11-13-2017, 01:25 AM

...

Actually his progression does work,

but he inadvertantly misled by oddly suggesting that he made several guesses.

He made only one guess.

And that was his shortcut for display convenience,

because he tried exactly what I just did.

When you start at 3 ---> to try and get square root three,

you have to descend from the number 3,

in your progression.

He cut out the bigger half of the cake,

by jumping from 3 -- directly -- to 2,

as the starting point of his progression.

One could choose a stage of increments,

from 3 down to 2,

in his progression -- {g + 3 / g} / 2

ie

start at g = 2.9 and see what happens,

or at 2.75,

or at 2.5.

In the exactly one more step using any of these--- 2.9, 2.75 or 2.5,

as when he started with 2,

you get the same exponential style results soaring into long decimal placement accuracy.

He didn't want to explain that.

which is why it was confusing.

So I was wrong, his progression works fine,

and in much less steps than the one I posted in the last post.

However!

my suggestion to start with the fraction 1351 / 780,

as the valid short cut,

eliminates three steps,

from his progression start point.

It should theoretically work for any square root,

like in sqrt 7,

you jump straight to the number three,

and apply the

{g + 7/g} / 2 ... formula ---- where g = 3

His work was interesting and precise.

Much better than the pyramid inch quagmire.

----------------------------------------------------------

Actually his progression does work,

but he inadvertantly misled by oddly suggesting that he made several guesses.

He made only one guess.

And that was his shortcut for display convenience,

because he tried exactly what I just did.

When you start at 3 ---> to try and get square root three,

you have to descend from the number 3,

in your progression.

He cut out the bigger half of the cake,

by jumping from 3 -- directly -- to 2,

as the starting point of his progression.

One could choose a stage of increments,

from 3 down to 2,

in his progression -- {g + 3 / g} / 2

ie

start at g = 2.9 and see what happens,

or at 2.75,

or at 2.5.

In the exactly one more step using any of these--- 2.9, 2.75 or 2.5,

as when he started with 2,

you get the same exponential style results soaring into long decimal placement accuracy.

He didn't want to explain that.

which is why it was confusing.

So I was wrong, his progression works fine,

and in much less steps than the one I posted in the last post.

However!

my suggestion to start with the fraction 1351 / 780,

as the valid short cut,

eliminates three steps,

from his progression start point.

It should theoretically work for any square root,

like in sqrt 7,

you jump straight to the number three,

and apply the

{g + 7/g} / 2 ... formula ---- where g = 3

His work was interesting and precise.

Much better than the pyramid inch quagmire.

----------------------------------------------------------