Creating a very long fraction

sebjlan

Hi,

I was wondering how you would create a very long fraction in PHP, looking like this:

<?php

echo 4 * ( 1 - (1/3) + (1/5) - (1/7) + (1/9) - (1/11) + (1/13) - (1/15) ... ) ;

?>

And so on...

That is,
4 times ( 1 minus one third, plus one fifth, minus one seventh ... )
switching between plus and minus all the time.

Is this possible?
If so, how?

I'm using it for a math assignment in school.

Thank you very much in advance.

Installer

I think this will give the correct result:

<?php
$first_multiplier = 4;
echo $first_multiplier . ' * (';
$second_multiplier = 0;
$dividend = 1;
$start_divisor = 1;
$end_divisor = 13;
$divisor_interval = 2;
$switch = true;
for ($divisor = $start_divisor; $divisor <= $end_divisor; $divisor += $divisor_interval) {
    $term = $dividend / $divisor;
    if ($switch = !$switch) {
        $term = -$term;
        echo ' - ';
    } else {
        echo ' + ';
    }
    echo $dividend . '/' . $divisor;
    $second_multiplier += $term;
}
echo ') = ';
$result = $first_multiplier * $second_multiplier;
echo $result;
?>

sebjlan

Great, thanks!
It seems to work perfectly fine!

Can you explain what the different functions and everything mean and do?

I mean, if you'd like.

🙂

Installer

<?php 
// First set the starting values
$first_multiplier = 4; 
echo $first_multiplier . ' * ('; 
$second_multiplier = 0; 
$dividend = 1; 
$start_divisor = 1; 
$end_divisor = 13; 
$divisor_interval = 2; 
// $switch will be used to toggle + and -:
$switch = true; 
// Loop to increment the divisor (standard for loop):
for ($divisor = $start_divisor; $divisor <= $end_divisor; $divisor += $divisor_interval) { 
    // $dividend doesn't change, $divisor changed in for clause:
    $term = $dividend / $divisor; 
    // The equal ( = ) sign in the next statement performs
    // an assignment, not a comparison, so !$switch ("not switch") makes
    // $switch true if it's false, false if it's true, sort of a binary switch: 
    if ($switch = !$switch) { 
        // If $switch is true, which it will be every other iteration
        // of the loop, then $term is made a negative value:
        $term = -$term; 
        echo ' - '; 
    } else { 
        echo ' + '; 
    } 
    echo $dividend . '/' . $divisor; 
    // Add each iteration term's value to cumulative value:
    $second_multiplier += $term; 
} 
echo ') = '; 
// Multiply using cumulative value:
$result = $first_multiplier * $second_multiplier; 
echo $result; 
?>

Hope this helps. I'm glad to know you're using this to learn something, not just to pass off to your instructor as your own work. 🙂

sebjlan

Great!

Thank you very much!

Installer

I'm very glad to have helped. 🙂