Golden ratio• Group members:• Eisha khattak• Novera ijaz• Bakhtawar adnan• Mashyam shafeeq• Group leader:• Arooba Ahsan

• Submitted to:• Ma’am khaula (maths

teacher)• Ma’am irum (computer

teacher)

What is golden ratio?

• The Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form, it looks like this:

• a/b = (a+b)/a = 1.6180339887498948420 …

More about golden ratio

• Phi is usually rounded off to 1.618. This number has been discovered and rediscovered many times, which is why it has so many names — the Golden mean, the Golden section, divine proportion, etc. Historically, the number can be seen in the architecture of many ancient creations, like the Great Pyramids and the Parthenon.

Leonardo Fibonacci

• Around 1200, mathematician Leonardo Fibonacci discovered the unique properties of the Fibonacci sequence. This sequence ties directly into the Golden ratio because if you take any two successive Fibonacci numbers, their ratio is very close to the Golden ratio. As the numbers get higher, the ratio becomes even closer to 1.618.

Golden ratio in nature

• The Golden ratio also appears in all forms of nature and science. Some unexpected places include:

• Flower petals: The number of petals on some flowers follows the Fibonacci sequence.

• Seed heads: The seeds of a flower are often produced at the center and migrate outward to fill the space.

• Pinecones: The spiral pattern of the seed pods spiral upward in opposite directions

• Shells: Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral.

• Spiral galaxies: The Milky Way has a number of spiral arms, each of which has a logarithmic spiral of roughly 12 degrees.

• Hurricanes: Much like shells, hurricanes often display the Golden spiral.

• Fingers: The length of our fingers, each section from the tip of the base to the wrist is larger than the preceding one by roughly the ratio of phi.

• Animal bodies: The measurement of the human navel to the floor and the top of the head to the navel is the Golden ratio.

• DNA molecules: A DNA molecule measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral. In the Fibonacci series, 34 and 21 are successive numbers.

The Miracle of Ka’aba

• The Holy Ka’aba is the golden ratio point of the Earth. It is exactly in the center of the Earth.

Golden Ratio in Logo’s

• Golden ratio is also present In logo’s for example:

• Apple.• Honda• Twitter• Facebook.

Golden Ratio in architecture.

• Golden ratio is also present in architecture. From the Greeks to the Romans to present day golden ratio is still used in architecture.

TablesNames F/H F/HP F/K S/F H/C C/N E/F

Arooba 63 38 14 15 7 6 8

Eisha 61 35 16 13 8 7 6

Bakhtawar

64 36 15 12 6 8 8

Novera 60 31 14 10 5 6 7

Meshyam

65 33 18 14 6 6 4

Tables in decimal form:Names F/H F/HP F/K S/F H/C C/N E/F

Arooba 1.657894 2.712485 1.07248 2.14285 0.021052 0.75 0.75

Eisha 1.742857 0.45714 1.2307 1.625 1.1428 0.857 0.8571

Novera 1.935 0.07142 0.71428 2.6 0.8333 0.8571 0.456

Bakhtawar

1.777 2.4 1.25 2.88 0.75 0.879 1.678

Meshyam

1.6789 3.46848 0.74768 0.3647 0.0356 1.883 0.73483

Tables in fractional forms:NAMES F/H F/HP F/K S/F H/C C/N E/F

AROOBA 1657894/100000

2712485/100000

107248/10000

214285/100000

0021052/100000

075/100 075/100

EISHA 1742857/10000

045714/10000

12307/10000

1625/10000

11428/10000

0857/1000

057/1000

BAKHTAWAR

1935/10000

007142/10000

01428/10000

26/10 08333/10000

08571/10000

0456/1000

NOVERA 1777/1000

24/1000 125/1000

288/1000

075/1000

0879/100

1678/1000

MESHYAM

16789/1000

346848/1000

0747/10000

03647/10000

0356/10000

18830/10000

073483/10000