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Description
This programme examines the nature of the number 'root 2'. It resolves a possible dilemma between a geometric and arithmetic approach to the value of this number. It then shows how the use of irrat...ional numbers will lead to slight errors in calculation.
Module code and title: M101, Mathematics: a foundation course M101; 06; 1976 19-03-1978 1976 00:24:18 + Show more... Jack Koumi Norman Gower; Don Mansfield; Allan I.,1936-2013 Solomon BBC Open University Geometry calculation; Irrational numbers; Nested intervals; Rational numbers Allan Solomon introduces the programme and discusses the properties of numbers as seen geometrically and arithmetically. Don Mansfield demonstrates how numbers are conceived geometrically. He shows the nature of natural numbers. Integers and Rational numbers. Norman Gowar shows how numbers are conceived from a computational point of view. He reaches the same ideas as Don Mansfield. Norman Gowar now tries to obtain root 2 the bisection method. He reaches the conclusion that this method will not generate root 2. He can only calculate it approximately. Don Mansfield now demonstrates that a specific length can be obtained quite easily for the value root 2 using geometric methods. There appears to be a conflict between the two approaches to numbers. Next Norman Gowar proves that root 2 is not a rational number, which is why he cannot calculate root two exactly. Don Mansfield argues that root 2 cannot be ignored as it is invaluable within geometry, as are many other irrational numbers. For geometric purposes there can be no gaps in a number line or sequence. Allan Solomon argues that it is only the presentation of the problem which generates the conflict. The calculative mathematician must extend his concepts to include irrational numbers. A test is can root 2 be used in calculations. Norman Gowar demonstrates how root 2 can be seen as an approximation of a rational number and that provided that the mathematician is prepared to accept a degree of error, root 2 can be used in calculations. Allan Solomon sums up the discussion. The possible conflict between the two mathematical approaches is resolved by the broadening of the arithmetic concepts and by the acceptance of a degree of error. Credits. 6HT/72398 00525_4243 2455 no