Shapes define how we look at things. Some shapes in nature are so interesting that they are an inspiration to several man-made structures.
One shape that changed the way humans functioned was the circle. Wheels are circular and have been the foundation of many inventions.
However, there are some circle-like shapes that have slightly different properties than that of a circle. We will take a look at those here…
Although you might think that conic sections can only be used in maths, if you observe closely these can be found all around you.
Take the example of the shape the Earth takes while revolving around the sun. While it looks circular, the sides are wider. This shape is called an ellipse.
There are two other shapes, parabolas and hyperbolas. Parabolic shapes can be explained using a simple example of a player throwing a basketball into a hoop. The imaginary figure that is formed is called a parabola.
Hyperbolas, on the other hand, can be best explained using your favourite potato chips. Next time you have it, notice how the central part of the structure (the chips!) bends and then tapers away.
Parabolas, ellipses, and hyperbolas fall under a category of mathematics called conics, which is short form for conic sections. This means that these structures are formed when a flat plane intersects with a cone. As we change the angle of the plane with respect to the cone, this section could be a circle, an ellipse, a parabola, or a hyperbola, as shown below.
What is a parabola?
It is a U-shape obtained by slicing a cone parallel to the edge of the cone.
Examples of parabola in real life:
- Lighthouses use parabola-shaped reflectors to help focus light into a beam that can be seen from a considerable distance.
- Water takes a path of parabola to fall on the earth from the fountain, starting upward, curving as it nears the peak, and straightening out somewhat as it heads back down. It’s the path followed by any thrown object.
- The Golden Gate Bridge (above) in San Francisco, California is famous for its parabolic spans on both sides.
- The stretched arc of a rocket launch is parabolic. When a rocket or other ballistic item is launched, it follows a parabolic path, also known as a trajectory. This parabolic trajectory has been employed in space flight for decades.
What is an ellipse?
It is a shape that has no sides, but is not a circle. More oval than a circle, yet its not an oval either. When you begin to understand the mathematical characteristics of an ellipse, you’ll find it very interesting.
Examples of ellipses in real life:
- The orbits of planets, satellites, moons, and comets, as well as the shapes of boat keels, rudders, and some aviation wings, can all be represented by ellipses.
- When a tumbler of water is tilted, an elliptical surface of water is seen.
- When vegetables are cut at an angle to their main axis, it results in an elliptical shape.
- Whispering galleries (above) at US Statutory capital and St. Paul’s Cathedral, London demonstrate the property of an ellipse. If you whisper from one end, a person standing at the other end will be able to hear you clearly.
What is a hyperbola?
It is a special type of curve which looks like two parabolas which are mirror images of each other. But it’s completely different in nature than a parabola.
Examples of hyperbolas in real life:
- The guitar is an eminent musical instrument that is characterised by its shape and a set of six strings. The body of a traditional stringed instrument is a good example of a hyperbola. The body is bent towards its centre on both sides, giving it a unique stance.
- Dulles Airport in the US. has a design of a hyperbolic paraboloid. It has one cross-section of a hyperbola and the other a parabola.
- When the cylindrical bed lights are turned on, a unique shade on the wall behind it can be seen. 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.
- The 108 feet high Kobe Port Tower in Japan is a popular tourist attraction 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.