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- 1. Golden Ratio: Math or Miracle? Sakshi Jha #scichallenge2017
- 2. Introduction What is the Golden Ratio: History and Meaning Golden Spiral Examples in Nature Applications and Uses Conclusion
- 3. What is the GR (ϕ) The Golden Ratio (GR) 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. This is represented by the Greek Letter ϕ (Phi) and = 1.618...
- 4. Why does the GR exist? The GR is evidence of the fact that nature likes to simplify things. It is also evidence of the pattern and diversity coexisting integral to evolution. Some would argue it confirms the presence of a Greater Being who made us all.
- 5. History of the GR It is known that many mathematicians, scientists, artists and architects have been fascinated by the GR. Pythagoras was among the mathematicians who have done work surrounding this astonishing number as well as Leonardo Da Vinci and astronomer Kepler. The Fibonacci series is also linked to the GR because dividing 2 consecutive Fibonacci numbers eg 34/21 tends towards the GR.
- 6. The Golden Spiral (GS) In geometry, a golden spiral is: a logarithmic spiral whose growth factor is the GR (ϕ).Therefore, a golden spiral gets wider (or further from its origin) by a factor of ϕ for every quarter turn it makes.
- 7. Examples in Nature Animals DNA Human Body Plants Geographical
- 8. Animals Many animals are divided into sections and show the GR in their structure eg the eyes, fins and tail of a dolphin all fall at GR along the length of the dolphin’s body.
- 9. DNA DNA has two grooves in its spirals with the GR being the proportion of the major to the minor groove
- 10. Human body The Human body has the most examples of the GR eg the ratio of the hand to the forearm approximates the GR.
- 11. Plants Golden Spirals can be found in pinecones, sunflowers, pineapples, and many other plants. The petals of plants commonly grow in Fibonacci numbers eg lillies, buttercups, roses, daisies.
- 12. Geographical Examples of the Golden spiral are all around us in the shape of the galaxies, hurricanes and waves.
- 13. Application and Use Architecture Music Beauty Art Make Math Interesting
- 14. Architecture The application of the GR in architecture has the following advantages: Brings balance and height to buildings. Allows for varying shapes. Makes buildings aesthetically pleasing.
- 15. Music The applications of GR in music are: Used in the timing of musical compositions eg the climax is reached often at the ϕ(61.8%) of the song. Used in the design of musical instruments eg violin. Even Beethoven and Mozart used the GR in their best works eg Beethoven’s fifth symphony.
- 16. Beauty The applications of the GR in beauty are: The most aesthetically pleasing and beautiful faces are those that conform to the GR hence this is applied in facial plastic surgery and cosmetic dentistry as a guide. The GR method is used in the application of make- up to look more beautiful.
- 17. Art The applications of GR in art are: Artists use the GR in finding the best design for their work eg Da Vinci’s Mona Lisa follows the GR in it’s layout. Using the GR is proven to make things more aesthetically pleasing so artists often incorporate it in their work.
- 18. Make Math Interesting The study of the GR makes math more interesting; students look beyond fractions and algebra and see a hidden world of math in everyday life. The GR helps to put the Fibonacci sequence into context, which is part of the curriculum, and because it’s so intriguing they will learn more. The GR shows that math is all around us and in every profession. This may persuade students to take math in their further education.
- 19. Conclusion The GR is a truly unbelievable construct and it is amazing how it relates to everyday life. The GR unveils a hidden harmony in all things which is really fascinating. I think the study of ϕ should also be included in the school curriculum because it can show students that there is more to math than they may think.