1. 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)

2. 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 …

3. 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.

4. 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.

5. 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

6. 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.

7. 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.

8. Golden Ratio in Logo’s Golden ratio is also present In logo’s for example: Apple. Honda Twitter Facebook.

9. 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.

10. Tables Names F/HF/HPF/KS/FH/CC/NE/F Arooba 63381415768 Eisha 61351613876 Bakhtaw ar 64361512688 Novera 60311410567 Meshya m 65331814664

11. Tables in decimal form: NamesF/HF/HPF/KS/FH/CC/NE/F Arooba1.6578942.7124851.072482.142850.0210520.75 Eisha1.7428570.457141.23071.6251.14280.8570.8571 Novera1.9350.071420.714282.60.83330.85710.456 Bakhtaw ar 1.7772.41.252.880.750.8791.678 Meshya m 1.67893.468480.747680.36470.03561.8830.73483

12. Tables in fractional forms: NAMESF/HF/HPF/KS/FH/CC/NE/F AROOBA1657894 /100000 2712485 /100000 107248/ 10000 214285/ 100000 0021052 /100000 075/100 EISHA1742857 /10000 045714/ 10000 12307/1 0000 1625/10 000 11428/1 0000 0857/10 00 057/100 0 BAKHTA WAR 1935/10 000 007142/ 10000 01428/1 0000 26/1008333/1 0000 08571/1 0000 0456/10 00 NOVERA1777/10 00 24/1000125/100 0 288/100 0 075/100 0 0879/10 0 1678/10 00 MESHYA M 16789/1 000 346848/ 1000 0747/10 000 03647/1 0000 0356/10 000 18830/1 0000 073483/ 10000