10 APPLICATIONS OF THE PARABLE IN EVERYDAY LIFE - CULTURE VOCABULARY - 2025

The applications of the parable in everyday life are multiple. From the use that satellite antennas and radio telescopes give to concentrate signals to the use that car headlights give when sending parallel beams of light.

A parabola, in simple terms, can be defined as a curve in which the points are equidistant from a fixed point and a line. The fixed point is called the focus and the line is called the directrix.

The parabola is a conic that is traced in different phenomena such as the movement of a ball driven by a basketball player or like the fall of water from a fountain.

The parabola has special importance in various areas of physics, resistance of materials or mechanics. At the base of mechanics and physics the properties of the parabola are used.

Sometimes many people say that math studies and work are unnecessary in everyday life because at first glance they are not applicable. But the truth is that there are multiple occasions in which such studies are applied.

Applications of the parable in everyday life

Satellite dishes

The parabola can be defined as a curve that arises when cutting a cone. If this definition were applied to a three-dimensional object, we would obtain a surface called a paraboloid.

This figure is very useful due to a property that parabolas have, where a point within it is moving in a line parallel to the axis, it will “bounce” off the parabola and send itself towards the focus.

A paraboloid with a signal receptor in focus can get all the signals that bounce off the paraboloid to be sent to the receiver, without pointing directly at it. Great signal reception is obtained using the entire paraboloid.

This type of antennas are characterized by having a parabolic reflector. Its surface is a paraboloid of revolution.

Its shape is due to a property of mathematical parabolas. They can be transmitting, receiving or full duplex. They are called that way when they are able to transmit and receive at the same time. They are usually used at high frequencies.

Satellites

A satellite sends information towards Earth. These rays are perpendicular to the directrix for the distance from the satellite.

When reflected off the dish of the antenna, which is generally white, the rays converge on the focus where a receiver is located that decodes the information.

Jets of water

The jets of water that come out of a fountain are parabolic in shape.

When numerous jets come out of a point with the same speed but with different inclinations, another parabola called a “safety parabola” is above the others and it is not possible for any other of the remaining parabolas to pass above it.

Solar cookers

The property that characterizes parabolas allows them to be used to create devices such as solar cookers.

With a paraboloid that reflects the sun's rays, it would easily place what is going to be cooked in its focus, making it heat up quickly.

Other uses are the accumulation of solar energy using an accumulator on the bulb.

Vehicle headlights and parabolic microphones

The previously explained property of parabolas can be used in reverse. By placing a signal emitter located towards its surface at the focus of a paraboloid, all signals will bounce off it.

In this way, its axis will be reflected in parallel outwards, obtaining a higher level of signal emission.

In vehicle headlights this occurs when a bulb is placed in the bulb to emit more light.

In parabolic microphones, it occurs when a microphone is placed in the focus of a paraboloid to emit more sound.

Hanging bridges

Suspension bridge cables adopt the parabolic shape. These form the envelope of a parabola.

In the analysis of the equilibrium curve of the cables, it is admitted that there are numerous tie rods and the load can be considered to be uniformly distributed horizontally.

With this description, the equilibrium curve of each cable is shown to be a simple equation parabola and its use is common in the art.

Real-life examples include the San Francisco bridge (United States) or the Barqueta bridge (Seville), which use parabolic structures to give the bridge greater stability.

Trajectory of celestial objects

There are periodic comets that have elongated elliptical paths.

When the return that comets make around the solar system is not demonstrated, it seems that they describe a parable.

sports

In every sport in which a toss is made, we find parables. These can be described by balls or thrown artifacts as in soccer, basketball, or javelin throwing.

This launch is known as a "parabolic launch" and consists of pulling up (not vertically) an object.

The path that the object makes when climbing (with the force applied to it) and descending (due to gravity) forms a parabola.

A more concrete example is the plays made by Michael Jordan, NBA basketball player.

This player has become famous, among other things, for his “flights” towards the basket where at first glance he seemed to be suspended in the air much longer than other players.

Michael's secret was that he knew how to use adequate body movements and a great initial speed that allowed him to form an elongated parabola, making his trajectory close to the height of the vertex.

illumination

When a cone-shaped light beam is projected onto a wall, parabolic shapes are obtained, as long as the wall is parallel to the generatrix of the cone.

References

1. Arnheim, C. (2015). Mathematical Surfaces. Germany: BoD
2. Boyer, C. (2012). History of Analytic Geometry. USA: Courier Corporation.
3. Frante, Ronald L. A Parabolic Antenna with Very Low Sidelobes. IEEE Transactions on Antennas and Propagation. Vol. 28, N0. 1. Jan 1980. Pp 53-59.
4. Kletenik, D. (2002). Problems in Analytic Geometry. Hawaii: The Minerva Group.
5. Kraus, JD (1988). Antennas, 2nd Ed. USA: McGraw-Hill.
6. Lehmann, C. (1984). Analytic geometry. Mexico: Limusa.