PAPYRUS MILO - AN EASY WAY TO MULTIPLY WITH UNIT FRACTION SERIES

by Franz Gnaedinger, Zürich, 24 March 1997



Excerpts from e-mails to Milo Gardner, Sacramento, California,
(slightly modified for the publication in the web)



What is 184 x 2 1/6 1/7 x 5 1/3 1/5 ?


Looking up the numbers in tables and rounding them off we find:

184 x 2 1/6 1/7 = 368 + 31 + 26 = 425
425 x 5 1/3 1/5 = 2125 + 142 + 85 = 2352

184 x 5 1/3 1/5 = 920 + 61 + 37 = 1018
1018 x 2 1/6 1/7 = 2036 + 170 + 145 = 2351

----- first result = 2352
---- second result = 2351
----- final result = average value = 2351 1/2 = 2351.5
---------------------------------- real value = 2351.403...



What is 317 x 3 1/3 1/11 x 4 1/5 1/13 ?

317 x 3 1/3 1/11 = 951 + 106 + 29 = 1086
1086 x 4 1/5 1/13 = 4344 + 217 + 84 = 4645

317 x 4 1/5 1/13 = 1268 + 63 + 24 = 1355
1355 x 3 1/3 1/11 = 4065 + 452 + 123 = 4640

----- first result = 4645
---- second result = 4640
----- final result = average value = 4642 1/2 = 4642.5
---------------------------------- real value = 4642.535...



What is 8923 x 2 1/13 1/47 x 5 1/11 1/43 ?

8,923 x 2 1/13 1/47 = 17,846 + 686 + 190 = 18,722
18,722 x 5 1/11 1/43 = 93,610 + 1,702 + 435 = 95,747

8923 x 5 1/11 1/43 = 44,615 + 811 + 208 = 45,634
45,634 x 2 1/+3 1/47 = 91,268 + 3,510 + 971 = 95,749


----- first result = 95,747
---- second result = 95,749
----- final result = average value = 95,748
----------------------- real value = 95,748.6005...



A calculation of interest - from PAPYRUS MILO, to be found
in around 2048 in the region of the former city of Amarna:


----------------- AMARNA BANK
--------------- SIMPLY THE BEST
--------------- WE PROUDLY OFFER
------------ 1/101 1/202 1/303 1/606
-------------- AS RATE OF INTEREST


Account of Vizier Milo, 24 Sycamore Lane, Amarna

*Fortune in year 1: 68954 Egyptian Dollars
Interest in year 1: 683 + 341 + 228 + 114 = 1366 ED

*Fortune in year 2: 70320 ED
Interest in year 2: 696 + 348 + 232 + 116 = 1392 ED

*Fortune in year 3: 71712 ED
Interest in year 3: 710 + 355 + 237 + 118 = 1420 ED

*Fortune in year 4: 73132 ED
Interest in year 4: 724 + 362 + 241 + 121 = 1448 ED

*Fortune in year 5: 74580 ED
Interest in year 5: 738 + 369 + 246 + 123 = 1476 ED

*Fortune in year 6: 76056 ED
Interest in year 6: 753 + 377 + 251 + 126 = 1507 ED

*Fortune in year 7: 77563 ED
Interest in year 7: 768 + 384 + 256 + 128 = 1536 ED

*Fortune in year 8: 79099 ED
Interest in year 8: 783 + 392 + 261 + 131 = 1567 ED

*Fortune in year 9: 80666 ED
Interest in year 9: 799 + 399 + 266 + 133 = 1597 ED

*Fortune in year 10: 82263 ED
Interest in year 10: 814 + 407 + 271 + 136 = 1628 ED

*Fortune in year 11: 83891 ED
Interest in year 11: 831 + 415 + 277 + 138 = 1661 ED

*Fortune in year 12: 85552 ED
Interest in year 12: 847 + 424 + 282 + 141 = 1694 ED

*Fortune in year 13: 87246 ED
Interest in year 13: 864 + 432 + 288 + 144 = 1728 ED

*Fortune in year 14: 88974 ED
Interest in year 14: 881 + 440 + 294 + 147 = 1762 ED

*FORTUNE IN YEAR 15: 90736 EGYPTIAN DOLLARS


And what is the real value?

68954 x (1 + 2/101) exp 14 = 68954 x 1.3158971 = 90736.365...

ALTHOUGH ALL THE NUMBERS HAVE BEEN ROUNDED OFF, THE FAULT
IS ONLY 37 CENTS ON A FORTUNE OF 90736 DOLLARS.

I thank Milo Gardner for having awoken my interest
for the Egyptian unit fraction series.