PHYS109 Midterm Review Sheet

# PHYS109 Midterm Review Sheet - PHYS 109 MIDTERM...

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PHYS 109 MIDTERM REVIEW 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.

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Thales most likely measured the distance away of a ship by using an instrument consisting of two sticks nailed into a cross (so that they could be rotated). One person would be on top of a tower, positioning one stick vertically while the other stick would be pointing at the ship. Then the person would rotate the device (while still keeping it at the same position it was when pointing the ship) to a point on the land. The distance of this
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PHYS109 Midterm Review Sheet - PHYS 109 MIDTERM...

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