Advances in GEOMETRY

1
Advances in GEOMETRY

• MATH 4620/5620
• FA-04

2
Geometry Problems of Rhind

• Numbered 41-60
• Largely concerned with amounts of grain stored in
  rectangular and cylindrical granaries
• The greatest achievement of Egyptians and work
  with geometry was their method of finding the
  area of a circle (refer to top of page 51)
• A (d - d/9)2 (8d/9)2

3
Moscow Papyrus

• Only 25 problems in this Papyrus, but one
  contains a masterpiece (from a geometric
  perspective).
• Problem 14 demonstrated that the Egyptians
  (1850 B.C.) were familiar with the correct
  formula for the volume of a truncated square
  pyramid (frustum) p. 52
• V h/3 (a2 ab b2),
• where h is altitude and a and b are lengths of
  the sides of the square base and top

4
The Great Pyramid

• Points that were amazing
• The size
• How it was built with such precision (by use of
  celestial body)
• Certain number properties (e.g. Pythagorean
  Theorem, Golden ratio)

5
Babylonians

• Tables and texts were part of their study
• No great docs or artifacts like the Egyptian
  papyri
• More theoretical in their use of mathematics
  (unlike the Egyptians)
• The excellent sexagesimal notation enabled them
  to calculate with fractions and integers which
  led to algebra.

6
Plimpton 322

• Babylonian clay tablet (deciphered in 1945)
• Written in old Babylonian script which dates it
  to 1900 B.C. and 1600 B. C.
• Confirms that the Babylonians knew the
  Pythagorean theorem long before Pythagoras (mid
  500s B. C.)