Eratosthenes was a Greek scholar who calculated the circumference of the Earth using shadows from sticks in Alexandria and Syene. He observed that on the summer solstice, a stick in Alexandria cast a shadow while a stick in Syene did not. Knowing the distance between the cities, he calculated the circumference of the Earth to within a few percent of the actual measurement. Eratosthenes made several other contributions including accurately calculating the tilt of the Earth's axis and inventing the leap day.

1. PRIMARY SCHOOL "VASIL APRILOV" - RUSE
DIVE IN THE SKY

2. Eratosthenes of Cyrene was a Greek mathematician, geographer,
poet, astronomer, and music theorist. He was a man of learning,
becoming the chief librarian at the Library of Alexandria. He invented
the discipline of geography, including the terminology used today.
He is best known for being the first person to calculate the
circumference of the Earth, which he did by applying a measuring
system using stadia, a standard unit of measure during that time
period. His calculation was remarkably accurate. He was also the
first to calculate the tilt of the Earth's axis (again with remarkable
accuracy). Additionally, he may have accurately calculated the
distance from the Earth to the Sun and invented the leap day
(February 29).

4. Eratosthenes' model depends on the assumption
that the earth is a globe and that the sun is far away
and therefore produces parallel rays of light all over
the earth. If the sun is nearby, then shadows will
change length even for a flat earth. A flat earth
model is sketched below. The vertical stick casts
shadows that grow longer as the stick moves to the
left, away from the closest point to the sun. (The sun
is at height h above the earth.)

7. Using the values 50 degrees and 60 degrees as
measured on the trip, with b=1000 miles, we find that
h is approximately 2000 miles. This relatively clos
sun would have been quite plausible to the ancients.
Continuing the calculation, we find that a is
approximately 2400 miles and the two distances R1
and R2 are approximately 3000 and 3900 miles,
respectively.

8. USING MATH TO FIND THE CIRCUMFERENCE OF THE EARTH

9. USING MATH TO FIND THE CIRCUMFERENCE OF THE EARTH
A denotes the base of the pole in Alexandria;
S the base of a pole in Syrene;
T the tip of the shadow cast by the pole in Alexandria;
P the top of the same pole;
E the center of the Earth.
Angle APT was measured to be 7o, so by Euclidean geometry interior
angles and are equal, thus angle
There are 360o in a complete circle, so the portion of the circumference of
the Earth between A and S is which is approximately or is
50.
The distance from Alexandria to Syrene is 800 km, so he concluded that the
circumference of the Earth must be

10. March, 22

12. On March 21-22 the sun is directly overhead at the
equator and appears 45 degrees above the horizon at 45
degrees north and south latitude. As the angle of sun
above the earth at the equator is 90 degrees while it is 45
degrees at 45 degrees north or south latitude, it follows
that the angle at the sun between the vertical from the
horizon and the line from the observers at 45 degrees
north and south must also be 45 degrees. The result is two
right angled triangles with legs of equal length. The
distance between the equator and the points at 45 degrees
north or south is approximately 3,000 miles. Ergo, the sun
would be an equal distance above the equator.

13. Bulgaria
Location: 0°00'00.0", 0°00'00.0", 0m
(Longitude referred to Greenwich meridian)
Time Zone: Greenwich
Date Begin Rise Az. Transit Alt. Set Az. End
(Zone) Civil Civil
Twilight Twilight
h m h m ° h m ° h m ° h m
2015 Mar 22 (Sun) 05:43 06:04 89 12:07 89N 18:10 271 18:31
2015 Mar 23 (Mon) 05:43 06:03 89 12:07 89N 18:10 271 18:31
2015 Mar 24 (Tue) 05:42 06:03 89 12:06 89N 18:10 272 18:30
2015 Mar 25 (Wed) 05:42 06:03 88 12:06 88N 18:09 272 18:30
2015 Mar 26 (Thu) 05:42 06:03 88 12:06 88N 18:09 272 18:30

14. September, 22 2014

17. There is no other way to get a distance for
the sun. Just looking at it from a single point
on earth will not tell you its distance, you
must look at it from several points and
account for the curvature or non-curvature of
the distance between those points.

18. http://wiki.tfes.org/Distance_to_the_Sun
https://en.wikipedia.org/wiki/Eratosthenes
https://en.wikipedia.org/wiki/February_29
http://wiki.tfes.org/File:Xlg_globe_3.jpg
http://metasofa.org/vansprouts/solarnoon.html