# Golden Ratio

Calculator

Calculate the Length of Segments Needed

to Divide an Element in the Golden Ratio.

Total (A+B)

Longer (A)

Shorter (B)

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## How to Use Golden Ratio Calculator

The golden ratio is defined as (A + B): A = A: B, where A is the longer section, B is the shorter section, and their sum (A + B) creates a perfectly balanced relationship.

In the “Longer Section” input field, (for example) enter a value for the longer section (A). This value can represent lengths, dimensions, or any numerical term of your choice.

As you input a value for the longer section for example (A), the calculator will work its magic:

- The “Shorter Section” field (B) will instantly display the corresponding length of the shorter section.
- The “Whole Section” will unveil the sum of A and B, showcasing the golden ratio’s harmonious balance.

Okay, But why is there not a “Calculate” button?

As you change any of the fields, the calculator will dynamically recalculate the values. It automatically maintains the golden ratio’s balance without the need for manual updates.

Experiment with various settings for the larger portion (A) to see how they affect the shorter segment (B) and the overall result.

The calculator is a rudimentary yet interactive tool for understanding the beauty of the golden ratio. If you want to keep the total value (A + B), just click the Copy button labeled “Copy Total.”

Perfect 👌

## The Golden Ratio Formula

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The golden ratio is symbolized by the Greek letter (phi). It is a unique mathematical constant found in many fields, including geometry, art, architecture, and nature.

φ = 1.6180339887499

The key characteristic of the golden ratio is that it arises when a line is divided into two parts such that the ratio of the whole length to the longer part is equal to the ratio of the longer part to the shorter part.

Mathematically, for quantities a and b with a > b > 0:

a / b = (a + b) / a = φ

This equality is a defining feature of the golden ratio. It means that if you have two quantities, a and b, and you divide a by b, it will be the same as dividing the sum of a and b by a. To put it another way, the ratio of the entire (a + b) to the bigger component (a) is the same as the ratio of the larger part (a) to the smaller part (b), and this ratio equals φ.

## Why Is the Golden Ratio Important?

The golden ratio is a mathematical concept that has been observed in various aspects of nature, art, and design.

The Golden Ratio is utilized in design to provide a sense of balance and harmony in everything from furniture to architecture. It’s used in finance to examine stock market patterns and forecast future prices.

The Golden Ratio is regarded to be attractive to the human sight and mind in psychology, which is why it’s frequently employed in advertising and marketing.

Here are some cool examples of how the golden ratio was used:

- In the Great Pyramid of Giza, the ratio of its height to its base is approximately the Golden Ratio.
- In the Mona Lisa, Leonardo da Vinci used the Golden Ratio to create the perfect facial proportions of his subject.
- In music, the Golden Ratio is found in the structure of the Fibonacci sequence, which is used to create harmonious melodies.
- In nature, the Golden Ratio is found in the branching patterns of trees, the geometry of snowflakes, and even in the shape of hurricanes.

## What is the Fibonacci Sequence?

The Fibonacci Sequence is a series of numbers where each number is the sum of the previous two. It starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… and continues indefinitely. The ratio between each number in the sequence approaches the Golden Ratio (1.618) as the sequence gets larger.

The formula to calculate the nth number in the sequence of Fibonacci numbers is:

The Fibonacci sequence is named after Leonardo Fibonacci, an Italian mathematician who introduced the sequence to Western Europe in his book Liber Abaci in 1202. Fibonacci numbers are found in many natural phenomena, such as the spiral arrangement of leaves on a plant, the number of petals on a flower, and the proportions of the human body.

Fn = Fn-1 + Fn-2

Where n > 1 and Fn-1 is the (n-1)th Fibonacci number and Fn-2 is the (n-2)th Fibonacci number. The ratio of any two consecutive numbers in the Fibonacci sequence approaches the golden ratio, which is approximately 1.618.

The Fibonacci sequence is used in computer algorithms, such as the Fibonacci heap data structure and the Fibonacci search technique

## The Golden Ratio in Nature

The golden ratio is a fascinating and enigmatic number that has been studied for ages by mathematicians, scientists, painters, and architects.

There is no scientific agreement on why the golden ratio is so common in nature or why it is seen as visually beautiful. However, here are some natural examples of The Golden Ratio:

- Spiral arrangement of leaves on a plant, such as a sunflower
- Ratio of the width to the length of a nautilus shell
- Hexagonal honeycombs
- The Human Face
- Spiral shape of a galaxy
- The cochlea of the inner ear

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