slides-02-01.qmd

---
title: "functions (slides)"
format: revealjs
slide-number: true
df-print: kable
---

# CSc 110 - Functions

## Functions

-   Functions are named operations that are available to do tasks
-   Some functions are *built-in* functions that Python provides
-   Programmers can also define their own functions
-   Functions are **called** (or **invoked**)

## Function definitions

```{python}
#| echo: true
#| eval: false
def two():
  return 2
```

This function definition has many parts:

-   `two` is the name of the function
-   `()` is the **parameter** list (Here, it is empty)
-   the body (or content) of the function is indented
-   `return 2` is a statement that causes the function to cease and produce the value 2

## Example of a simple function

```{python}
#| echo: true
#| eval: false
def add_one(n):
  return n + 1
```

-   `add_one` is the name of the function
-   `(n)` is the **parameter** list
-   the body (or content) of the function is indented
-   `return n + 1` is a statement that causes the function to cease and produce the value n + 1

## Another example

```{python}
#| echo: true
#| eval: true
def cook_food(order):
  message = "Your " + order + " is ready!"
  return message

meal = cook_food("pasta")
print(meal)
meal = cook_food("burger")
print(meal)
```

-   The function `cook_food` prepares a meal. 
-   Then returns a string that says the meal is ready. 
-   The returned message is stored in the `meal` variable. 
-   Finally, `print` function displays that message to the caller.

## Function to calculate area of a circle

Remember this from the last set of slides?

```{python}
#| echo: true
#| eval: false
# assign a radius value
radius = 3
# compute the rounded area of a circle
area = round(3.1415 * radius ** 2, 2)
# print the area
print(area)
```


## Function to calculate area of a circle

Function name is `calculate_area`. Given a `radius` parameter, it returns the rounded `area` of the circle.
```{python}
#| echo: true
#| eval: false
def calculate_area(radius):
  area = 3.1415 * radius ** 2
  return round(area, 2)

def main():
  print(calculate_area(3)) # 28.27
  print(calculate_area(6)) # 113.09
  
main()
```


## Write a function

Write a function that calculates the volume of a sphere:

1.  Its name is `sphere_volume`
2.  It takes one argument: `radius`
3.  It calculates the volume of the sphere (use `3.1415` for $\pi$):

$$
v = {4 / 3} \cdot \pi \cdot radius^3
$$

4.  It returns the rounded value for the calculated volume
5.  Test case: `sphere_volume(.75)` should return `1.77`.

## Write a function -- sphere volume

```{python}
#| echo: true
#| eval: true
def sphere_volume(radius):
  "calculates the volume of a sphere of given radius"
  volume = (4 / 3) * 3.1415 * radius**3
  return round(volume, 2)

def main():
  print(sphere_volume(.75)) # 1.77
  print(sphere_volume(2)) # 33.51
  print(sphere_volume(5.5)) # 696.89

main()
```

## Write a function

Write a function that calculates the area of a sphere:

1.  Its name is `sphere_area`
2.  It takes one argument: `radius`
3.  It calculates the volume of the sphere (use `3.1415` for $\pi$):

$$
a = 4 \cdot \pi \cdot radius^2
$$

4.  It returns the value for the calculated sphere area
5.  Test case: `sphere_area(.75)` should return `7.07`.

## Write a function -- solutions 1

```{python}
#| echo: true
#| eval: true
def sphere_area(radius):
  "calculates the area of a sphere of given radius"
  area = 4 * 3.1415 * radius**2
  return round(area, 2)

def sphere_volume(radius):
  "calculates the volume of a sphere of given radius"
  volume = (4 / 3) * 3.1415 * radius**3
  return round(volume, 2)

def main():
  r = .75
  v = sphere_volume(r)
  a = sphere_area(r)
  print(v, a)

main()
```

## Write a function
Comparing two formulas:
$$
a = 4 \cdot \pi \cdot radius^2
$$

$$
v = {4 / 3} \cdot \pi \cdot radius^3 
$$
We can use area when calculating volume:
$$
v = {1 / 3} \cdot a \cdot radius
$$

Modify your `sphere_volume` function by calling `sphere_area` inside the function.

## Write a function -- solutions 2

```{python}
#| echo: true
#| eval: true
def sphere_area(radius):
  "calculates the area of a sphere of given radius"
  area = 4 * 3.1415 * radius**2
  return round(area, 2)


def sphere_volume(radius):
  "calculates the volume of a sphere of given radius"
  volume = (1 / 3) * sphere_area(radius) * radius
  return round(volume, 2)


def main():
  r = .75
  v = sphere_volume(r)
  a = sphere_area(r)
  print(v, a)

main()
```

## Write a function

Write a Python function named `hypotenuse` that takes two arguments: `a` and `b` representing the length of the two non-hypotenuse sides of a right triangle.
The function calculate the hypotenuse according to the Pythagorean theorem: $c = \sqrt(a^2 + b^2)$. Return it rounded at two decimals.

Test cases: `hypotenuse(3, 4)` should return `5.0`, `hypotenuse(10, 10)` should return `14.14`

Name your file `hypotenuse.py` and submit to gradescope.


## Write a function

```{python}
#| eval: true
#| echo: true
def sqrt(n):
  '''
  This function calculates the square root of a number
  Args:
    n: integer or float
  Returns:
    The square root of n
  '''
  return n**0.5

def hypotenuse(a, b):
  '''
  This function calculates the hypotenuse of a right angle triangle.
  Args:
    a: number (integer or float) representing one of the non-hypotenuse sides
    b: number (integer or float) representing one of the non-hypotenuse sides
  Returns:
    Float representing the length of the hypotenuse given a and b
  ''' 
  h = sqrt(a**2 + b**2)
  return round(h, 2)

def main():
  '''
  This function calls the hypotenuse function to calculate and then
  print out the hypotenuse of a right angle triangle of sides 3 and 4
  and the hypotenuse of a right angle triange of sides 10 and 10
  '''
  result = hypotenuse(3, 4)
  print(result)
  
  result = hypotenuse(10, 10)
  print(result)
  
main()
```