# **Golden Ratio for Class 5 Maths**

The golden ratio is the mathematical relation between the aspects of objects. Here students will learn about the golden ratio, the golden mean ratio, the golden ratio in nature, and the Fibonacci sequence numbers that also connect the students with patterns in maths for class 5.

## What Is Golden Ratio?

A golden ratio is the proportion of the bigger to the smaller quantity

equals the ratio of the sum of the two amounts to the larger quantity.

## Golden Mean Ratio:

It is often known as Golden Mean or Phi (Φ) and is equal to 1.618….

## How to Calculate Golden Ratio?

Suppose that a line segment,

AB is divided into two parts

AO and OB, such that the

Larger part AO = a and the Smaller part OB = b then

## Golden Ratio in Numbers

In Mathematics, a Fibonacci sequence is a series of numbers such that the number equals the sum of the preceding numbers.

The sequence usually starts from 0 and 1 or 1 and 1 or 1 and 2.

## Fibonacci Sequence Numbers

0, 1, 1, 2, 3, 5, 8, 13, 21, ……….

1 + 1 = 2

2 + 1 = 3

3 + 2 = 5

5 + 3 = 8

**Fibonacci Numbers Relation With Golden Ratio:**

Any two successive Fibonacci Numbers ratio is very close to the golden ratio.

Numbers (A) | Numbers (B) | Ratio (B/A) |
---|---|---|

2 | 3 | 3 / 2 = 1.5 |

3 | 5 | 5 / 3 = 1.666... |

5 | 8 | 8 / 5 = 1.6 |

## Golden Ratio in Nature:

1. Some plants have leaves that follow golden spiral so that each part of the leaves may receive an equal amount of sunlight or water.

2. The seed in the sunflower grows in a spiral. This spiral pattern occurs naturally because, after every turn, a new cell is formed.

**The pattern in Maths for Class 5**

## Question 1:

Draw a Golden Spiral for the Fibonacci Numbers:

1, 1, 2, 3, 5, 8, 13, 21.

### Answer 1:

The Golden Spiral for the Fibonacci Numbers 1, 1, 2, 3, 5, 8, 13, and 21 are shown below.

## Question 2:

Find the Missing Numbers in the Given Series:

**21,34,55,,89,144,_____,_____,______,987.**

### Answer 2:

Each term is the sum of the two preceding terms in the given series.

The first missing term is:

The first missing term is:

89 + 144 = 233

The second missing term is:

144 + 233 = 377

The third missing term is:

233 + 377 = 610

Therefore, the complete series is:

**21,34,55,,89,144,233,377,610,987.**

## Question 3:

Write the Length of the Side of Each Square if the Given Figure Follows the Golden Curve.

### Answer 3:

The given figure follows the Fibonacci sequence.

The side of the orange square should be:

2 + 3 = 5

The side of the yellow square should be:

5 + 8 = 13

The side of the blue square should be:

8 + 13 = 21

The complete figure is

## Question 4:

Find the Difference Between the Area of the Blue Square and the Yellow Square.

### Answer 4:

Step 1: The formula to calculate the area of the square is

Area = Side × Side

The side of the blue square is 8.

Area of the blue square = 8 × 8

= 64 square unit

Step 2:

The side of the yellow square is 5.

Area of the yellow square = 5 × 5

= 25 square unit

Step 3:

The difference in the area = 64 – 25

= 39 square unit

## Question 5:

Divide 100 Into Two Parts Such That It Follows the Golden Ratio.

### Answer 5:

To follow the Golden ratio, the two parts should be such that the ratio of the bigger to the smaller part should equal 100 to the larger part.

The correct answer is 61.8 + 38.2 = 100.

## Question 6:

Give an Example of a Rectangle That Follows the Golden Ratio.

### Answer 6:

The rectangle with a Golden ratio should be a combination of a square and a rectangle with the dimension of Fibonacci numbers.

One such example is the combination of the square of side 34 units and a rectangle of dimensions 55 units and 34 units.

Thus, one example of a Fibonacci rectangle is a rectangle of length 89 units and width 34unitst.

## Question 7:

Complete the Right Side of the Pattern Following the Golden Curve.

### Answer 7:

The complete pattern is shown below: