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Hi Jim,

256/81 if the Ancient Egyptians actually used it would be written as 3 + 1/9 + 1/27 + 1/81 or the inverse as 1/4 + 1/16 + 1/256 = 81/256.

Just wondering how your formula might function with problem #10 of the Moscow Mathematical Papyrus?

Which reads as follows: Example of calculating [the surface area of] a basket [hemisphere].

You are given a hemisphere with a mouth [magnitude] of 4 + 1/2 [in diameter].

What is its surface?

Take 1/9 of of 9 [since]the basket is half an egg [hemisphere].

You get 1.Calculate the remainder [when subtracted from 9] which is 8.

Calculate 1/9 of 8. You get 2/3 + 1/6 + 1/18.

Find the remainder of this 8 After subtracting 2/3 + 1/6 + 1/18. You get 7 + 1/9.

Multiply 7 + 1/9 by 4 + 1/2. You get 32. Behold this is its surface [area]!

You have found it correctly.

Here is how they calculated it.

When you study the papyri you will find 8/9 was not noted as 8/9 but always noted as 2/3 + 1/6 + 1/18, you will also find they did not simply multiply numbers as we do they used unit fractions and the additive method as follows:

9 x 1/9 = =1

8 x 2/3 = 5 1/3

8 x 1/6 = 1 1/3

8 x 1/18 = 1/3 + 1/9

adding

5 1/3

1 1/3

7 1/9

7 1/9 x 4 1/2 = 32 is calculated in the following manner by doubling.

7 1/9 + 7 1/9 = 14 + 1/5 + 1/45

14 + 1/5 + 1/45 = 28 + 1/4 + 1/9 + 1/12

Adding the results:

~~14 + 1/5 + 1/45~~

28 + 1/4 + 1/9 + 1/12 ,,,,,,,,,,,,,,,,= 28 4/9

equals 32

Can't stress enough the fact they did no think as we do mathematically. Tell me when their methods are employed will you derive pi? Hope that helps!

Jacob

256/81 if the Ancient Egyptians actually used it would be written as 3 + 1/9 + 1/27 + 1/81 or the inverse as 1/4 + 1/16 + 1/256 = 81/256.

Just wondering how your formula might function with problem #10 of the Moscow Mathematical Papyrus?

Which reads as follows: Example of calculating [the surface area of] a basket [hemisphere].

You are given a hemisphere with a mouth [magnitude] of 4 + 1/2 [in diameter].

What is its surface?

Take 1/9 of of 9 [since]the basket is half an egg [hemisphere].

You get 1.Calculate the remainder [when subtracted from 9] which is 8.

Calculate 1/9 of 8. You get 2/3 + 1/6 + 1/18.

Find the remainder of this 8 After subtracting 2/3 + 1/6 + 1/18. You get 7 + 1/9.

Multiply 7 + 1/9 by 4 + 1/2. You get 32. Behold this is its surface [area]!

You have found it correctly.

Here is how they calculated it.

When you study the papyri you will find 8/9 was not noted as 8/9 but always noted as 2/3 + 1/6 + 1/18, you will also find they did not simply multiply numbers as we do they used unit fractions and the additive method as follows:

9 x 1/9 = =1

__9 - 1 = 8__8 x 2/3 = 5 1/3

8 x 1/6 = 1 1/3

8 x 1/18 = 1/3 + 1/9

adding

5 1/3

1 1/3

__1/3 + 1/9__7 1/9

7 1/9 x 4 1/2 = 32 is calculated in the following manner by doubling.

7 1/9 + 7 1/9 = 14 + 1/5 + 1/45

14 + 1/5 + 1/45 = 28 + 1/4 + 1/9 + 1/12

__7 1/9 x 1/2 = 3 + 1/2 + 1/18__Adding the results:

28 + 1/4 + 1/9 + 1/12 ,,,,,,,,,,,,,,,,= 28 4/9

__3 + 1/2 + 1/18__................................= 3 5/9equals 32

Can't stress enough the fact they did no think as we do mathematically. Tell me when their methods are employed will you derive pi? Hope that helps!

Jacob

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