don steward
mathematics teaching 10 ~ 16

Saturday, 24 September 2011

babylonian quadratic equation solving

without using algebraic symbols, some Babylonians devised a procedure for solving a type of problem that would normally be solved by creating a quadratic equation

the problem was likely to be expressed in terms of the semi-perimeter and area of a rectangle being given

a specific questions would model a method that enables the lengths of the two sides to be calculated

a harder example:
the perimeter of a rectangle is 20 and the area is 23
what are the lengths of the two sides?

David Wells addresses this and other methods of solving similar problems in his excellent book,  'Hidden Connections, Double Meanings' (pages 113 to 116)

he highlights the economical (and lovely) technique of calling the roots 5 + b and 5 - b                        (because they sum to 10 this must be so)
then multiplying these roots gives a convenient rearranged form, that is easily solved

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