Stealing the Gold?

The following is a quotation from 'Basic Draughting Practice', an engineering-drawing manual for school use from Nelson & Sons, written by R. Thomson of the Royal Military College of Science.

"The basic sheet (A0) is a rectangle of one square metre in area, the sides of which are in the ratio √2 : 1. This shape, the 'golden section', in which the diagonal of a square becomes the long side of a rectangle based upon the square, has long been recognized as a perfectly balanced rectangle."

Good grief! It is nothing of the sort! The Golden Section results from the division of a line segment in mean-and -extreme ratio, whereby the ratio of the shorter part to the longer equals that of the longer part to the whole line. Mathematically for a line segment divided into two parts, a and b,
a : b = b : (a + b)
and a rectangle in these proportions is held to be the most aesthetically pleasing possibility. The ratio occurs frequently in the proportions of living organisms and, interestingly, is approached more and more closely by successive pairs of numbers in the Fibonacci series:
0, 1, 1, 2, 3, 5, 8, ...
The approximate value of the Golden ratio is, decimally, 0·618... or dozenally 0·74E..., whereas the 1 :√2 ratio of 'A' paper sizes is decimally 0·707.. or dozenally 0·859... , and it is noteworthy that our dear old foolscap paper size - eight by thirteen - is a close approach to the Golden Section and that 'A' sizes are not.

Just as the crazed, envious decimalists are trying to appropriate the ream, pretending that it means five hundred instead of forty dozen, so now they attempt to purloin the Golden Section for the greater glory of the metric sytem, even if it means lying to children...

(Ed: the ream has in fact been 500 sheets for quite some time: 20 quires of 25 sheets, once 20 quires of 24 sheets...)

The Truth will out!

In the course of a recent schools' TV programme - 'Mathematical Investigations' - it was desired to show that the binary sequence: 1, 2, 4, 8, ... could, by grouping these numbers, give all the intermediate integral values, e.g. 1 + 2 + 4 = 7, etc. For a practical example, the programmers had to use the traditional, elegant system of weights: 1oz, 2oz, 4oz,... "Don't take any notice of ounces" said the presenter, hurriedly.

Well, of course! It would never do to reveal that the metric weight sets need five weights, with two the same, to do the job of four in the oz/lb system, would it? Don Hammond, Dozenal Journal no 4.