# Python math.hypot() Method

In this tutorial, we will explore how we can use this function in Python to perform various operations using various N-dimensional vectors.

The `math.hypot()` method is a built-in Python method that allows us to calculate the Euclidean norm, `sqrt(sum(x**2 for x in inputs))`. In simple terms, the method allows us to calculate the length of the vector from the origin to a point in N-dimensional space.

## Import the Math Module

Before using `math.hypot()`, ensure you have the `math` module imported in your project. You can use the `import` keyword as shown:

``````import math
``````

## Python `hypot()` Method

### Syntax

The syntax of the `hypot()` function is expressed below:

``````math.hypot(*coordinates)
``````
• The `*coordinates` parameter is a variable-length argument, allowing for any number of numerical input values. These represent coordinates in N-dimensional space.

### Function Return Value

The function returns a float value representing the Euclidean norm of the given coordinates.

### Example 1 - Two-dimensional space (Euclidean distance)

``````import math
# coordinates in 2D space
x = 3
y = 4

# calculate Euclidean norm (hypotenuse in right angle triangle)
result = math.hypot(x, y)

print(result)
``````

Output:

``````5.0
``````

In the example above, we pass two arguments to the `math.hypot()` function. These arguments are interpreted as coordinates in a two-dimensional space.

The function thus calculates the Euclidean distance from the origin `(0, 0)` to the point `(3, 4)`, which is equivalent to finding the hypotenuse in a right-angle triangle with other sides of lengths `3` and `4`.

### Example 2 - Three-dimensional space

``````import math

# coordinates in 3D space
x = 3
y = 4
z = 5

# calculate Euclidean norm
result = math.hypot(x, y, z)

print(result)
``````

Output:

``````7.0710678118654755
``````

In this case, we pass three arguments to the `math.hypot()` function. The function will then interpret the arguments as coordinates in 3-dimensional space.

It then calculates the Euclidean distance from the origin `(0, 0, 0)` to the point `(3, 4, 5)`.

### Example 3 - N-dimensional space

``````import math

# coordinates in N-dimensional space
coordinates = [3, 4, 5, 6, 7]

# calculate Euclidean norm
result = math.hypot(*coordinates)

print(result)
``````

Output:

``````11.61895003862225
``````

In the example above, the function calculates the Euclidean distance in a space of arbitrary (N) dimensions.

NOTE: In this example, the function will interpret the provided parameter as coordinates of a 5-dimensional space. This means the function will return the Euclidean distance from the origin to the point specified in the coordinates.

Keep in mind that the `math.hypot()` function is not limited to only two or three arguments. It can accept any number of arguments and it will calculate the Euclidean norm (distance from the origin) in that N-dimensional space.

### Error and Exception

The `math.hypot()` function will throw a `TypeError` if any of the arguments passed to it are not numeric (either integer or float).

``````import math

# non-numeric input
x = "3"
y = 4

# calculate Euclidean norm
result = math.hypot(x, y)
``````

Output:

``````TypeError                                 Traceback (most recent call last)
...
5 y = 4
7 # calculate Euclidean norm
----> 8 result = math.hypot(x, y)

TypeError: must be real number, not str
``````

Remember to always ensure that the arguments passed to the `math.hypot()` function are of a numeric type to avoid exceptions.

## Conclusion

In this tutorial, we explored the fundamentals of working with the `hypot()` function in the Python's `math` module to calculate the Euclidean distance between origin and the specified coordinates.