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.
他在战前读了生物学家狄尔西·汤姆普森发表于1917年的经典著作《生长与形状》，其中包括对生物结构的数学讨论。
He was particularly fascinated by the appearance in nature of the Fibonacci numbers—the series beginning
他对自然界的斐波纳契数列特别有兴趣：
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.
每一项都是前面两项的和。
They occurred in the leaf arrangement and flower patterns of many common plants,
这体现在很多常见植物的叶子和花朵中。
a connection between mathematics and nature which to others was a mere oddity, but to him deeply exciting.
对于其他人来说，数学与自然界之间的联系是很古怪的，但艾伦却对此感到很兴奋。
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，他和琼玩完网球，躺在布莱切利庄园的草地上，他又在观察雏菊的生长。
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,
他们开始讨论那些花儿，琼给他讲解她如何给植物叶子分类。叶子绕着茎，盘旋向上生长，
counting the number of leaves and the number of turns made before returning to a leaf directly above the starting-point.
从下往上计数叶子数和盘旋的圈数，直到某片叶子正好与第一片叶子在竖直方向上重合。
These numbers would usually appear in the Fibonacci series.
这时得到的数值通常是斐波纳契数。
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.
艾伦拿起一个冷杉球果，这清晰地体现了斐波纳契数，雏菊也是这样的。
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.
琼很好奇的是，这些数是否仅仅是一组数列，是否还有其它的性质。
This was pretty much the view of D'Arcy Thompson, who played down the idea that the numbers had any real significance in nature.
汤姆普森的想法是，这些数在自然界中是有实际意义的。
They made a series of diagrams to test this hypothesis which did not satisfy Alan, who continued to think about 'watching the daisies grow'.
他们绘制了一些图表，但这不能使艾伦满意，他还要继续深入思考雏菊的生长。