Last Updated on December 7, 2024 by Editorial Team
Many of us have observed a couple of curves facing away from each other. This shape is called a hyperbola.
In simple terms, a hyperbola is an open curve with two branches. It forms when a plane intersects a double cone, resulting in a shape that looks like two “C”s turning away from each other.
Understanding hyperbolas is important because they appear in many practical situations. Once you grasp the concept, it might be interesting to explore how hyperbolas are seen in real life.
In this article, we’ll take you through ten examples of this unique shape.
Hyperbola – Some real-life instances
Observing the entities around us can give out instances of various shapes. A ball is a circle, a Rubix is a cube, and an eraser can be a rectangle or cuboid. Similarly, there are few areas and applications where we can spot hyperbolas.
1. Guitar

The guitar is an eminent musical instrument that is characterized by its shape and a set of six strings. This instrument is often a serene pick for musicians.
The body of a traditional stringed instrument is a good example of a hyperbola. The body is convexed towards its center on both sides, giving it a unique stance.
Even in classroom teaching about hyperbolas, this instrument is often picked as an instance to demonstrate.
2. Concave lens

Entities that are fabricated to be used with eyes often implement the concept of a hyperbola. The concave lens is one of the noteworthy examples here.
Lens shaped like a hyperbola may be often employed in areas where the lights need to be scattered, these lenses are taken. For this reason, most of the optical lenses in cameras are often concave.
Moreover, When liquid climbs by capillary action between two microscopic slides that are vertical and almost touching, a part of the hyperbola is formed on the surface which is termed as “meniscus”.
3. Curved Monitors

Some versions of the latest PC monitors and also some televisions came with curved monitors. This adaptation makes the user’s eyes effortlessly discern details on the screen compared to flat monitors.
Comparing these monitors with flat picks, these curves are hyperbolic. Even in the design of these displays, the manufacturers employ hyperbolic estimations.
Curved monitors are often used by professionals and games to get bigger and easier access to details in the display.
4. In Space Sciences
Hyperbola and relevant concepts are frequently employed by space scientists in making estimations regarding satellites and space crafts. As the effect of gravity may not be ignored for these heavy objects during launch, to reach the final destination as desired, the path may need to be angled to some extent.
For this, concepts of hyperbola become associative. It wouldn’t be fair to estimate that these objects expedite in a straight line; the path is influenced by gravitational force transforming the path to curve.
To analyze the perfect attributes of this actual path, it is estimated as a hyperbola, making reckoning facile.
5. Inverse relation Graphs

Graphical representations of various equations and relationships between variables form interesting shapes in the sheet.
Inverse relationships between two variables form a hyperbolic shape on the graph. Any real-life variables that are inverse in the relationship are thereby examples of Hyperbola.
For instance, the brightness of the sun decreases with an increase in distance from the Earth. When the values of both these values are presented graphically, it depicts a Hyperbola.
6. Dulles Airport- And Hyperbolic Airdrome!

Designed by Eero Saarien, this airport in the United States manages to be distinct with its unique stance. This structure is based on a hyperbolic paraboloid.
At the first glance, its roof may be identified as being hyperbolic with the surface. This international aerodrome made a divergent attempt to entice the public with the use of interesting formations.
7. Hyperbolic Gears
Multiple shafts in a device or vehicle may not be supplementary to using ordinary gears. In these scenarios, hyperbolic gears or hypoid gears are used.
These gears use hyperbolic fundamentals to transfer energy among skewed axles. A few other gear types like Spiral bevel gears also employ similar notions to transmit torque to other shafts.
8. The Kobe Port tower

This 108-foot-high port tower in Japan entices tourists for its shape and design. It looks like a concave lens (hyperbolic).
Designed by the Koichi Lto-Naka Takeo duo in 1963, this tower was built with a pipe lattice. The shape was actually inspired by a traditional Japanese musical instrument, Tsuzumi, which is hyperbolic in shape.
9. Bed Light Shades

Usually, the bed lights are cylindrical in shape. But when they are turned on, we can see a unique shade on the wall behind it. It is often hyperbolic.
The reason is that these lights often open on the upper and bottom sides. A circular scattering of light intersected by a plain wall brings out the hyperbolic shade.
These shapes are often employed in adorning the walls as well.
10. Cooling Towers

In industries like paper, coal, or oil large cooling towers and chimneys can be observed, These are often designed in hyperbolic shape to ensure that the air outside is cooler than the inside.
This way, the outside air forces the inside hot dust to push out thereby removing impurities from the machinery chamber effortlessly.
Hyperbola Examples in Nature
Hyperbolas are not just abstract mathematical concepts; they can also be found in nature in surprising ways. Their unique shape often appears in patterns and structures that help to explain natural phenomena. Here are a few examples of how hyperbolas manifest in nature:
- Satellite Dish Antennas: Many satellite dishes are designed with a parabolic shape, but the technology behind satellite signals often involves hyperbolic reflections. The design ensures that signals from a satellite (which are essentially points at the focus) are reflected and directed along a hyperbolic path to the receiver.
- Astronomical Orbits: Some celestial bodies follow hyperbolic trajectories, particularly comets or spacecraft on escape trajectories from a planet. When these objects move under the influence of gravity but have enough velocity to escape the gravitational pull of a body, their orbits can be hyperbolic.
- Sound Waves: The pattern of sound waves from a source in a free space can sometimes follow a hyperbolic path, especially when the source is moving or in the presence of specific acoustic environments.
- Light Reflection: In optics, light passing through certain lenses or reflecting off curved surfaces can follow a hyperbolic path. An example is the path taken by light around black holes, where gravitational lenses bend the light into a hyperbolic trajectory.
- Gravitational Lensing: In the study of gravitational waves and light bending near large masses (like stars or black holes), light paths are often hyperbolic, influenced by the massive object’s gravity.
- Water Flow Around Objects: In fluid dynamics, when a stream of water flows around an object, the flow lines can sometimes form hyperbolic shapes, especially when the flow is disturbed by an obstacle, creating vortexes.
- Biological Structures: The shape of certain sea creatures’ shells, like that of the nautilus, might be seen to have a hyperbolic-like growth pattern, though it’s more often classified as logarithmic or spiral.
- Hyperbolic Geometry in Fungi: Some types of fungi display hyperbolic growth patterns, especially in the way certain branching structures form in the wild, maximizing surface area for spore dispersal.
Wrapping up,
The significance of math notions in real life is often immeasurable. The applications are evident in a number of areas without boundaries.
Taking this to our edge, we can make a serviceable list of examples of these notions to understand them better. Check out the above examples of Hyperbola and make sure you are well-versed with this shape.
Soaking into such intriguing shapes, you may ensure advancement in the level of math, implying better preparation.
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,