Clive Wrote:
-------------------------------------------------------
> Rob Miller Wrote:
> --------------------------------------------------
> -----
>
> > And, Pi/4 multiplied by the "parent" or
> > "encapsulating" square area...
> > will approximate the area of that "child"
> circle
> > in ratio to the square.
> >
> > this "could" concern the RMP 50.. because it
> shows
> > how the square and circle are seen in
> geometry...
> > and math.... combined.
>
> Hi Rob:
>
> You must find a means of linking this ratio to the
> RMP 50.

It might be obvious given one of your comments below regarding "roots"??


> This problem "adjusts" the width of a circle with
> a constant then squares the result...

Ahmes solution does subtract one from the "Whole" ...to "square" towards result.

might hold some answers right there?? ....more research required though.


>whereas our
> method is squaring the width and multiplying by
> the constant...pi.


- Squaring the [R] 'radius' or [1/2 [SIDE of Square]] x Pi to get the area...

- [[1] SIDE of Square] or [D] diameter x Pi to get the circumference or perimeter...



> That verifies, in a
> "nut-shell", that pi was "not used" to solve the
> problem.

the "concept" of Pi... i agree...appears to be an alternative solution coveyed in Ahmes example.

but, the approximation in ratio of the 22/7 could have been an indirect use.. or assumed use based on formulas applied?? Or, the simple result of rectangulation of slopes creating the 14:11 ratio or 11:14 ... which relates to 22/7 by 4 parts combined.?

Yet i also agree with the below statement...

> What irks me most is those who have studied this
> document use problem 50 to make claim that the AE
> only knew pi to an accuracy of 3.16+, when in fact
> the author didn't use pi to resolve the problem.
> They can't have it both ways...
> From another view it is equivalent to stating that
> the problem does not refer to pi, therefore the
> author didn't know of its existence...guilty
> before proven innocent.
>


true...i agree.
Very sound logic.... neither 3.16 appears to be suggested.. nor, lack of Pi knowledge can be concluded...

what happens when you press on a balloon.. you oblate the shape the more pressure you apply... I see more indication of Pi variants then, lack of ([D]:[C] 0r [R]:[A] knowledge) but, this is speculation for now until further investigations and research are done towards a conclusion..


> > Ahmes didn't get 100% on the Rhind Papyrus,
> or
> > some of the results were shown to be in
> error.....
> > so, i don't think his solution was "the"
> solution
> > ....just "a" solution....
>
> Now we are getting there....good analysis.

Thanks...

> Study the errors...they always help.

I will... good advice!


> How often have you written an incorrect word or
> entered the wrong number in a math question.

Plenty!
I am trying to slow down and proof my stuff...I am terrible with misspelling and typing to fast and missing a digit... etc.

> > there is much speculation as to whether AE
> knew or
> > experimented with roots or not. Even
> professor
> > Assem Deif has written recent articles
> speculating
> > such...
>
> They knew the root values very well.
> As you are aware, root values can be derived from
> basic geometry, so why and what was there for them
> to expand upon?

interesting...! thanks Clive.. I will try to support this as well.

> > I was just offering what i could see via the
> > geometric approach....
> > doesn’t mean it applies to AE... and the RMP
> > directly...
>
> Why not?
> Don't run off when you have a legitimate
> point...try expand with more samples to back your
> statements. "Simple" drawings speak volumes...you
> are doing fine.
>

will do.

> > Use of Square to get to the Pi... seems legit
> for RMP 50.
>
> Too vague, try rephrase in greater detail....
>

I say Pi in ref to circle usually... given, the diameter defines the # of Pi in the circumference or perimeter.

My suggestion is; that if the AE knew the "roots" and specifically [SQRT2 & reciprocal]; then, they could more
easily extract any measure of a relating Pi, by breaking it down to squares. through the relationships defined above.

i will C if i can do up some simple diagrams that might reflect the above comments...??

Art... geom shapes... etc.. always convey better then words.. given so many interpretations of the very same ..or, similar words... "if"...., as you say... they are simple enough.



> > i trust that should assist to better explain
> the
> > diagram previously posted.
> > good evening.
>
> You did well Rob...excellent input.
>

Thanks Clive...I appreciate the comments and advice...