Math Module consists of mathematical functions and constants. It is a built-in module made for mathematical tasks.
The math module provides the math functions to deal with basic operations such as addition(+), subtraction(-), multiplication(*), division(/), and advanced operations like trigonometric, logarithmic, and exponential functions.
In this article, we learn about the math module from basics to advanced, we will study the functions with the help of good examples.
What is a Math Module in Python?
Math Module is an in-built Python library made to simplify mathematical tasks in Python.
It consists of various mathematical constants and functions that can be used after importing the math module.
Example: Importing Math Module
After importing the math module, you can use various constants and functions, let’s study some of them
Constants in Math Module
The Python math module provides various values of various constants like pi, and tau. We can easily write their values with these constants. The constants provided by the math module are :
- Euler’s Number
- Pi
- Tau
- Infinity
- Not a Number (NaN)
Let’s see constants in math module with examples:
1. Euler’s Number
The math.e constant returns the Euler’s number: 2.71828182846.
Syntax:
math.e
Example: This code imports the math module and then prints the value of the mathematical constant e.
Python3
import math
print (math.e)
|
Output:
2.718281828459045
2. Pi
You all must be familiar with pi. The pi is depicted as either 22/7 or 3.14. math.pi provides a more precise value for the pi.
Syntax of Python math PI
math.pi
Example 1: This code imports the math module and then prints the value of the mathematical constant pi.
Python3
import math
print (math.pi)
|
Output:
3.141592653589793
Example 2: Let’s find the area of the circle
The code utilizes the math module in Python, defines a radius and the mathematical constant pi, and calculates the area of a circle using the formula‘ A = pi * r * r'. It demonstrates the application of mathematical concepts and the usage of the math module for numerical calculations
Python3
import math
r = 4
pie = math.pi
print(pie * r * r)
|
Output:
50.26548245743669
3. tau
Tau is defined as the ratio of the circumference to the radius of a circle. The math.tau constant returns the value tau: 6.283185307179586.
Syntax:
math.tau
Example: This code imports the math module and then prints the value of the mathematical constant ‘tau'.
Python3
import math
print (math.tau)
|
Output:
6.283185307179586
4. Infinity
Infinity basically means something which is never-ending or boundless from both directions i.e. negative and positive. It cannot be depicted by a number. The Python math.inf constant returns of positive infinity. For negative infinity, use -math.inf.
Syntax:
math.inf
Example 1: This code imports the math module and then prints the values of positive and negative infinity.
Python3
import math
print (math.inf)
print (-math.inf)
|
Output:
inf
-inf
Example 2: Comparing the values of infinity with the maximum floating point value
This code imports the math module and then compares the values of positive and negative infinity to the values of 10e108 and -10e108, respectively.
Python3
import math
print (math.inf > 10e108)
print (-math.inf < -10e108)
|
Output:
True
True
5. NaN Values
The Python math.nan constant returns a floating-point nan (Not a Number) value. This value is not a legal number. The nan constant is equivalent to float(“nan”).
Example: This code imports the math module and then prints the value of math.nan. math.nan represents Not a Number, which is a special value that is used to indicate that a mathematical operation is undefined or the result is not a number.
Python3
import math
print (math.nan)
|
Output:
nan
List of Mathematical function in Math Module
Here is the list of all mathematical functions in math module, you can use them when you need it in program:
|
| ceil(x) | Returns the smallest integral value greater than the number |
| copysign(x, y) | Returns the number with the value of ‘x’ but with the sign of ‘y’ |
| fabs(x) | Returns the absolute value of the number |
| factorial(x) | Returns the factorial of the number |
| floor(x) | Returns the greatest integral value smaller than the number |
| gcd(x, y) | Compute the greatest common divisor of 2 numbers |
| fmod(x, y) | Returns the remainder when x is divided by y |
| frexp(x) | Returns the mantissa and exponent of x as the pair (m, e) |
| fsum(iterable) | Returns the precise floating-point value of sum of elements in an iterable |
| isfinite(x) | Check whether the value is neither infinity not Nan |
| isinf(x) | Check whether the value is infinity or not |
| isnan(x) | Returns true if the number is “nan” else returns false |
| ldexp(x, i) | Returns x * (2**i) |
| modf(x) | Returns the fractional and integer parts of x |
| trunc(x) | Returns the truncated integer value of x |
| exp(x) | Returns the value of e raised to the power x(e**x) |
| expm1(x) | Returns the value of e raised to the power a (x-1) |
| log(x[, b]) | Returns the logarithmic value of a with base b |
| log1p(x) | Returns the natural logarithmic value of 1+x |
| log2(x) | Computes value of log a with base 2 |
| log10(x) | Computes value of log a with base 10 |
| pow(x, y) | Compute value of x raised to the power y (x**y) |
| sqrt(x) | Returns the square root of the number |
| acos(x) | Returns the arc cosine of value passed as argument |
| asin(x) | Returns the arc sine of value passed as argument |
| atan(x) | Returns the arc tangent of value passed as argument |
| atan2(y, x) | Returns atan(y / x) |
| cos(x) | Returns the cosine of value passed as argument |
| hypot(x, y) | Returns the hypotenuse of the values passed in arguments |
| sin(x) | Returns the sine of value passed as argument |
| tan(x) | Returns the tangent of the value passed as argument |
| degrees(x) | Convert argument value from radians to degrees |
| radians(x) | Convert argument value from degrees to radians |
| acosh(x) | Returns the inverse hyperbolic cosine of value passed as argument |
| asinh(x) | Returns the inverse hyperbolic sine of value passed as argument |
| atanh(x) | Returns the inverse hyperbolic tangent of value passed as argument |
| cosh(x) | Returns the hyperbolic cosine of value passed as argument |
| sinh(x) | Returns the hyperbolic sine of value passed as argument |
| tanh(x) | Returns the hyperbolic tangent of value passed as argument |
| erf(x) | Returns the error function at x |
| erfc(x) | Returns the complementary error function at x |
| gamma(x) | Return the gamma function of the argument |
| lgamma(x) | Return the natural log of the absolute value of the gamma function |
Numeric Functions in Math Module
In this section, we will deal with the functions that are used with number theory as well as representation theory such as finding the factorial of a number. We will discuss these numerical functions along with examples and use-cases.
1. Finding the ceiling and the floor value
Ceil value means the smallest integral value greater than the number and the floor value means the greatest integral value smaller than the number. This can be easily calculated using the ceil() and floor() method respectively.
Example:
This code imports the math module, assigns the value 2.3 to the variable a, and then calculates and prints the ceiling and floor of a.
Python3
import math
a = 2.3
print ("The ceil of 2.3 is : ", end="")
print (math.ceil(a))
print ("The floor of 2.3 is : ", end="")
print (math.floor(a))
|
Output:
The ceil of 2.3 is : 3
The floor of 2.3 is : 2
2. Finding the factorial of the number
Using the factorial() function we can find the factorial of a number in a single line of the code. An error message is displayed if number is not integral.
Example: This code imports the math module, assigns the value 5 to the variable a, and then calculates and prints the factorial of a.
Python3
import math
a = 5
print("The factorial of 5 is : ", end="")
print(math.factorial(a))
|
Output:
The factorial of 5 is : 120
3. Finding the GCD
gcd() function is used to find the greatest common divisor of two numbers passed as the arguments.
Example: This code imports the math module, assigns the values 15 and 5 to the variables a and b, respectively, and then calculates and prints the greatest common divisor (GCD) of a and b.
Python3
import math
a = 15
b = 5
print ("The gcd of 5 and 15 is : ", end="")
print (math.gcd(b, a))
|
Output:
The gcd of 5 and 15 is : 5
4. Finding the absolute value
fabs() function returns the absolute value of the number.
Example: This code imports the math module, assigns the value -10 to the variable a, and then calculates and prints the absolute value of a.
Python3
import math
a = -10
print ("The absolute value of -10 is : ", end="")
print (math.fabs(a))
|
Output:
The absolute value of -10 is : 10.0
Refer to the below article to get detailed information about the numeric functions.
Logarithmic and Power Functions
Power functions can be expressed as x^n where n is the power of x whereas logarithmic functions are considered as the inverse of exponential functions.
1. Finding the power of exp
exp() method is used to calculate the power of e i.e. [Tex]e^y
[/Tex] or we can say exponential of y.
Example: This code imports the math module and then calculates and prints the exponential values of three different input values: an integer, a negative integer, and a float.
Python3
import math
test_int = 4
test_neg_int = -3
test_float = 0.00
print (math.exp(test_int))
print (math.exp(test_neg_int))
print (math.exp(test_float))
|
Output:
54.598150033144236
0.049787068367863944
1.0
2. Finding the power of a number
pow() function computes x**y. This function first converts its arguments into float and then computes the power.
Example: This code first prints the string “The value of 3**4 is : ” to the console. Then, it calculates the value of 3 raised to the power of 4 using the pow() function and prints the result to the console.
Python3
print ("The value of 3**4 is : ",end="")
print (pow(3,4))
|
Output:
The value of 3**4 is : 81.0
3. Finding the Logarithm
- log() function returns the logarithmic value of a with base b. If the base is not mentioned, the computed value is of the natural log.
- log2(a) function computes value of log a with base 2. This value is more accurate than the value of the function discussed above.
- log10(a) function computes value of log a with base 10. This value is more accurate than the value of the function discussed above.
This code imports the math module and then calculates and prints the logarithms of three different numbers. The math module provides several functions for working with logarithms, including log(), log2(), and log10().
Python3
import math
print ("The value of log 2 with base 3 is : ", end="")
print (math.log(2,3))
print ("The value of log2 of 16 is : ", end="")
print (math.log2(16))
print ("The value of log10 of 10000 is : ", end="")
print (math.log10(10000))
|
Output:
The value of log 2 with base 3 is : 0.6309297535714574
The value of log2 of 16 is : 4.0
The value of log10 of 10000 is : 4.0
4. Finding the Square root
sqrt() function returns the square root of the number.
Example: This code imports the math module and then calculates and prints the square roots of three different numbers: 0, 4, and 3.5. The math module provides several functions for working with mathematical operations, including the square root function sqrt().
Python3
import math
print(math.sqrt(0))
print(math.sqrt(4))
print(math.sqrt(3.5))
|
Output:
0.0
2.0
1.8708286933869707
Refer to the below article to get detailed information about the Logarithmic and Power Functions
Trigonometric and Angular Functions
You all must know about Trigonometric and how it may become difficult to find the values of sine and cosine values of any angle. Math module provides built-in functions to find such values and even to change the values between degrees and radians.
1. Finding sine, cosine, and tangent
sin(), cos(), and tan() functions returns the sine, cosine, and tangent of value passed as the argument. The value passed in this function should be in radians.
Example: This code first imports the math module, which provides a variety of mathematical functions. Then, it defines a variable a and assigns it the value of pi/6, where pi is the mathematical constant representing the ratio of a circle’s circumference to its diameter.
Python3
import math
a = math.pi/6
print ("The value of sine of pi/6 is : ", end="")
print (math.sin(a))
print ("The value of cosine of pi/6 is : ", end="")
print (math.cos(a))
print ("The value of tangent of pi/6 is : ", end="")
print (math.tan(a))
|
Output:
The value of sine of pi/6 is : 0.49999999999999994
The value of cosine of pi/6 is : 0.8660254037844387
The value of tangent of pi/6 is : 0.5773502691896257
2. Converting values from degrees to radians and vice versa
- degrees() function is used to convert argument value from radians to degrees.
- radians() function is used to convert argument value from degrees to radians.
Example: This code imports the math module, which provides mathematical functions and constants. It then defines two variables: a and b. a is assigned the value of math.pi/6, which is approximately 0.5235987755982988 radians. b is assigned the value 30, which is 30 degrees.
Python3
import math
a = math.pi/6
b = 30
print ("The converted value from radians to degrees is : ", end="")
print (math.degrees(a))
print ("The converted value from degrees to radians is : ", end="")
print (math.radians(b))
|
Output:
The converted value from radians to degrees is : 29.999999999999996
The converted value from degrees to radians is : 0.5235987755982988
Refer to the below articles to get detailed information about the trigonometric and angular functions.
Special Functions
Besides all the numeric, logarithmic functions we have discussed yet, the math module provides some more useful functions that does not fall under any category discussed above but may become handy at some point while coding.
1. Finding gamma value
The gamma() function is used to return the gamma value of the argument.
Example: This code imports the math module, which provides mathematical functions and constants. It then defines a variable gamma_var and assigns it the value 6. Next, the code calculates and prints the gamma value of gamma_var using the math module’s gamma() function. The math.gamma() function calculates the gamma value of a given argument.
Python3
import math
gamma_var = 6
print ("The gamma value of the given argument is : "
+ str(math.gamma(gamma_var)))
|
Output:
The gamma value of the given argument is : 120.0
2. Check if the value is infinity or NaN
isinf() function is used to check whether the value is infinity or not.
Example: This code imports the math module and then checks whether the values of math.pi, math.e, and float('inf') are infinite using the math.isinf() function. The math.isinf() function takes a single argument, which is the value to be checked for infinity. It returns True if the value is infinite and False
Python3
import math
print (math.isinf(math.pi))
print (math.isinf(math.e))
print (math.isinf(float('inf')))
|
Output:
False
False
True
isnan() function returns true if the number is “NaN” else returns false.
Example: This code imports the math module and then checks whether the values of math.pi, math.e, and float('nan') are Not a Number (NaN) using the math.isnan() function. The math.isnan() function takes a single argument, which is the value to be checked for NaN. It returns True if the value is NaN and False.
Python3
import math
print (math.isnan(math.pi))
print (math.isnan(math.e))
print (math.isnan(float('nan')))
|
Output:
False
False
True
Refer to the below article to get detailed information about the special functions.
We have explained math module and it’s uses with example. Math module is very important mode in Python and every beginner should know how to use it.
It is used in various basic Python codes, school projects, etc. Hope you understood how to use math module in Python.
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