Convert the Cartesian coordinates to polar and backward. Polar coordinates are a convenient way of representing points on a surface with the two values: distance from the centre of coordinates and the angle between the vector and the pole axis. The conversion formulae between the Cartesian and polar systems,which is valid for positive x and y, are … Continue reading “📘 Working with polar coordinates in Perl 6”

# Category: Chapter 2. Numbers

## 📘 Computing standard deviation using Perl 6

For the given data, calculate the standard deviation value (sigma). Standard deviation is a statistical term that shows how compact data distribution is. The formula is the following: where N is the number of elements in the array x; is the average value (see Task 56, Average on an array). Let’s use some test data from Wikipedia and take … Continue reading “📘 Computing standard deviation using Perl 6”

## 📘 Computing the distance between two points using Perl 6

Calculate the distance between the two points on a surface. There are two points on a surface, each with their own coordinates, xand y. The task is to find the distance between these two points. A straightforward solution would be to use the Pythagorean theorem: my ($x1, $y1) = (10, 3);my ($x2, $y2) = (9, 1);say sqrt(($x1 … Continue reading “📘 Computing the distance between two points using Perl 6”

## 📘 Generating a histogram of random numbers using Perl 6

Test the quality of the random generator by using a histogram to visualise the distribution. The quality of the built-in generator of random numbers fully depends on the algorithm the developers of the compiler used. As a user, you cannot do much to change the existing generator, but you can always test if it delivers … Continue reading “📘 Generating a histogram of random numbers using Perl 6”

## 📘 Neumann’s random generator written in Perl 6

Implement the von Neumann’s random number generator (also known as Middle-square method). This algorithm is a simple method of generating short sequences of four-digit random integers. The method has its drawbacks, but for us, it is an interesting algorithmic task. The recipe has these steps: Take a number between 0 and 9999. Calculate the square … Continue reading “📘 Neumann’s random generator written in Perl 6”

## 📘 Generating random numbers using Perl 6

Generate a random number between 0 and N. Use the randmethod, which returns a random number between 0 and the value of its invocant: say 1.rand; # between 0 and 1say 2.5.rand; # between 0 and 2.5say pi.rand; # between 0 and 3.14… The rand method is defined in the Cool class, which is the base class for the Int, Num, and Rat types. It … Continue reading “📘 Generating random numbers using Perl 6”

## 📘 Divide by zero in Perl 6

Do something with the division by zero. Division by zero in itself is not an immediate error in Perl 6. The following code does not generate an exception and prints the message after the problematic division. my $v = 42 / 0;say ‘It still works!’; However, as soon as the result stored in the $v variable … Continue reading “📘 Divide by zero in Perl 6”

## 📘 Reducing a fraction using Perl 6

Compose a fraction from the two given integers—numerator and denominator—and reduce it to lowest terms. 5/15 and 16/280 are examples of fractions that can be reduced. The final results of this task are 1/3 and 2/35. Generally, the algorithm of reducing a fraction requires searching for the greatest common divisor, and then dividing both numerator … Continue reading “📘 Reducing a fraction using Perl 6”

## 📘 Finding prime factors using Perl 6

Find the prime factors of a given number. Prime factors are the prime numbers that divide the given integer number exactly. In Task 28, List of prime numbers, we’ve seen how to make a lazily evaluated list of prime numbers. This list is used in the program as a generator of the factor numbers for the … Continue reading “📘 Finding prime factors using Perl 6”

## 📘 Printing a list of prime numbers using Perl 6

Print thelist of the first ten prime numbers. In Task 27, Prime numbers, we’ve seen how to check if the given number is prime. To print the list of the first ten numbers, organize a lazy list.The code is quite compact and Perlish by nature: my @numbers = grep {.is-prime}, 1..*;say @numbers[^10]; The first line has to … Continue reading “📘 Printing a list of prime numbers using Perl 6”