Approximation means estimating the value of something that is not quite accurate, but almost correct. It plays a vital role in science and technology. Let`s start with the most common example. Have you ever used the exact pi value? Of course not. It is an infinite irrational number with a very long meaning. If we continue to write the exact value of Pi , perhaps even this article will not be enough for this:
3.14159 26535 89793 23846 26433 83279 ...
So here where approximation plays a role. We usually approximate Pi as
3.14 or in rational terms
22/7 . When you got to high school, you probably saw a wider application of approximations in mathematics, which use differentials to approximate the values of quantities, such as (36.6) ^ 1/2 or (0.009) ^ 1/3. In computer science, we can use approximation to find the value or approximate the value of something using loops.
For example: approximation of the cube root of any number. Take a look at the process below:
Output of the above code:
2.9963000000018987 is close to the cube root of 27 pre>
As we can see, 2.99 is not the exact value of
(27) ^ 1/3but is very close to the exact value 3. This is what we call approximation. Here we have used a series of calculations to approximate the value. First, we declare a variable
guess = 0.0which we will keep incrementing in a loop until it approaches the cube root of 27. Another variable
epsilonis chosen as little as possible to get more accurate meaning. The line
while abs (guess ** 3 - cube) & gt; = epsilon:will take care of this. If it breaks out of the loop with a value greater than
epsilon, it means that we have already crossed the approximate value and failed in the test. Otherwise, it will return the guess value.