Media not available in the Digital Archive
Description
In this programme two concrete problems are represented in mathematical terms and the resulting equations solved to provide a solution to the problems. The iterative technique is used to solve one ...of the problems. This is done first with a calculator and then with a computer.
Module code and title: M101, Mathematics: a foundation course M101; 01 1976 12-02-1978 1978 00:24:30 M101/01 was re-made in 1982 + Show more... Jack Koumi Norman Gowar; John Mason BBC Open University Algebra; Animations; Computers; Equations; Golden Section; Iteration; Paper-folding Norman Gowar introduces the programme and describes the qualities of standard paper sizes which allow them to retain their same shape when cut in half. He sets the problem of finding what particular of length to width gives this result. A diagram of the paper sizes is used, with abstract symbols, X and y, to show how a formula representing this ratio can be obtained. John Mason manipulates these symbols to obtain the formula. He goes back to the original problem to check that his result makes sense. Norman Gowar sets a further problem. What ratio of length to width will allow a square to be cut from a piece of paper so that the remaining piece will remain as a rectangle with a similar ratio to the original. Again the problem is pictured in a diagram and abstract symbols assigned to the paper sizes giving a formula. John Mason manipulates this equation which gives a quadratic equation and this resolves as 1.618 The so called "Golden Section'. Norman Gowar next discusses the technique of iteration. John Mason rearranges the formula. Norman Gowar works through the equation using the iteration process. The equation is then solved by a computer, programmed for the iteration process. John Mason explains with a flow chart how the process is written as a formula and worked through the computer. Norman Gowar demonstrates how to call up a programme on the computer terminal. As an experiment he feeds in the value of -1 as a solution to the formula. Credits. 6HT/72267 00525_4238 2424 no