Euler number in python

Python e: Python Euler’s Constant with Math

In this tutorial, you’ll learn how calculate the Python e , or the Euler’s Number in Python. The number is equal to approximately 2.71828, and represents the base of the natural logarithm. The number is also often used in calculating compound interest and other natural phenomena.

You’ll learn how to use the Python math library to calculate the Euler number, e . This can be done use the built-in constant math.e as well as the function math.exp() .

The Quick Answer: Use math.e

What is Euler’s Number?

Euler’s number, often referred to simply as e , is a mathematical constant that serves many purposes, including in calculating compound interest. The number is found in many natural phenomena and, because of this is found in many different mathematical calculations.

For example, the value e is used so often in calculating logarithms that the natural logarithm, which uses e as its base, is simply referred to as ln() . The constant is used frequently in compound interest, standard normal distributions, and in calculus.

The value of e is roughly 2.71828, but the more precise the value is, the more accurate your calculations will be. Because of this, it’s helpful to use the constant value or calculate it from scratch.

In the next section, you’ll learn how to use the Python math library to use the constant for the value of e .

How to Use Python Math to Find the e Constant

The Python math library comes packaged with a number of important constants, among them pi and e .

Because we need to reference these values often, it can be important to know how to access them.

Let’s see how we can access the value for e using the math library:

# Print the value of e with math.e import math e = math.e print(e) # Returns: 2.718281828459045

Let’s see what we’ve done here:

In the next section, you’ll learn how to use math.exp() function to calculate Euler’s number.

Want to learn more about calculating the square root in Python? Check out my tutorial here, which will teach you different ways of calculating the square root, both without Python functions and with the help of functions.

How to Use the Python Math Exp Function to Calculate Euler’s Number

The math library comes with a function, exp() , that can be used to raise the number e to a given power.

Say we write exp(2) , this would be the same as writing e 2 .

Let’s take a look at how we can use Python to do this:

# Print the value of e with math.exp() import math print(math.exp(2)) # Returns: 7.38905609893065

The Python documentation actually notes that using the math.exp() function may be a more accurate way of getting the value of e .

Since the we can use the math.exp() function to raise e to a provided power, we can actually just pass the value of 1 into the function to return the value of e .

Let’s see how we can do this using Python and the math library:

# Print the value of e with math.exp() import math print(math.exp(1)) # Returns: 2.718281828459045

In the next section, you’ll learn how to use Python and the math library to use the value of e to calculate a natural logarithm.

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How to Use e to Calculate the Natural Logarithm in Python

One special logarithm often used in many practical real-world problems is to use what is known as the natural logarithm. Because the use of the natural logarithm is so common, it’s given a special way of being written ln() , which is the same as writing log_e() .

Now that we know how to get the value of e, we can now calculate a natural logarithm in Python:

# Calculate the natural logarithm with math import math value1 = math.log(1, math.e) value2 = math.log(2, math.e) value3 = math.log(3, math.e) print(value1) print(value2) print(value3) # Returns # 0.0 # 0.6931471805599453 # 1.0986122886681098

Now, one interesting thing to note is that when no base is passed into the math.log() function, it defaults to the value of e . Because of this, we don’t actually need to pass it into the function.

Let’s verify this by passing in a few test items to see if we get the same values as indicated above:

# Calculate the natural logarithm with math import math value1 = math.log(1) value2 = math.log(2) value3 = math.log(3) print(value1) print(value2) print(value3) # Returns # 0.0 # 0.6931471805599453 # 1.0986122886681098

We can see that this returns the same values!

Want to learn how to calculate and use the natural logarithm in Python. Check out my tutorial here, which will teach you everything you need to know about how to calculate it in Python.

Conclusion

In this tutorial, you learned how to use Python to calculate and use the value of e , Euler’s number. You learned how to use the Python math library which comes with a constant value as well as a function to calculate the value from scratch. You also learned how to use the Python e constant to calculate the natural logarithm.

To learn more about the Python math library, check out the official documentation here.

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Python e Constant | Use math.e in the Best Way

Out of the many modules available in python, one of them is the math module. Using this math module, we can access several mathematical functions. This module consists of several functions such as logarithmic functions, trigonometric functions, representation functions, etc., as well as mathematical constants. In this article, we shall be looking into one such mathematical constant – python e constant.

What are mathematical constants

By using the math module in python, we can access mathematical constant from the module. We can use these constants for carrying out mathematical operations and defining formulas in python. The values returned by these constants are equal to their values as defined in mathematics. The mathematical constants in python’s math module are :

Note: Here, math.inf and math.nan is available for python versions 3.5 onwards, and math.tau is available for python versions 3.6 and onwards.

About Python Math e

The math e is a mathematical constant in python. It returns the value of Euler’s constant which is an irrational number approximately equal to 2.71828. Euler’s constant is used in Natural Logarithms, calculus, trigonometry, differential equations, etc.

The Syntax of Accessing the Euler’s Constant from the math module is:

The return value of math.e constant is a floating-point value of Euler’s constant.

Examples of Python Math e

Let us take a python code to understand the math e constant. First, we shall import the math module. And then, we will print the return value of math.e constant.

The output of the constant is:

Else, we can also use math e constant like this:

from math import e print(e)

It will generate same output.

We can also use the math constant to create formulas.

Suppose, if we want to define the particular function, f(x) = (e^x – 1)/x, then we can use math e constant to achieve that. We shall be defining a user-defined function func() which takes a single argument which is the value of ‘x’ from the formula. Here, math.e shall represent ‘e.’

import math def f(x): return ((math.e ** x) - 1)/x print(f(2))

Python e Constant Using math.exp()

The exp() is a function present in the math module which is used to output the exponential power of the euler’s constant.

The syntax is:

It takes one argument ‘n’, which can be any positive or negative number. The argument is taken as the power value to which the Euler’s constant has to be raised.

As the output, it returns the python e constant raised to the given power (e^n).

import math print(math.exp(1))

The output will be e ^ 1. It is similar to math.e

Python e Constant Using numpy.exp()

Similar to the exp() function in the math module, we also have an exp() function in the numpy library. The syntax of the exp() function in numpy is:

numpy.exp(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) 

It accepts an array as the argument. The output of the function is an n-dimensional array that consists of the calculated values. The array values are taken as the power to the python e constant.

First, we shall import the numpy library in python. Then, we shall take an array containing a single element – 1.

Then, we shall pass that array as an argument to the numpy.exp() function and print the result.

import numpy as np array = np.array(1) print(np.exp(array))

The output is:

We can also print multiple powers of the python e constant at the same time. For that, we shall add multiple values in the array as the powers to the constant.

import numpy as np array = np.array([1,2,3,4,5,6,7,8,9,10]) print(np.exp(array))

[2.71828183e+00 7.38905610e+00 2.00855369e+01 5.45981500e+01 1.48413159e+02 4.03428793e+02 1.09663316e+03 2.98095799e+03 8.10308393e+03 2.20264658e+04]

Plotting math e

The graph of math e plotted will be an exponentially increasing graph. We shall try to plot the first 10 powers of the Euler’s constant using math e constant.

For that, we shall have to import the matplotlib library also along with the math module. Then with a for loop, we shall generate the powers of Euler’s constant by raising numbers to the math e constant and store it into a list. Then we shall plot that list using the plot() function.

import math import matplotlib.pyplot as plt list1 = [] for i in range(0,10): list1.append(math.e ** i) plt.plot(list1) plt.show()

As seen, it is an exponentially increasing graph.

Using Constant e as Base for log

The main application of Euler’s constant is in the natural logarithm. We can use the constant e as the base for the log. For that, we shall make use of the log() function present in the math module. We pass the value whose log has to be calculated as the first argument and the base as the second argument.

import math print(math.log(2,math.e))

Also, Read:

That was all about python e constant. If you have any questions in mind, let us know in the comments below.

Until next time, Keep Learning!

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How to get Euler’s Number in Python

Euler’s number is one of the most important numbers in all of Mathematics.

Python is a popular programming language when it comes to math and processing data.

These two combined means that you’ll need to be able to get the Euler’s number to use it in your Python code.

In this post, we’ll learn the many ways you get the Euler’s number in Python.

Using the math module

The easiest way to get the Euler’s number is to use the math module that you can import in your Python code.

Because we are relying on the math module, we can be assured that the Euler's number will be accurate.

Using math.exp()

Also using the math module, we can use the function exp() to get the Euler’s number.

This function takes in a parameter which is the power to which the Euler’s number is raised.

Because we know any number raised to the power of 1 is itself, we can use this to get the Euler’s number.

In this post, we explored how you can use the math module in two different ways to get the Euler's number.

Hopefully, you’ve found this useful to you when you’re writing Python code.

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