1 / 29

The Golden Ratio

The Golden Ratio. What is it? 1.618033988749895... Also known as Phi (rhymes with fly) it is an irrational number like pi ( 3.14159265358979... ), but one with many unusual mathematical properties. 1.618033988749895. The Golden Ratio.

frances-prince
Download Presentation

The Golden Ratio

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Golden Ratio What is it? 1.618033988749895... Also known as Phi (rhymes with fly) it is an irrational number like pi ( 3.14159265358979... ), but one with many unusual mathematical properties.

  2. 1.618033988749895 The Golden Ratio This ratio (Phi) was known to the Greeks as the "dividing a line in the extreme and mean ratio.” It was known to Renaissance artists as the "Divine Proportion.” It is also called the Golden Section, Golden Ratio and the Golden Mean.

  3. 1.618033988749895 The Golden Ratio Phi, like Pi, is a ratio defined by a geometric construction Just as pi (p) is the ratio of the circumference of a circle to its diameter, phi is the ratio of the line segments that result when a line is divided in one very special and unique way.

  4. 1.618033988749895 The Golden Ratio The ratio of the length of the entire line (A) to the length of larger line segment (B) is the same as the ratio of the length of the larger line segment (B) to the length of the smaller line segment (C).

  5. 1.618033988749895 The Golden Ratio This happens only at the point where: A is 1.618 ... times B and B is 1.618 ... times C.

  6. 1.618033988749895 The Golden Ratio You can also use this golden ratio to form a golden rectangle: This rectangle is unique because the resulting rectangle On the right is similar to the original rectangle After drawing a square within the rectangle. This can be done again, and again and again…….

  7. 1.618033988749895 The Golden Ratio Until the pieces become too small to see. The spiral Drawn within the squares is known as the golden spiral

  8. 1.618033988749895 The Golden Ratio The reciprocal of Phi is known as phi (with a lower case p.) This reciprocal relationship is unique in mathematics. The reciprocal of Phi (1. 6180339887 …) is 0.6180339887. Which is Phi minus 1.

  9. 1.618033988749895 The Golden Ratio What makes phi even more unusual is that it can be derived in many ways and shows up in relationships throughout the universe.

  10. 1.618033988749895 The Golden Ratio Mathematically: Leonardo Fibonacci discovered the series which converges on Phi… a simple numerical series that is the foundation for a mathematical relationship with Phi. Starting with 0 and 1, each new number in the series is simply the sum of the two before it. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . The ratio of each successive pair of numbers in the series approximates phi (1.618. . .) , as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60.

  11. 1.618033988749895 The Golden Ratio In Geometry, Phi can be found in the following figures Inscribed within a circle.

  12. 1.618033988749895 The Golden Ratio In the human body:

  13. 1.618033988749895 The Golden Ratio In the human body:

  14. 1.618033988749895 The Golden Ratio In Nature:

  15. 1.618033988749895 The Golden Ratio In Nature: 3 Lilies 5 Buttercups, Roses 8 Delphinium 13 Marigolds 21 Black-eyed susans 34 Pyrethrum 55/89 Daisies

  16. 1.618033988749895 The Golden Ratio In Nature:

  17. 1.618033988749895 The Golden Ratio In Nature: DNA has spirals in phi proportions DNA in the cell appears as a double-stranded helix referred to as B-DNA. This form of DNA has a two groove in its spirals, with a ratio of Phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms.

  18. 1.618033988749895 The Golden Ratio In the solar system: SATURN

  19. 1.618033988749895 The Golden Ratio THE UNIVERSE Studies have revealed that the math adds up if the universe is finite and shaped like a dodecahedron, The faces of which Are pentagons that Exhibit Phi.

  20. 1.618033988749895 The Golden Ratio In Architecture

  21. 1.618033988749895 The Golden Ratio In Architecture

  22. 1.618033988749895 The Golden Ratio In Architecture

  23. 1.618033988749895 The Golden Ratio In Art

  24. 1.618033988749895 The Golden Ratio In music: There are 13 notes in the span of any note through its octave. A scale is comprised of 8 notes, of which the 5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is 2 steps from the root tone, that is the 1st note of the scale.

  25. 1.618033988749895 The Golden Ratio In music:

  26. 1.618033988749895 The Golden Ratio In Everyday items: A perfect golden rectangle

  27. 1.618033988749895 The Golden Ratio In Everyday items: Blood pressure recommendations: 130/80 which is 1.625 which is freakishly close to 1.618033988749895

  28. 1.618033988749895 The Golden Ratio Is all this a coincidence? How could this all be explained? Math…….Go figure!

  29. 1.618033988749895 The Golden Ratio SMILE!

More Related