W1292 Useful Randomness
Prerequisites[edit]
Research[edit]
 [1](wikipedia)Pythagorean's Theorem
 Random Number Generation (Wikipedia)
 How Random is Your Randomness?
 The Search for π
 Random Function for Int (Swift Documentation)
 Random Function for Double (Swift Documentation)
Introduction[edit]
In Swift it is possible to return random numbers within a range as a method. Using .random,will allow you to choose a number within a range. The for loop below demonstrates a range of numbers and random numbers printed each time the loop runs. Below we have demonstrated the randomness applied to an Int.
Int
for _ in 1...5 {
print(Int.random(in: 1..<50))
}
// Prints "49"
// Prints "32"
// Prints "15"
// Prints "9"
As you can see above, .random is highlighted in the correct location of where it should be applied.
The Double
In Swift .random can also be applied to Doubles just like Int previously. It is the same idea, but with a double instead of Int and a different output.
for _ in 1...5 {
print(Double.random(in: 1..<50))
}
// Prints "49.0"
// Prints "32.0"
// Prints "15.0"
// Prints "9.0"
Pythagorean theory[edit]
Pythagorean's theorem is an important concept in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) also known as c is equal to the sum of the areas of the squares on the other two sides. The other two sides are known as a and b, a being the adjacent and b being the opposite. This theorem is often written as a+b=c.
Trigonometric ratios[edit]
Sin and Cos are both concepts of Geometry that tie into Pythagorean's Theorem. SohCahToa is a acronym used to remember the formulas to solve simple sin and cos functions, Toa known as tangent will be explained later. Focus on sin and cos for now. Recollect the names of each triangle side which was previous described in the Pythagorean's Theorem before moving on.
Sine(Sin)
 Soh is Sin = opposite(b)/hypotenuse(c)
Cosine(Cos)
 Cah is Cos = adjacent(a)/hypotenuse(c)
Tangent(Toa)
 Toa is Tan = opposite(b)/adjacent(a)
Applications in Swift[edit]
In Swift, you can apply Sine , Cosine ,and Tangent in multiple different ways. In my example, we will start by importing a library; this will allow us to apply the prebuilt math formulas, hence the import Foundation. If you are not familiar with swifts libraries, it is ok this will be covered in a future lesson.
import Foundation
//importing the library, will allow the use of the sin,cos,and tan functions
//Double.pi is a Double since pi has decimals
let sine = sin(90.o * Double.pi / 180)
print("Sine \(sine)")
let cosine = cos(90 * Double.pi / 180)
print("Cosine \(cosine)")
let tangent = tan(90 * Double.pi / 180)
print("Tangent \(tangent)")
//Output:
//Sine 1.0
//Cosine 6.12323399573677e17
//Tangent 1.63312393531954e+16
Excursions[edit]
If you would like to experiment that is great!
 Start by opening the swift REPL by typing in swift as seen below.
 Proceed to import your Foundation.
 Finally, explore this concept on your own to have the best learning experience.
 You can reference my previous for loop and experiment, try changing the line value to have different results.
 Always remember to have fun!
Background[edit]
Coming Soon  
Add section on throwing dart at ¼ of square 
The value of π can be calculated by:
 Randomly throwing "darts" at a unit circle
 Counting the total number of "darts", N
 Counting the number of "darts" that fall within the unit circle, C
 The ratio of the area inside the circle to the total area is C/N
 The value of π is four times this value (because the area of the total square is 2 units x 2 units)
Prepare[edit]
Create a new directory in your ~/Experiences directory named "W1292". Use emacs to edit a file named "main.swift":
Helpful Hint  
You can run your program from within emacs with F5r 
Helpful Hint  
You can find the square root of a number using the squareRoot function. This function is included in the Foundation library, so it must be imported. For example: import Foundation
let d = 12.0
print(d.squareRoot())

Observe, Ponder, and Journal Section 1  
Complete your program, then answers these questions.

Exercises[edit]
Exercises  

Key Concepts[edit]
Key Concepts  
