"Reciprocals" are two numbers which when multiplied together equal one. i.e. 0.8 x 1.25 = 1 There aren't very many of them. Another: 0.64 and 1.5625. They are usually thought of as percentages: 80 and 125, or 64 and 156.25 They come in useful any time you need to enlarge something then reduce it to the original size, particularly if you need to get good quality on a photocopier or laser printer: Enlarging to print on a 600dpi laser printer, then reducing to create a better screen...print at 156.25%, then shoot at 64% on the photocopier. We also saw a reference to it being used in drawing street maps: 1) Draw the map with black lines of as many widths as necessary. 2) Copy to another layer and change to white 3) Scale the layer down by 80% (for example) ticking the box which says 'Scale line widths' 4) Scale it back up by a reciprocal amount (125% in this case) but this time don't scale the line widths. That can be done automatically in many recent layout programs but knowing how it works can still be useful. In part this is still due to me taking the odd mixture of Advanced Maths and Art at a London grammar school, but credit for putting it into words is due to "Bob" in the UK.