Fibonacci Sequence

The Fibonacci sequence is a series of numbers where each number is the sum of the two previous numbers. The sequence starts with 0 and 1, and then continues with 1, 2, 3, 5, 8, 13, 21, and so on.

The golden ratio is a special number that is often found in nature and art. It is approximately equal to 1.618. The golden ratio can be found by dividing a line segment into two parts so that the ratio of the longer part to the shorter part is equal to the ratio of the whole line segment to the longer part.

The Fibonacci sequence and the golden ratio are closely related. The ratio of any two consecutive Fibonacci numbers approaches the golden ratio as the numbers get larger. This means that the Fibonacci sequence can be used to approximate the golden ratio.

The Fibonacci sequence and the golden ratio have been found in many different places in nature and art. For example, the spiral shape of a seashell is a Fibonacci spiral. The petals of a flower are often arranged in Fibonacci numbers. The golden ratio is also found in the proportions of many buildings and paintings.

The Fibonacci sequence and the golden ratio are fascinating mathematical concepts that have been studied for centuries. They are found in many different places in the world around us, and they continue to inspire mathematicians, artists, and scientists alike.