# More Kahun thoughts:

Presented by Bruce C. Friedman

Page images created: January 2002

Minor Correction: April 16, 2005

The data, as it appears in, columns 11 and 12 of the Kahun IV, 3 "fragment".

I believe the analysis by R. Gillings correctly identifies the numbers on the page but is otherwise in error.

Column 11:

 Line # SUM/Series Multiplier Checked: Yes or No I 1/12, 1/3 1 Yes II 1/6, 2/3 2 No III 2/3, 1 4 No IIII 1/3, 3 8 Yes V 1/12, 2/3, 3 9 Yes

[See reference Line # one (I)] Column eleven is a demonstration of Egyptian multiplication by doubling. In this case 1/12+1/3 is doubled three times to produce:
[ref II] 1/6 + 2/3
[ref III] 2/3 + 1
[ref IV] 1/3 + 3
Note the diagonal slash [checked Y] denoting that REF I and IV have been combined to yield:
[ref V] 1/12 + 2/3 + 3 = 9 X (1/12 + 1/3)= 3.75 = The Mean Variant
We do not have clear evidence of how the [ref I] value was chosen or why the goal of column 11 is to find 9 times this value. But we do see this is part of the scribes effort to distribute the quantity  into the ten portions shown in column 12.
The [ref V] value: 1/12 + 2/3 + 3 = 3.75
The first portion listed in column 12 is 1/12 + 2/3 + 13 = 13.75 [This is the greatest distribution]
The ref I value multiplied by nine [the number of gaps between 10 portions] give us the mean variant!
MV = 3.75

The first numbers in Column 12 (twelve) are 10, 100.
Although this is often read as one number, 110, my analysis is predicated on this as 10 (ten portions) and 100 (a quantity of one hundred).

The list of ten portions from column 12:
(Hi)=13.75 shown as 13, 2/3, 1/12
The other portions shown as the Hi portion less 5/6 in successive steps which ends with the Lo portion.
(Lo)=6.25 shown as 6, 1/6, 1/12
This 5/6 (or 10/12) is the typical gap of 2/3, 1/6.
TG = 5/6

 Line # Decimal Sum Unit Fraction Series Checked: Yes to all I 13.7500 1/12 + 2/3 + 13 = 165/12 Yes II 12.9166 1/12 + 1/6 + 2/3 + 12 = 155/12 Yes III 12.0833 1/12 + 12 = 145/12 Yes IIII 11.2500 1/12 + 1/6 + 11 = 135/12 Yes V 10.4166 1/12 + 1/3 + 10 = 125/12 Yes VI 9.5833 1/12 + 1/6 +1/3 + 9 = 115/12 Yes VII 8.7500 1/12 + 2/3 + 8 = 105/12 Yes VIII 7.9166 1/12 + 1/6 + 2/3 + 7 = 95/12 Yes IX 7.0833 1/12 + 7 = 85/12 Yes X 6.2500 1/12 + 1/6 + 6 = 75/12 Yes TOTAL 100.0000 95 + 60/12=1200/12 = 100 NA

The total of the above ten entries is 100.
The integers total 95 and all the other fractions total 60/12.

Given that we only have one way [actually there's another way] to distribute this quantity using a 3,4,5 triangle, can you explain how this was done or if this was even an actual consideration made by the scribe?

Again look at the actual fragment!

Column 11 Column 12 Note that the special/unusual double symbol, which here appears to represent the quantity 1/6, is also seen on the ACHMIM wood tablets.

 LOCAL GUIDE TO THE OLD PAGES ALSO SHOWN UNDER THE HEADING OF "BRUCE" ON THE IMAGE GRID. GRID NAME TOPIC/LINK OLD NAME O1 RMP/EMLR HOME O2 EMLR CLEAN O3 EMLR UGLY O4 LINKS LINKS & SPHINX O5 EMLR QUEST O6 HIERATIC H. QUESTIONS O7 HIERATIC H. ANSWERS O8 KAHUN KAHUN INTRO O9 KAHUN KAHUN GEOMETRY O10 KAHUN MORE KAHUN

MATHORIGINS.COM

KAHUN INTRO AND ANALYSIS

GEOMETRIC ANALYSIS OF THIS FRAGMENT

ACHMIM WOOD TABLETS! MATH

IMAGE GRID