Basic approximations in Python

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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 ‚Äã‚Äãof 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 

As we can see, 2.99 is not the exact value of (27) ^ 1/3 but 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 = 0.0 which we will keep incrementing in a loop until it approaches the cube root of 27. Another variable epsilon is 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.

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