Circumference of the Earth Quiz
How many degrees are there in a circle?
a. 300
b. 180
c. 360
d. 270
If a circle is divided into 6 equal pieces, how many degrees will the interior angle of each piece be?
90
45
15
60
If two parallel lines are cut by a transversal, the alternate interior angles created:
are of equal value.
always add up to 90 degrees
always add up to 360
are never of equal value
Tangent of angle “theta” equals:
Adjacent over hypotenuse
Adjacent over opposite
Opposite over adjacent
Hypotenuse times theta (in radians)
What is 51 multiplied by 500? a. 52000
b. 21000
c. 25500
d. 250500
6. Solve for x: 7/500 = 360/x
7
b. 500
c. 180
d. ~25700
Because of its large distance from the Earth, the Sun’s rays are said to fall on the Earth:
in parallel lines
in circular rays
in criss-crossing lines
only after bouncing off of another heavenly body(s)
The shape of the Earth is said to be:
flat
round
trapezoidal
square
The length of a “meter stick” is:
50 centimeters
3 feet
1 meter
2 meters
1 km is miles a. 1.2
b. 0.6
c. 0.25
d. 6
Bonus
From 1-100, please rate how well you believe you did on this quiz (0=very poorly, 100=excellent)
answer:
Problem
Eratosthenes, an ancient astronomer, historian, geographer, philosopher, and mathematician was also the director of the great library of Alexandria. One day he read that in the southern frontier outpost of Syene, near the first cataract (waterfall) of the Nile, at noon on June 21 vertical sticks cast no shadows. This observation may have been easily passed over by others, but Eratosthenes was no ordinary guy. Eratosthenes had the presence of mind to conduct an experiment, to actually observe whether in Alexandria vertical sticks cast shadows near noon on June 21. And, he discovered that sticks do.
Eratosthenes asked himself how, at the same moment, a meter stick (length = 1 meter) in Syene could cast no shadow and a stick in Alexandria, far to the north, could cast a shadow. Consider a map of ancient Egypt with two vertical sticks of equal length, one struck in Alexandria, the other in Syene. Suppose that, at a certain moment, each stick casts no shadow at all. This is perfectly easy to understand… provided the Earth is flat. Two shadows of equal length would make sense as well, since the Earth would be inclined at the same angle to the two sticks. But how could it be that at the same instant there was no shadow at Syene and a substantial shadow at Alexandria? The Earth must be curved…dare we, maybe even ROUND?
Eratosthenes figured out that the shadow length of the stick in Alexandria (in today’s terms, about 0.1219 meters or 4.8 inches). Eratosthenes also knew that the distance between Alexandria and Syene was (in today’s units) approximately 800 kilometers (~500 miles).
Eratosthenes, using only sticks, eyes, feet, and brains (plus a taste for experiment) was able to deduce the circumference of the Earth with an error of only a few percent. How did he do it? (No outside resources help on this one, please)
