The Mathematics of Apples

There is nothing that I like more than having slices of a nice crisp apple at the end of any meal.  Apples have a very specific shape and if you cut them precisely the right way, you'll notice a star in the center. If you look at an apple, it is pretty much spherical except for the dimple at one end. 

Apples first developed in Central Asia thousands of years ago.  Over time, apples spread to Europe and the United States.  If an apple is grown from seed, it is often different from its parent so apples are mostly grown by grafting apple cultivators onto a rootstock so the trees grow faster and have the desired characteristics. 

Recently a paper was published on the shape of an apple.  Mathematicians and physicists used observation, experiments, theory, and calculations to figure out how apples grow and form. It started with a simple theory on how apples form and grow but it took off when they were able to connect observations of actual apples at various stages of their growth with experiments, theory, and calculations.

The first thing they did was to collect apples from quite early to ready to pick and map the measurements for each stage.  They focused on the growth of the dimple or cusp over time and how it related to the apple . Then they needed a theory to explain the growth so they focused on the singularity theory which is used to explain everything from black holes to the light patterns found at the bottom of the pool. Although the cusp of an apple has little in common with the light patterns at the bottom of the pool or a droplet coming off a column of water, it is the same shape as the others.  In addition, singularity theory is also responsible for explaining the slight deformation at the stalk end.

So once they had a theoretical framework, they began using numerical simulation also known as mathematical modeling to develop an understanding of the different growth rates of the fruit cortex and core cause the cusp to form. The cusp appears to develop due to the different rates of growth between the bulk of the apple and the place where the stem is. They used a gel to recreate a physical representation of the growth and by changing the growth and composition of the gel, they were able to mimic the development of the fruit.

This is just the first step in looking at a larger topic. They've explored a biological singularity but now they need to figure out how the molecular and cellular mechanisms work in regard to the formation of the cusp itself.  Eventually, they hope to develop a broader theory of biological shape.  I think this is absolutely fascinating.  Let me know what you think, I'd love to hear.  Have a great day.