Babylonian Geometry

The Babylonians were aware of the connections between algebraic calculations and geometry. They included geometrical terms such as length and area in their algebraic solutions. It is apparent, however, that these terms served only to give names to unknown quantities as they had no objection to mixing dimensions, (eg adding lengths to areas). From the examples given by the Babylonians we know that they must have been familiar with:

• the general rules for the area of a rectangle, right angled triangle, isosceles triangle, trapezoid (with one side perpendicular to the base), and parallelograms.
  
  
• the Pythagorean Theorem
  
  
• the fact that in an isosceles triangle, the line joining the vertex
  to the midpoint of the base is perpendicular to the base.        
• the proportionality of the corresponding sides of similar triangles.

Other examples indicated that the Babylonians estimated as 3. They thus estimated the circumference of a circle as 3 times the diameter (C = 3 d), and the area of a circle as one twelfth the square of the circumference (A = C ² / 12); both of which are correct for = 3. (A recently discovered tablet had the improved approximation of = 3 ¹/₈.)

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