The Fibonacci Sequence in Nature : The Mystery of Golden Ratio

In mathematics, the limit of Fibonacci series is known as Golden Ratio. This ratio is approximately equal to 1.618. In nature, one can come across this ratio in many areas of art and science. Fibonacci sequence actually has a very unique characteristic. Dividing a number with previous number allows you to get approximately similar result. However, the result will be the same after the 13th number inside the series: 1.618 that is Golden Ratio.

There are many examples of golden ratio:
The ratio of the length of forearm to the length of the hand is equal to 1.618, that is, Golden Ratio. Another well-known examples on human body are.

The ratio between the length and width of face

Ratio of the distance between the lips and where the eyebrows meet to the length of nose

Ratio of the length of mouth to the width of nose.

Ratio of the distance between the shoulder line and the top of the head to the head length

Ratio of the distance between the navel and knee to the distance between the knee and the end of the foot

Ratio of the distance between the finger tip and the elbow to the distance between the wrist and the elbow
GOLDEN TRIANGLE:

The golden triangle can be characterised as an isosceles triangle ABC with the property thatbisecting the angle C produces a new triangle CXB which is a similar triangle to the original.

Golden triangles inscribed in a logarithmic spiral

THERE ARE MANY OTHER RELEVANT EXAMPLE OF GOLDEN RATIO......do find out:-)

"THE BEAUTY OF MATH"

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=123456789 87654321

Babylonian Numbers

Babylonians were the first people to develop the written number system. Their number system is based on Sexagesimal System. It appeared around 1900 BC to 1800 BC.

The Babylonian number system had only two basic elements; l and < .
59 numbers are built from these two symbols.

Example:
For example, 1,45,29,36 represents the sexagesimal number
1 x 60³ + 45 x 60² + 29 x 60 + 36
= 1 x 216000 + 45 x 3600 + 29 x 60 + 36
= 216000 + 162000 + 1740 + 36
The decimal notation is 379776.

1,45,29,36 in Babylonian Numerals

Babylonians did not have a digit for zero, instead they used a space to mark the nonexistence of a digit in a certain place value.
Example:
4,0,8 in Babylonian Numerals

MATHS and aMAZES

The story of the Minotaur

Mazes are very ancient and appear many times in history. According to ancient legend, Daedalus constructed the so called "Cretan Labyrinth" in Knossos, to house the legendary Minotaur. The Minotaur was a fearsome creature, half man and half bull killed by Theseus in the famous legend in which he escapes using a ball of string provided by Ariadne.

Although we don't have direct evidence in the form of buried walls for the shape of the Cretan Labyrinth, there is a traditional idea about its shape, and a very nice geometrical construction for drawing one. This gives us our first link between mathematics and mazes. You can draw this on paper, or if you are on a beach it looks very good drawn into the sand with the help of a stick. To draw a traditional Cretan Labyrinth, start with the cross and dots on the right.

The picture below shows you how to complete the Cretan Labyrinth. Notice that the when you connect the lines you alternate left and right round the square. Now you can complete the picture.