User Review - Flag as inappropriateVictor Klee and Stan Wagon's book is out-of-date with respect to an Egyptian Fractions chapter, citing the conversion of 5/121 by a greedy algorithm solution and an improved but un-concise solution ( published by Bleicher):

5/121 = 1/35 + 1/1225 + 1/3477 + 1/7081 + 1/11737

on page 206. In 2002, 2005, 2008 and 2010 an improved RMP 2/n table red number method was broken and published on-line in the context of the EMLR, RMP 36 and RMP 37 such that:

5/121 = 1/11*(5/11)

with 5/11 *(3/3) = 15/33 = (11 + 3 + 1)/33 = 1/3 + 1/11 + 1/33

reaching

5/121 = 1/11*(1/3 + 1/11 + 1/33) = 1/33 + 1/121 + 1/363

as Ahmes,the RMP scribe, in 1650 BCE solved

2/95 by 1/5*(2/19)*(12/12) = (19 + 3 + 2)/1140 = 1/60 + 1/380 + 1/570

Wikipedia has posted the 2/95 solution on its Rhind Mathematical Papyrus page

http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus

Stan Wagon also discussed Fibonacci's 1202 AD Liber Abaci and the conversion of 4/23 by the un-concise modern solution on page 177:

4/23 = 1/7 + 1/33 + 1/1329 + 1/23536559

rather than following Fibonacci's solution

(4/23 - 1/6) = (24 -23)/138

recorded in one of three unit fraction notations.

Ahmes' arithmetic discussed on

http://ahmespapyrus.blogspot.com/2009/01/ahmes-papyrus-new-and-old.html

would have solved 4/23 with LCM 6 finding

4/23*(6/6) = 24/138 = (24 + 1)/138 = 1/6 + 1/138

In RMP 36 and RMP 37 Ahmes used a subtraction method that would have reported

(4/23 - 1/6) = 1/138 by recording

4/23 = 1/6 + 1/138

Hence, Greeks, Arabs and medieval scribes like Fibonacci copied Egyptian number theory, dated to 2050 BCE, to record exact rational number' unit fraction mathematics.

Best Regards to the ancient scribes and modern math historians. Modern books on ancient math and modern unsolved problems need to be updated from time to time.

Milo Gardner