(Wikipedia)

Pi or π is a mathematical constant whose value is the ratio of any circle’s circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle’s area to the square of its radius.  The symbol π was first proposed by the Welsh mathematician William Jones in 1706.  It is approximately equal to 3.14159 in the usual decimal notation (see the table for its representation in some other bases).  π is one of the most important mathematical and physical constants: many formulae from mathematics, science, and engineering involve π.

π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers.  Consequently, its decimal representation never ends or repeats.  It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics.  Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.

Why pi?  I dredged my math memories for possible simple sources of “random” numbers that would both act as a primitive stream cipher/one time pad and yet have some possible connection with Kryptos.  I vaguely remember a mention of using irrational numbers in ciphering strategies.  pi seems appropriate to me because if you look at the shape of Kryptos, aside from a resemblance to a sine wave if you put the two halves together you get a circle.  An irrational number never ends and never repeats.

Read a little further in Wikipedia for a nice little random correlation.

The earliest evidenced conscious use of an accurate approximation for the length of a circumference with respect to its radius is of 3+1/7th in the designs of the Old Kingdom pyramids in Egypt.  The Great Pyramid at Giza, built c.2550-2500 B.C, was precisely 1760 cubits around with a height of 280 cubits (1760/280=2xPi).  Egyptologists such as Professors Flinders Petrie and I.E.S Edwards have shown that these circular proportions were deliberately chosen for symbolic reasons by the Old Kingdom scribes and architects.  The same apotropaic proportions were used earlier at the Pyramid of Meidum c.2600 B.C.  This application is archaeologically evidenced, whereas textual evidence does not survive from this early period.

How do we use it?

I tried mod26 arithmetic both ways with the assumption that the underlying text would be substituted or transposed.  I had hoped the letter frequencies would reveal which.

First 100 digits of pi.  I kept the 3 at the beginning so this is the first 101 digits.

3.1415926535 8979323846 2643383279 5028841971 6939937510 582097
4944 5923078164 0628620899 8628034825 3421170679

Using an alphabet A-Z = 0-25, I lined up the digits of pi to the K4 ciphertext and did the subtraction and then the addition.  Using the same numbers to letters conversion, I retrieved the letters I hoped were underlying ciphertext.

Check my math if you want but you can also just see the letters.  Letter frequency analysis by Simon Singh.

Subtraction (this would reverse the process if Sanborn had added the pi digits to K4)

LAGQPFVIBEPDSLFIGCTXQDFNSNIMPGW
FSQQLSSHLIKJPVBWSRZTECJUUBWNEJ
ASLVPOLSGVFJIOABKROKBWBAGHQZSVRAIRK

Subtraction

Addition (this would reverse the process if Sanborn had subtracted the pi digits to K4)

RCOSZXZULKZTKZXOKIJFLHRVYSYSTUP
PSUWCAUZZKWBVNTCGBBTOSNUMPEFMR
KKPBPCBUSDFVMEMFKGGCRIFQGNYPWFXIMNY

Addition

We can rule out transposition. 

I used a monoalphabetic solver that can work with patristocrat ciphers (no spaces).

The results were not very convincing.

Subtraction

 

RVND AST I PLAYERSING BODY SHE HIM AN USED
DREE FRICK AT PUEJQBLGKXXPUHLKVERT A
WRENTS KIWVPCJWCPUPVNFDQETJVIJC

 

Addition

BY HIRT RULER DER THE JAXLQBFVIVIDUNNIUSY
CURRES OF MDYGOOD HIM UP NZXP BEEN ON YOU
IWXFPZPXEGGYBJXKGMVNSXTJPMV
 
One may say I didn’t try all of the available ciphers to see if the underlying text was something besides transposition or substitution.  The problem with that is something I’ll address later but let’s just say that Ed Scheidt must have known that we wouldn’t have much more than guesses guiding us along and to make the secondary cipher something that would further mask the letter frequencies implies that we would need an absolute certainty about the masking technique.  Otherwise we could never be sure we had used the right method to un-mask K4 and thereby justify an extended analysis on the recovered text.

Kryptosfan