...

Pyramid Diagram Process:

These two --- half base lengths --- create diagonal base length X:

378 feet

and

378.1521448 feet. ---> = 1188 / Pi = 378 x {aPi / Pi}

We want to know length X.

You know the modern process.

Ancient Egyptians could not perform that square root operation.

Try it with pen and paper, and no calculator.

So this is how the ancient square root two process works:

378 feet x {99 / 70} = 534.6 feet

378.1521448 x {140 / 99} = 534.7606088 feet

add the two values

534.6

plus

534.7606088 ----> = 1069.360609 feet ----> DIVIDE BY TWO

ancient sqrt two result:

534.6803044

modern sqrt two result:

534.68032 feet -------------> differential = 0.0000156 feet = 0.0001872 inches

ancient square root two --- length X --- accuracy: ---> 0.999999971 <---

When just comparing ancient sqrt 2 to modern sqrt 2 in accuracy,

ancient sqrt 2 displayed very low accuracy.

However, the ancient square root two math operation for length X,

dramatically increased accuracy in the results,

by a factor

of 10,000 !

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

In terms of accuracy in the Lunar Month 29.53059 days,

0.999999971 accuracy

produces a Lunar Month of 29.53058914 days, off by 0.074 seconds

This accuracy is of course, magnificent,

from my standpoint of accuracy requirements.

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

That is extreme accuracy,

produced by ancient sqrt 2 fractions that initially displayed low accuracy.

Ancient square root two.

99 / 70 and 140 / 99,

A simple fundamental ancient short cut around modern context square root two.

This process could be used in a variety of applications when needed.

...

Pyramid Diagram Process:

These two --- half base lengths --- create diagonal base length X:

378 feet

and

378.1521448 feet. ---> = 1188 / Pi = 378 x {aPi / Pi}

We want to know length X.

You know the modern process.

Quote:378 squared -- plus -- 378.1521448 squared = A ---> then square root of A = length X.

Thus length X = 534.68032 feet <----

Ancient Egyptians could not perform that square root operation.

Try it with pen and paper, and no calculator.

So this is how the ancient square root two process works:

378 feet x {99 / 70} = 534.6 feet

378.1521448 x {140 / 99} = 534.7606088 feet

add the two values

534.6

plus

534.7606088 ----> = 1069.360609 feet ----> DIVIDE BY TWO

ancient sqrt two result:

534.6803044

modern sqrt two result:

534.68032 feet -------------> differential = 0.0000156 feet = 0.0001872 inches

ancient square root two --- length X --- accuracy: ---> 0.999999971 <---

When just comparing ancient sqrt 2 to modern sqrt 2 in accuracy,

ancient sqrt 2 displayed very low accuracy.

However, the ancient square root two math operation for length X,

dramatically increased accuracy in the results,

by a factor

of 10,000 !

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

In terms of accuracy in the Lunar Month 29.53059 days,

0.999999971 accuracy

produces a Lunar Month of 29.53058914 days, off by 0.074 seconds

This accuracy is of course, magnificent,

from my standpoint of accuracy requirements.

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

That is extreme accuracy,

produced by ancient sqrt 2 fractions that initially displayed low accuracy.

Ancient square root two.

99 / 70 and 140 / 99,

A simple fundamental ancient short cut around modern context square root two.

This process could be used in a variety of applications when needed.

...