Unlocking the secrets of the Fibonacci function through mathematical equations

Looking for a better way to calculate the fibonacci function using a mathematical formula.

I've tried the following formula without success:

fib(n) = ((1 + 5^0.5) / 2)^n - ((1 - 5^0.5) / 2)^n / 5^0.5

const fib=(n)=>{
    return ((1+(5**0.5))/2)**n-((1-(5**0.5))/2)**n/(5**0.5)
}

If anyone has a different approach, I would greatly appreciate it. Thank you.

Answer №1

The solution is accurate, but make sure to include some additional parentheses.

const fibonacci=(n)=>{
    return (((1+(5**0.5))/2)**n-(((1-(5**0.5))/2)**n))/(5**0.5)
}
for(let i = 0;i<9;i++){
  console.log(fibonacci(i))
}

Answer №2

The initial step would be to establish the value of φ

var φ = (1 + 5 ** 0.5) / 2;

Following that, a more concise alternative is:

var fib = (n) => (φ ** n - ((-φ) ** -n)) / (2 * φ - 1);

To ensure the result is an integer, you could also incorporate the use of Math.round().

Answer №3

It appears you are attempting to replicate Binet's Formula. To make the formula more digestible, you can break it down into simpler components:

const fib = n => {
  const alpha = 5**0.5
  const beta = alpha / 2;
  return (1 / alpha) * ((0.5 + beta) ** n - (0.5 - beta) ** n);
}

console.log(fib(10));

Similar questions

If you have not found the answer to your question or you are interested in this topic, then look at other similar questions below or use the search

In the world of React-Three-Fiber and ThreeJS, the sprite alpha can often appear quite jagged

Currently, I am tackling a project for a client and encountering an issue with transparent logos in threejs. When utilized in the application, these logos exhibit an unattractive dark border that does not align with our desired aesthetic. Despite several a ...

Creating dynamic rows for Firebase data in React BootstrapTable can be accomplished by dynamically rendering each row

Hey everyone, I'm currently working on a web app project where I am creating a table. Below is the code snippet for it: class Table1 extends Component { render() { return ( <div> <BootstrapTable data={this.props.data}> ...

How can I vertically align a photo or image on Facebook?

Can anyone explain how Facebook manages to vertically align its photos without using padding or margins? I've looked into their img tag and its parent, but neither seem to have any spacing properties. Although there is a vertical-align attribute prese ...

I'm trying to create a drop-down list in JS that will save selected options to a database using PHP. I'm feeling a bit lost, anyone

My goal is to upload a pdf file with specific options that determine its category. The challenge arises when creating multiple options, as the second option depends on the first choice and involves JavaScript functionality for which I am unsure how to stor ...

Send information from the textbox

I am trying to extract data from an input field and use it to create a QR code. While passing the value as text works, I am facing issues with passing the actual input value. Does anyone have a straightforward example of this process? import React, {Comp ...

The property was computed but cannot be set - specifically for a toggle component

I am currently working on developing a switch toggle component in Vue that includes a v-model and @updated. However, I am encountering difficulties when trying to update the model once the user toggles the switch. Initially, I faced an issue regarding muta ...

JavaScript - Unexpected fluctuations in variable values

After studying Japanese language, I decided to try my hand at experimenting with JavaScript by creating a simple FlashCard game for a project. The game generates an array of random numbers, fills the divs with 6 possible choices using jQuery, randomly sele ...

Content that is dynamically generated by a database

I have been working on creating a unique wall feature for my website, inspired by Facebook. My aim is to allow users to submit form data and have it validated before storing it in a database. Additionally, I want this stored data to be displayed in a desig ...

Choose a word at random from a JSON string

Utilizing JSONP, I have successfully retrieved a list of words from an external source to randomly select one for use in a game. The current source being used is as follows: function processResult(obj) { console.log(obj); var data = ...

Unconventional login processes showcased in Redux-Saga's documentation

When looking at the login flow example in the redux-saga documentation, it is clear that the expected action sequence is well-defined. However, does the LOGOUT action always follow the LOGIN action? In real-world scenarios, such as when a user's sessi ...

Send JavaScript variable using a query parameter

I am working on passing a JavaScript variable across all pages in my project. The goal is to calculate the total value from various pages and display it at the end of navigation. Below is an example of my JS code: <script> $(document).ready ...

Using Zend_Form with Jquery for Efficient File Upload Error Handling

After making changes to my JavaScript, the code now looks like this: $('.zend_form input:not([type="file"]), .zend_form textarea').each(function() { data[$(this).attr('name')] = $(this).val(); }); Greetings, I recently watched a ...

Troubleshooting problem: AJAX autocomplete URL returning XML

I found my code reference here: http://example.com/code-reference if ($hint=="") { $hint="<a href='" . $z->item(0)->childNodes->item(0)->nodeValue . "' target='_blank'>" . $y->item(0)->childNodes-> ...

Exploring a JSON file to generate a customized array for implementing autocomplete functionality in jQuery

I'm currently working on developing an autocomplete feature for a search bar that will display names of places in Norway. The data is being fetched from a REST API URL provided by a third party. As an example, when the input is "st" there are two res ...

What are the steps to modify the sign in page on keystone.js?

I recently started using keystone.js and I'm having trouble locating the sign in page within the files. I've searched through all of the keystone.js files but can't seem to find where it's written. Can someone please guide me on how to ...

Ajax alert: The index 'id' is not defined

I'm currently learning PHP and scripting, but I am encountering some difficulties when it comes to sending information to PHP. I would appreciate any help you can offer. Thank you for your assistance. Here is the issue at hand: Error Message: Noti ...

React displaying an error indicating that the setTimeout function is undefined?

While attempting to integrate the XTK library with React, I encountered an issue where it kept throwing an error stating that the setTimeout function is not a valid function. Surprisingly, my code appears to be flawless and works perfectly fine when used d ...

Yii employs the use of quickdlgs to efficiently generate fresh entries within the CGrid view

Within my web application, I am attempting to implement an iframe button using quickdlgs to create new records. However, upon clicking the iframe button, instead of being directed to the 'create' webpage, I am presented with an empty iframe. Here ...

Is there a way to execute a PHP script using Ajax without needing any return values?

Currently, I am attempting to execute a php script with ajax without needing any output or echos. Is there a method to achieve this? Below is the approach I have taken: $('button')[1].click(function () { $.ajax({ met ...

Days and Their Corresponding Names Listed in Table

Currently, I am working on creating a "timesheet" feature that requires the user to input 2 dates. The goal is to calculate each month and year based on the input dates and then display them in a dropdown menu combobox. I would like to dynamically update ...