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Geometrical Properties of Citrus Fruits

Lemons, limes, oranges, grapefruits, tangerines and other citrus fruits are classified as a hesperidium, basically large berries growing from trees, according to the University of Georgia. They are characterized by the presence of Vitamin C and their high acid content. Florida grows the most citrus fruit in the United States as its wet and warm weather aids their cultivation. These edible berries exhibit some of the most basic geometrical properties found in nature.

Shape
- The lemon is less round and more of an oval shape.
  
  Citrus fruits are round and grow in the shape of a sphere, or they are oblong. Oranges and grapefruits are examples of globular round fruits. Lemons and limes grow with more angular ends and are larger in the middle. The globe shape is symmetrical both horizontally and vertically, while the oblong lemon shape is symmetrical in only one direction. Keep in mind that fruit does not portray perfect symmetry throughout its entire body as it is naturally produced.
Patterns
- The separated sections of citrus display regular patterns.
  
  The edible sections--called the endocarp--exhibit wheel-like patterns throughout the fruit that can be seen by slicing into it on the diameter. Separated by a venous skin, the sections are laid out in 10 14 radii from the center of the fruit containing usually one seed each. These patterns remain consistent regardless of the overall shape of the fruit.
Volume and Density
- Citrus fruit volume can be measured with water.
  
  The volume and density of citrus fruits refers to the amount of space the fruit takes up and can be measured by a water displacement method. This method was practiced on a bergamot fruit in an International Agrophysics study by S. Rafiee et al., in 2007, by comparing the volume of displaced water to the measured weight of the fruit itself. The University of Georgia posts the volume of the edible portion of a citrus fruit at 86 percent to 90 percent water which makes a water comparison mathematically simple.
Surface Area
- The nubby citrus rind is often cut up and used in food for its aroma.
  
  The surface of the citrus fruit is generally textured and rough.The surface area can be estimated by using the formulas for a sphere for the rounder fruits like a grapefruit or an orange, but it takes a few more steps for the more cylindrical lemons and limes. This bumpy rind is a characteristic of the berry and can be peeled away to access the meat of the fruit, which is the edible portion. The rind takes up a larger portion of the fruit as a whole if it is grown in Mediterranean climates, as opposed to subtropical climates, according to the University of Georgia.

Nature