However, it is rarely used today because there are now too many planes in the sky. Rather than using something small like a ball, the radio beam is shaped like a fan: narrow in the horizontal direction, and wide in the vertical direction to cover a large area. If it does, then something must be in front of you, and the longer it takes to come back, the further away the object must be. You can think of it as throwing a ball in a dark room and seeing whether or not it comes back to you. The source sends a radio signal, with a frequency higher than those used for radio or TV broadcasts to avoid interference, and has a receiver that detects echoes from any object in its path. The control centre has a rotating source that scans 360º every 2-3 seconds. When thinking of radar, I’m sure many of you will picture a spinning green needle that sweeps around a black circular disk, like the one shown below. Who would have imagined…Īir traffic control uses RADAR (RAdio Detection And Ranging) to detect moving planes. So, what about ‘real-life’? We can see negative numbers in financial management, fractions in baking recipes, but where can we apply complex numbers? It turns out imaginary numbers are crucial in air traffic control. We can plot any complex number on an Argand Diagram, which is no different than any other coordinate plane you have seen, except the x-axis is now the “real” axis, and the y-axis is the “imaginary” axis. A number can be purely real or imaginary, or it can contain both a real and imaginary part which is what we call a complex number is. But, if we now consider a second dimension, the “imaginary dimension”, then a whole new world of numbers awaits. Generally, we tend to think of numbers on a line, which is what we call the ‘numberline’. So, someone decided to give this “mysterious” number a name: imaginary number i, which is defined to be √-1. It appears that we cannot square a number that gives a negative value, but yet we see these numbers come up in mathematics. Whenever we square a real number, we always end up with a result that is positive. You might think that real numbers encompass all numbers in mathematics, and this is even what mathematicians thought until relatively recently, but there is actually another dimension of numbers that the real numbers do not include. From natural numbers to irrational numbers, these numbers together form the set of real numbers. Irrational numbers became part of the number line when Hippasus, a Pythagorean Philosopher, argued that some numbers, such as the square root of 2, cannot be represented by a fraction. It was hard for people to interpret and visualize them at first, but people slowly accepted these numbers because they made calculations easier. Over time, several problems came up: what if someone does not have enough sheep to pay me back with? What happens when the sheep does not belong to one person, but two? To answer these questions, the negative and rational (fractional) numbers were introduced to the number line. To count what they have, they used natural numbers, which included all positive integers. For instance, what does it mean to have -1 apples, or ¼ of a sheep? In fact, the number line we know today was very different 1000 years ago…īefore we used money as a currency, people bargained and traded using whatever they had, such as the amount of animals they own, like sheep. At first it might seem intuitive to think of fractions, negative numbers, maybe even decimals, but the more we stop to think about it, the more we might start to question their legitimacy and meaning.
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