The Mathematics Behind Leaf GrowthAccording to Vihart, a mathematician sharing her knowledge on YouTube, botanists have noticed that plants are quite consistent when it comes to the angle between one leaf and the next. After a lot of research, they have discovered that the angle can be found by dividing the total number of degrees in a circle (360) by the irrational number phi (Φ, approximating 1.618) and subtracting the resulting number from 360. You end up with an angle of approximately 137.5 degrees, which allows new plant leaves to grow in without being blocked from the sun from leaves above. If you look at the picture below, the angle made by a petal and the one that grew right after (in this case, the one that is the next highest, not the one that is immediately adjacent) approximates 137.5 degrees. I’ve highlighted the pair in red and the pair in blue, but any two petals that are next to each other in terms of depth along the stalk should make an angle of 137.5 degrees. We can see from the picture that barely any of the leaves directly overlap with each other, so all the petals can access sunlight equally. Thus, all a plant really needs to do is keep growing leaves or petals 137.5 degrees away from the last leaf or petal. Succulents make this phenomenon particularly easy to observe, so here are some more pictures. Try to spot the magical 137.5 degree angle at work!
Until next time,