The ellipse, a seemingly insignificant shape in geometry, holds paramount significance in mathematics as well as in the real world. Sometimes, it is overshadowed by the more famous circle, but is otherwise essential in several facets of our life. When students begin their mathematical journey, the practical existence of ellipses becomes more than just an academic piece of work.
So, in this article, we will talk about how ellipses are significant in day-to-day life with the help of real-life examples. By the end of this article, students will be able to have a genuine appreciation for the underlying and key significance of ellipses in human life.
How to identify an ellipse?
Let us begin with understanding how to identify an ellipse. When conical-shaped figures are cut at an angle, it gives rise to different conic sections and one of them is an ellipse. Start by taking a glass filled nearly 3/4th with water. Now, tilt the glass slightly to one corner. The shape formed by the surface of the water is an ellipse. Given below are a few more detailed characteristics of an ellipse that make it easy for you to identify it when you see one!
1. The shape –
An ellipse looks like a circle or an oval that has been squashed.
2. Two focal points or foci –
An ellipse has two focal points, also known as foci. Both these points are located inside the perimeters of the ellipse. The sum of the distances from any point on the ellipses to both these focal points or foci remains constant.
3. Major axis and minor axis –
There are two main axes of the ellipse – the longer one is called the major axis and the shorter one is called the minor axis. Both these axes intersect at the center of the ellipse. The major axis traverses the longest distance within the perimeter of the ellipse while the minor axis traverses the shortest distance.
4. Eccentricity –
Eccentricity is denoted as ‘e’ and describes how elongated or squashed an ellipse is. The typical range is between o to 1, where 0 is a circle and 1 is an ellipse.
Fields where ellipses are dominant
In various fields, ellipses are dominant geometric forms, having the ability to give rise to various mathematical models, technological innovations, and artistic masterpieces. Let us have a look at some of the diverse fields of study and research where ellipses reign supreme.
Almost all celestial and planetary orbits, eclipses, and binary star systems are elliptical in shape, making it necessary for astronomers to understand the ellipse and all of its properties.
Elliptical gears fuel vehicles and robots and the wings of an aircraft leverage aerodynamic efficiency. These examples are cream of the crop amongst several other applications of an ellipse.
Any form of art, be it dance or paintings, finds applications of ellipses in terms of elegance and symmetry respectively.
4. Sports and recreational activities
Elliptical shapes have profound use in the sporting and recreational industry. Several racetracks, swimming pools, and bicycle chainrings are elliptical in shape.
5. Technology and optics
Manipulation of light is sometimes necessary and using elliptical mirrors and lenses makes it easy. Also, elliptical parabolic microphones can efficiently capture and focus sound waves. Elliptical reflectors are known to enhance antenna performance.
Applications of ellipse in real life
The applications and examples of ellipses in real life are vast. We have handpicked a list of commonly seen examples that you can resonate with easily, so read on to know more.
Have you been to malls or amusement parks where there are several mirrors, each giving you a different image of yourself? Those are usually elliptical in shape. Also, some hand-held mirrors sport a similar shape.
2. Elliptical buildings
Masterpieces like the Roman Colosseum of Rome are elliptical buildings. Architecture makes use of elliptical figures to design windows, arches, and various building facades.
3. Elliptical handles of gym equipment
Some gym equipment and exercise machines like elliptical trainers have handles that traverse an elliptical path suitable for low-impact cardio workouts.
4. Elliptical headlights and taillights
Modern automotive styling focuses on both aesthetics and visibility. The lens used for the headlight and taillight of cars is usually elliptical in nature and may appear so only from a certain angle. They are sleek to keep up with standards of aerodynamic design.
One of the most common examples of ellipses found in daily life is an egg. A simple yet elegant example, eggs are elongated ellipses in shape.
6. Elliptical orbits of planets and satellites
The orbits of planets around the sun and artificial satellites (which are used for GPS and communication) traverse an elliptical path around the Sun and the Earth respectively. Kepler’s law also states that the path traversed by each planet around the sun is an ellipse.
7. Elliptical jewelry and patterns in clothes
Jewelry designs in elliptical shapes and patterns are a common sight. Also, fabrics used by fashion designers for textiles and clothes are subjected to elliptical shapes and patterns.
8. The elliptical cross-sectional surface of pipes
In Engineering, the usage of elliptical pipes is not rare. Most of the plumbing-related applications in Engineering use elliptical pipes.
9. Elliptical Logos
Logos are of key importance when it comes to branding. So, it is essential that logos have the power to captivate their audiences. Some successful logos that are elliptical are those of the movie franchise – Batman, the famous singing reality show American Idol and the famous automobile Ford! I am sure as soon as you read the names, the logo must have flashed across your eyes! Well, that is the power of a successful logo design!
10. Elliptical clock dials
Taking the aesthetic appeal a notch higher are elliptical wall clock dials! These serve a dual purpose of showcasing time and also prove to be a unique decorative piece.
11. Elliptical fountain patterns
Watershows and fountain dances in amusement parks and theme parks often use lights and water fountains to form unique patterns based on ellipses that are a visual delight to the audiences!
12. Elliptical eclipses
Both solar and lunar eclipses when viewed from various locations from Earth appear elliptical due to Earth’s curvature axis.
13. Elliptical flower petals
Now this is another visual delight! Upon closer watch, flowers such as lilies and tulips have elliptical petals that are aesthetic and produce great fragrance.
We’re sure that by now you must have gotten a better understanding and visualization of ellipses. These real-life examples of ellipses are reminders to us that mathematics and geometry aren’t just confined to the limits of the classroom. By existing in the real world, they showcase the harmonious fusion of functionality and aesthetics. Ellipses are often overlooked, but their importance is profound in nature.
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’,