By Counting Proportions


Biffin in his book "The Auricula" emphasises the importance of proportion in selecting and judging auriculas.
He observed that a miner unfamiliar with floriculture could naturally make similar selections to himself as to which were best from a tray of plants, and that proportion was probably the most significant factor.
Favouring Maddock's definition (1:3:6) for the relative diameters of the tube, eye (or paste) and pip; he concluded that defining the ideal proportions was a "difficult aesthetic problem".
There follows a first attempt a tackling this problem using, as a starting point, the mathematics of Euclid.

Euclid defines a proportion as two equal (but not identical) ratios.
A ratio is a comparison of two magnitudes (we would use the word 'size' rather than 'magnitude') of the same type.
So a/b = c/d is a proportion. 2/1 = 6/3 is a proportion as is 3/1 = 9/3, but 4/1 = 4/1 is not as the ratios are identical.
The Greek mathematicians soon found that the most aesthetic way of dividing a line into two parts 'a' and 'b' was if a proportion resulted.
That is a/b = b/(a+b). This occurs when the equal ratios are approximately 0.618 (or its inverse 1.618) the so called golden number.

To evaluate variously proportioned auricula pips I have written a piece of JAVASCRIPT that counts the number of proportions a given pip configuration produces. This is divided by the theoretical maximum number of potential proportions producing a percentage score or rating. Identical (or duplicate) proportions are not counted.
To get used to the script, first try something simple like the evaluation of two concentric circles by suppling only the tube (or eye) size together with the size of the pip overall.
Sizes may be input in any consistent format (e.g. that used by the florists of old 1,2 and 4 for GLENNY). I find using 100 for the pip size easier , making GLENNY 25, 50 and 100; and MADDOCK 16.7, 50 and 100.
EXAMPLE To test the alpine standard of the centre being four sevenths the size of the pip - use 4 for the size of he eye and 7 for the pip size - producing a rating of 11.47%. Of course using 57 and 100 will give a similar poor low score.
The terms "bridged" and "centred" symmetry refer to such patterns as 'IHOHI' and 'IHOOHI' respectively, the difference between the symmetry of the eyes and the teeth. Use "bridged" to mimic the situation where the anthers leave a gap at the tube centre and "centered" when you want to evaluate configurations where the anthers are closed over the centre of the tube.
Also the script makes assumptions on how near misses should be treated. The program tries to simulate the eyesight of the average auricula judge!! Between Mr. Maggoo and Hawk-eye, but exactly where I should not like to comment.

To use the script click on EVALUATE STANDARDS OF PERFECTION fill in the form (click in the boxes you wish to type in) and click "TRY THIS". You can edit your previous input and click "TRY THIS" again for similar data.