154 6. CALCULATIONthis book for your own reference library. You will need it many
times in years to come.That book remains on the author's shelf, unopened since about 1985. The
publishers in their confidence had overlooked the fact that the eternal truths of
mathematics need not be reconstructed every time they are needed. Machines
can store them and do the unimaginative computational work more efficiently and
accurately than people can.
One result of all this magnificent computer engineering is that mathematics
education faces a dilemma. On the one hand, the skills involved in doing elemen-
tary arithmetic, algebra, and calculus are now as obsolete as the skill of writing a
letter in longhand. What is the point of teaching students how to solve quadratic
equations, factor polynomials, carry out integration by parts, and solve differential
equations when readily available programs such as Mathematica, Maple, Matlab,
and others can produce the result in a split second with guaranteed accuracy? On
the other hand, solving mathematical problems requires quantitative reasoning, and
no one has yet found any way to teach quantitative reasoning without assuming
a familiarity with these basic skills. How can you teach what multiplication is
without making students learn the multiplication table? How can you explain the
theory of equations without making students solve a few equations? If mathematics
education is to be in any way relevant to the lives of the students who are its clients,
it must be able to explain in cogent terms the reason for the skills it asks them to
undergo so much boredom to learn, or else find other skills to teach them.
Questions and problems
6.1. Double the hieroglyphic number ^
6.2. Multiply 27 times 42 the Egyptian way.
6.3. (Stated in the Egyptian style.) Calculate with 13 so as to obtain 364.
6.4. Problem 23 of the Ahmose Papyrus asks what parts must be added to the
sum of 4, 8, 10, 30, and 45 to obtain 3. See if you can obtain the author's answer
of 9 40, starting with his technique of magnifying the first row by a factor of 45.
Remember that | must be expressed as 2 8.
6.5. Problem 24 of the Ahmose Papyrus asks for a number that yields 19 when its
seventh part is added to it, and concludes that one must perform on 7 the same
operations that yield 19 when performed on 8. Now in Egyptian terms, 8 must be
multiplied by 2 4 8 in order to obtain 19. Multiply this number by 7 to obtain
the scribe's answer, 16 2 8. Then multiply that result by 7, add the product to the
result itself, and verify that you do obtain 19, as required.
6.6. Problem 33 of the Ahmose Papyrus asks for a quantity that yields 37 when
increased by its two parts (two-thirds), its half, and its seventh part. Try to get
the author's answer: The quantity is 16 56 679 776. [Hint: Look in the table of
doubles of parts for the double of 97. The scribe first tried the number 16 and
found that the result of these operations applied to 16 fell short of 37 by the double
of 42, which, as it happens, is exactly 1 3 2 7 times the double of 97.]