雙語暢銷書《艾倫圖靈傳》第5章:解謎接力賽(110)
Before the war he had read the classic work Growth and Form by the biologist D'Arcy Thompson, published in 1917 but still the only mathematicAl discussion of biological structure.
He was particularly fascinated by the appearance in nature of the Fibonacci numbers—the series beginning
他對自然界的斐波納契數列特別有興趣：1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...
1，1，2，3，5，8，13，21，34，55，89……
in which each term was the sum of the previous two.
每一項都是前面兩項的和。They occurred in the leaf arrangement and flower patterns of many common plants,
這體現在很多常見植物的葉子和花朵中。a connection between mathematics and nature which to others was a mere oddity, but to him deeply exciting.
對於其他人來說，數學與自然界之間的聯繫是很古怪的，但艾倫卻對此感到很興奮。One day he and Joan were lying on the Bletchley Park lawn—after a game of tennis, perhaps—and looking at the daisies.
有一天，他和瓊玩完網球，躺在布萊切利莊園的草地上，他又在觀察雛菊的生長。They started talking about them and Joan explained how she had been taught to record and classify the arrangement of leaves on plants by following them upwards round the stem,
他們開始討論那些花兒，瓊給他講解她如何給植物葉子分類。葉子繞着莖，盤旋向上生長，counting the number of leaves and the number of turns made before returning to a leaf directly above the starting-point.
從下往上計數葉子數和盤旋的圈數，直到某片葉子正好與第一片葉子在豎直方向上重合。These numbers would usually appear in the Fibonacci series.
這時得到的數值通常是斐波納契數。Once Alan produced a fir cone from his pocket, on which the Fibonacci numbers could be traced rather clearly, but the same idea could also be taken to apply to the florets of the daisy flower.
艾倫拿起一個冷杉球果，這清晰地體現了斐波納契數，雛菊也是這樣的。In this case it was rather harder to see how to count off the petals, and Joan wondered whether the numbers did not then arise merely as a consequence of the method of following them.
瓊很好奇的是，這些數是否僅僅是一組數列，是否還有其它的性質。This was pretty much the view of D'Arcy Thompson, who played down the idea that the numbers had any real significance in nature.
湯姆普森的想法是，這些數在自然界中是有實際意義的。They made a series of diagrams to test this hypothesis which did not satisfy Alan, who continued to think about 'watching the daisies grow'.
他們繪製了一些圖表，但這不能使艾倫滿意，他還要繼續深入思考雛菊的生長。
