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Where does the mark go on a half litre glass? The mathematics behind the design of a glass involves several different uses of calculus.
Module code and title: M101, Mathematics: a foundation course M101; 15; 1983 19-07-1983 1984 1983 00:24:30 + Show more... Pip Surgey Mike Simpson; Anne Walton BBC Open University Area; Calculus; Computer animation; Curves; Differentiation; Formula iteration; Integration; Newton Raphson; Volume of revolution This programme looks at some of the mathematics which results from the design of a glass formed from a volume of revolution. Students are asked how they would calculate where on the glass to place a mark corresponding to a volume of half a litre. In answering the question, the programme involves students in exploring the design of the glass, beginning with an initial sketch of the curve and ending with its volume of revolution by way of decisions about the dimensions of the glass and calculation of the area under the curve. The programme starts by asking "where is the mark?" A computer animation is used. Having obtained a sketch of the curve to remind students about the curve sketching techniques they met earlier in the block, the programme moves on to find the overall dimensions of the glass. This section includes use of the Newton Raphson technique for formula iteration. As a digression from the main theme of the programme, the area under the curve is found next. This is partly to revisit this section of the block, but also to remind students about integration by parts. Next, the idea of volume as the limit of the sum of discs is revisited using a computer animation, and the overall volume of the glass is then calculated (this involves integration by parts again). Finally, the programme shows how the primitive found during the calculation of the volume can be used to get an equation giving the height of the mark, and students are left with the problem of solving this equation, using the Newton Raphson formula once again. HOU4530 FOUM197E 2471 no