Unveiling a Few Secrets of Nature and Engineering (Part 1 of 2)

Welcome to this two-part series, where we explore the fascinating interplay between nature and geometry. In this installment, we dive into some of the most captivating geometrical shapes found in the natural world. Let’s begin!

Majestic Sunflower. If we count the spirals created by seeds, we will always find that they follow Fibonacci sequence. Below are 3 examples. Note that the black pattern is the same in each of the 3 images. Only the colored lines indicating the selected spirals are different. Each selected spiral exhibits Fibonacci sequence. Incredible indeed! Photo Credit: clevelandcountymastergardeners.org

The Geometry of Nature

Nature abounds with mesmerizing geometrical shapes, many of which follow well-known mathematical principles. Among these, the Fibonacci sequence stands out, evident in patterns like the arrangement of sunflower seeds, pinecone scales, and seashell spirals. This sequence often aligns with the "Golden Ratio," a concept celebrated for its aesthetic and structural efficiency.

Sunflower seed pattern exhibit Fibonacci sequence.  Photo Credit: momath.org/National Museum of Mathematics.

Other mathematical patterns in nature include fractals, hexagons, concentric circles, and logarithmic spirals. These patterns can be observed across various natural and plant structures, tailored to their specific functions and environments. Examples of fractals in nature include snowflakes, lightning bolts, tree branches, broccoli florets, clouds, coastlines, mountain ranges, river passages, fern leaves, and more. Any natural structure with self-repeating patterns at different scales is considered fractal in nature. Fractal geometry provides a framework to describe these complex shapes with precision.

Perfect geometrical shape of a snail. Photo Credit: worldatlas.comwildlifeflorida.org

Incredible geometrical shape of a cobweb. Photo Credit: pexels.com/Chait Goli

Incredible Instances of Nature’s Engineering

Here are some remarkable examples of natural engineering and their inherent benefits:

1. Evolution and Engineering

Throughout evolution—both for living and non-living entities—nature has optimized designs to maximize function while minimizing materials. By selecting the most efficient geometries, nature reduces weight, maximizes efficiency with minimal inputs, builds resilience against environmental challenges (wind, rain, heat, cold, etc.), and ensures longevity. This principle is a valuable lesson for modern design engineers, especially in an era where overuse of finite resources is a growing concern.

Mesmerizing fractal shapes of lightning bolts. Photo Credit: sciencenews.org

2. Functional Body Shapes

Body shapes in nature often evolve to meet functional requirements. For instance, insects and reptiles have body structures that maximize surface contact with the ground, providing frictional resistance and aiding locomotion.

A caterpillar’s body touches the ground it walks on. Photo Credit: wildlifeflorida.org

Snakes, for example, rely on their scales for movement. To propel forward, snakes use the large scutes on the underside of their bodies. Each scute digs into the ground like a small shovel, and as muscles pull it back toward the tail, the snake pushes forward, one scute at a time. This mechanism is an excellent example of nature’s efficient engineering.

Body parts of a snake helps its locomotion. Photo Credit: Pixabay.com

3. Fruits: Geometry with Purpose

The oval or circular shapes of fruits likely serve a larger purpose. Much like an egg, which has directional structural properties, fruits use their shape to optimize their fall and impact. When ripened fruits fall, their shape ensures they absorb the impact forces efficiently, enabling their shells to split and disperse seeds effectively. This splitting behavior may depend on the structural network of the fruit’s shell, influenced by the fruit’s average weight, height from the ground, and the soil’s hardness.

4. The Streamlined Shapes of Birds and Fish

The streamlined, oval shapes of birds and most fish serve both functional and protective purposes. Scientists suggest that this shape reduces the frontal area exposed to predators while minimizing fluid friction as they move through air or water. This same principle is applied to boats and ships for enhanced efficiency.

Oval shape of a bird’s body. Photo Credit: Pexels.com/A. G. Rosales

Oval shape of a fish’s body. Photo Credit: unsplash.com/Claudio Guglieri

5. The Shapes of Bird Eggs

Bird eggs come in four main shapes: round (spherical), elliptical, oval, and pyriform (conical). For example, the little bee-eater lays nearly perfect spherical eggs, while cliff-dwelling birds like the common murre lay pyriform eggs. The latter are less likely to roll off cliffs as they tend to roll in tight circles—a trait likely shaped by natural selection. Examples of hole-nesting birds, such as woodpeckers and chickadees, lay spherical or

round eggs. The eggs do not fall out of their nests. Birds that nest on cliffs include swallows, auks, and kittiwakes. Their eggs are conical shaped and so do not drop off the cliffs.

Cliff nesting bird colony. Guillemots (the dark ones), kittiwakes (the light ones), and probably few razorbills sharing the Great Stack. Photo Credit: medium.com/Anse Bogdanova-Jatniece

Stay tuned for Part 2, where we’ll explore even more intriguing intersections between nature and engineering!

Did You Know?

·      The Fibonacci sequence is the series of numbers where each number is the sum of the two preceding numbers. For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55……

·      Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities

·      A fractal is a curve or geometric figure, each part of which has the same statistical character as a whole. In essence, a fractal is a pattern that repeats forever, and every part of the fractal looks very similar to the whole image. Fractals are useful in modeling structures like the eroding coastlines or snowflakes. The Mandelbrot set is the most famous example of fractal.

#nature #geometry