Page 50 - index

2023 ‫מועד אביב‬ - 49 - ‫ פרק שני‬- ‫אנגלית‬

Text II (Questions 18-22)

(1) In the 1920s, while working in southern Iraq, archaeologist Edgar Banks discovered
a small 3,700-year-old clay tablet inscribed with a table of numbers in cuneiform – the
system of writing used by the ancient Babylonians. Part of the table's fourth column
was missing because one edge of the clay tablet was broken. In the 1940s, scholars

(5) examining the tablet, designated P322, realized that the numbers in each row of the
table had something to do with the lengths of the sides of right triangles. The full
significance of the table, however, was not understood. Since the 1940s, several
hypotheses about P322 have been advanced.

One supposition was put forth in 2017 by mathematicians Daniel Mansfield and
(10) Norman Wildberger of the University of New South Wales in Sydney, Australia. When

Mansfield and Wildberger first came across a picture of P322, they suspected that it was
some form of trigonometric table (a table dealing with measurements of right triangles
that is useful to astronomers, engineers, surveyors and navigators, among others),
although the numbers did not seem quite right. They wondered whether the missing
(15) piece of P322, which by that time had been reconstructed, might hold the answer. Once
they saw the reconstruction, they became convinced that P322 is indeed a trigonometric
table – but not anything like those we are familiar with, believed to have been invented
by the ancient Greeks 2,100 years ago. While the Greek trigonometric tables express
the relationships between the sides of right triangles in terms of angles and lengths of
(20) the sides, P322 does so only in terms of lengths of the sides.

Mansfield and Wildberger contend that P322 is not only the oldest extant
trigonometric table but is actually superior to the Greek ones. This, they say, is because
the Babylonians used a number system based on the number sixty, as opposed to later
systems, which are based on the number ten. The base-60 system is still used today for

(25) measuring time: sixty seconds make a minute and sixty minutes make an hour.
Mansfield and Wildberger maintain that the use of a base-60 system enabled the
Babylonians to make more precise calculations than can be done in a base-10 system.

Questions

18. The main purpose of the text is to discuss -

(1) a theory of trigonometry and its origins
(2) an archaeological find and its significance
(3) the ancient Babylonians and their number system
(4) Mansfield and Wildberger's mathematical works

)‫© כל הזכויות שמורות למרכז ארצי לבחינות ולהערכה (ע"ר‬
.‫ בלא אישור בכתב מהמרכז הארצי לבחינות ולהערכה‬- ‫ כולה או חלקים ממנה‬- ‫ או ללמדה‬,‫אין להעתיק או להפיץ בחינה זו או קטעים ממנה בכל צורה ובכל אמצעי‬