I was never very good at maths! At school I was put into a form who were taught New Maths. Luckily for me, we had a really great teacher who was able to reveal the mysteries of the subject in a way that made sense and I managed to get an ‘O’ level!. The New Maths was a lot more visual, especially Venn diagrams, which I could relate to more easily than algebra. One thing that has stayed with me is that the area of intersection (or overlap) of two sets is A ∩ B (A cap B) (below). It does not get more simpler than this!
Nothing very profound then, but the old Venn diagrams sprang to mind when I noticed these lovely overlapping Wych elm, Ulmus glabra, leaves (below) where the area of overlap was dramatically highlighted by the setting sun.
Some of the patterns were more complicated than others, with A overlapping B and C, and D overlapping A, and E overlapping C and E; you get my drift!
Areas of overlap like this presumably result in a certain loss of efficiency in the shaded part of the lower leaf; as the amount of sunlight gets drastically cut down. Of course, these areas of overlap are only transitory, as the sun moves across the sky during the day, but as a rule, it is probably best for a tree not to have too many overlapping leaves. When leaves are completely shaded (shade leaves) their size and shape changes, as explained in this blog I came across.
I am certainly not the first person to have been struck by the beauty of these patterns – try Googling ‘overlapping leaves’ – and it is an easy game to play! Not all leaves are as good as the Wych elm however, at producing satisfying patterns. Here’s a sycamore for example (below).
I think, what’s nice about the Wych elm leavers is i) that they are serrated and ii) they are a rather simple overall (oval) shape.
Let’s finish with a nice one (below) which is something like A ∩ B, B ∩ C and D etc … I’ve forgotten how to express it as a simple formula! Never mind, just nice shapes to enjoy!
There is probably a whole branch (sic.) of plant physiology devoted to understanding the effects of light and shade on leaves!