller we get E the colser we get to the sqrt

Answer 18

oh

Answer 19

we can solve a quadratic for E :)

Answer 20

\[\sqrt{130}=10+E\]

Answer 21

so like that

Answer 22

yes

Answer 23

square both sides

Answer 24

the babylon way is just using the average of g and n/g the rest of it is just playing about with math

Answer 25

so to find the average