Golden Ratio Connection

 

Golden Ratio Connection















The Golden Ratio, often represented by the Greek letter phi (Φ), is approximately 1.618. It's deeply connected to the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, …).

The connection is: As you move further along in the Fibonacci sequence, dividing a number by the number before it gets closer and closer to the Golden Ratio.

Example:

  • 5 / 3 = 1.666…
  • 8 / 5 = 1.6
  • 13 / 8 = 1.625
  • 21 / 13 = 1.615…
  • 34 / 21 = 1.619…
  • 55 / 34 = 1.617…

As you continue calculating these ratios with larger Fibonacci numbers, the result gets increasingly closer to 1.618, the Golden Ratio. This is not a coincidence; it's a mathematical property of the Fibonacci sequence. The Golden Ratio can be described as the limit of the ratio of consecutive Fibonacci numbers.




Comments

Post a Comment

Popular posts from this blog

Al-Khwarizmi: The Genius Who Counted the Future

Image
 Al-Khwarizmi: The Genius Who Counted the Future In the golden heart of the Islamic world, during a time of knowledge and light, stood a man who would silently shape the modern world. Muhammad ibn Musa al-Khwarizmi , born around 780 CE , was not just a mathematician. He was a thinker, an explorer of logic, and a true architect of ideas. Al-Khwarizmi worked in Baghdad , in the famous House of Wisdom , a place where books from Greek, Indian, and Persian cultures were translated, studied and improved. Surrounded by other brilliant minds, he focused deeply on mathematics and astronomy , crafting methods that would survive centuries. He didn’t just solve problems—he gave the tools to solve any kind of problem. One of his most important works was called “The Compendious Book on Calculation by Completion and Balancing.” It’s a long name, but this book introduced the world to algebra , a word that came from the Arabic term al-jabr . In this book, Al-Khwarizmi explained how to solve equa...
Read more

Functions

Image
  Functions In Arduino, functions are blocks of code that perform a specific task. They help organize your code, make it reusable, and improve readability. Key aspects of Arduino functions: Purpose:  Functions encapsulate a series of instructions, performing a defined action. This makes complex programs easier to manage. Structure:  A function has a name, optionally takes inputs (arguments), and may return a value. The general structure is: returnType functionName(parameter1Type parameter1Name, parameter2Type parameter2Name, ...) { // Code to be executed return returnValue; // If returnType is not void } Return Type:  Specifies the data type of the value the function returns (e.g.,  int ,  float ,  void ).  void  means the function doesn't return any value. Name:  A unique identifier for the function. Choose descriptive names. Parameters/Arguments:  Input values passed to the function. Defined by their data type and name. A func...
Read more

Expressions and Variables

Image
        Expressions and Variables              Okay, let's break down expressions and variables in math: Expressions Think of an expression as a mathematical phrase. It's a combination of numbers, variables, and operations (like addition, subtraction, multiplication, division, etc.). The key thing to remember is an expression  doesn't  have an equals sign. It's a statement that can be evaluated. Examples: 5 + 3  (This is a simple numerical expression) 2 * x  (This expression includes a variable) 4y - 7  (A combination of a variable, multiplication, and subtraction) a / (b + 1)  (Division involving variables) x^2 + 3x - 2  (An expression with powers) Important Note:   5 + 3 = 8  is  not  an expression. It's an  equation  because it has an equals sign. Variables A variable is a symbol (usually a letter like  x ,  y ,  a ,  b , etc.) that represents a ...
Read more