PHYS 109 MIDTERM REVIEW
[jk6ge@virginia.edu]
1. Explain briefly what features of the Babylonian numbering and measuring
systems were superior to ours: sketch the way they represented 1, 2, 10, 25, 60, 75.
What was not so good about their system?
The Babylonians had an incredibly sophisticated number system, due to lots of
administrative works that needed units of measurements. Their standards of units
(12months, 30days/month, 360days/year, 30fingers/cubit, 120cubits/cord, etc) were all
multiples of 60. Since fractions were important, 60 was the ideal number because it is the
lowest number that can be divided by 2, 3, 4, 5 and 6.
The first nine numbers of the number system is represented as vertical lines while and
the chevron ( < ) indicates numbers that are multiples of 10:
25 would be written as
and 75 as
because 60 is represented
in the same way as 1 is;
As indicated above, this, the absence of zero and thus the inability to represent it,
is actually the reason why their number system is not that good. Sixty and one look
exactly the same, and on top of that, there is no way to express decimals.
2. Approximately when and where was Thales? What did he contribute to the
development of science? How did he measure the height of a pyramid? How did he
measure the distance away of a ship? How did his explanations of thunder, for
example, differ from what had been believed before?
Thales was around 624-537 BCE in Miletus (near the East coast of modern day
Turkey). He came up with the idea of
discovery of nature
, a way of explaining how
natural phenomena, such as thunderstorms or earth quakes, were actually related to
natural laws and its interactions and not by gods (natural vs. supernatural). He is also
credited for bringing Geometry from Egypt to Greek and creating the five theorems of
elementary geometry, which are:
a. A circle is bisected by any diameter.
b. The base angles of an isosceles triangle are equal.
c. The angles between two intersecting straight lines are equal.
d. Two triangles are congruent if they have two angles and one side equal.
e. An angle in a semicircle is a right angle.
He measured the height of a pyramid by using shadows. There are several
accounts retelling his method: one says that he “
measured the shadow of the object at the
time when a body and its shadow are equal in lengh.”
Another conveys a more
geometrical account, saying that he used a stick and measured the length of its shadow,
and set up a proportion/ratio to that of a pyramid’s shadow to find out the actual height.