Fibonacci - Arithmetic Sequence

• The Fibonacci sequence:

  • Introduced in The Book of Calculating
  • Series begins with 0 and 1
  • Next number is found by adding the last two numbers together
  • The number obtained is the next number in the series
  • Pattern is repeated over and over: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...
• Leonardo Pisano Bigollo (1170—1250), known as Fibonacci, published the Liber Abbaci, or Book of Calculation, which focused on financial computations and encouraged the use of Hindu-Arabic numerals
• The Golden Ratio:

  • Expressed in algebra as (a + b) / a = a / b (1.618033987...)
  • Geometrically visualized as a rectangle formed by a square and another rectangle, repeated infinitely inside each section
  • Denoted by the Greek letter Phi (φ), representing an irrational number approximately 1.618
• The Golden Ratio, also known as the Golden Part, Golden Proportion, or Divine Proportion, is generally denoted by the Greek letter Phi (φ), representing an irrational number approximately 1.6180339887...
• Examples of the Golden Ratio:

  • Used in art, architecture, and design to achieve elegance, balance, and harmony
  • Can be applied as a method to achieve harmony in composition
• In nature, plants exhibit characteristics of the Golden Ratio by establishing a Fibonacci sequence in the number of leaves
• The Golden Ratio is applied in various fields like architecture, the automotive industry, music, fashion, handwriting, and general design
• The Great Pyramid of Giza, constructed around 4700 BC, is said to follow the Golden Ratio with a base to height ratio of approximately 1.5717
• The Taj Mahal, completed in 1648, used the Golden Ratio in its construction, with the order and percentage of arches following the ratio
• The Eiffel Tower in Paris, France, erected in 1889, follows the Golden Ratio as it narrows down from a wider base to the tip
• Arithmetic Sequence:

  • A sequence where each term is obtained by adding a constant (common difference) to the preceding term
  • Example: 3, 6, 9, 12, 15... with a common difference of 3
• The nth term of an arithmetic sequence is defined as: a_n = a_1 + (n – 1) * d, where a_1 is the first term, a_n is the last term, n is the number of terms, and d is the common difference
• fibonacci sequence - introduced in the first book of calculating
• fibonacci sequence - series begins with 0 and 1
• fibonacci sequence - next number is found by adding the last two numbers together
• fibonacci sequence - number obtained is the next number in the series
• Leonardo Pisano Bigollo - published the Liber Abbaci or the book of calculation
• Fibonacci - means son of bonacci
• Phi - most significant application of the FS
• Phi - very important number that is known as the GR
• Phi - Greek character
• Golden Ration - expressed in algebra as (a+b) divided by a is equal to a/b
• 1.618 - irrational number and rounded off
• Phi is the initial letter of phidias' name adopted to designate the GR
• Mark Barr - American mathematician and proposed using the first letter of phidias' to represent the GR in the 1900
• Golden Ratio AKA's - extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, mean of phidias'
• latin of divine section?

  sectio divina
• Golden Mean Gauge - invented by Dr. eddy levin DDS and use in dentistry and is used as the standard for dental profession
• dentistry - reason for gauge's creation

  the human face
• can use also in architecture, automotive industry, music and musical introduction, fashion, handwriting, general design
• examples of golden mean gauge in architecture and etc. are banglad city gate, windson castle, great wall of china, parthenon greece, dome of st. paul london, england
• Phidias' - pantheon/temple of athena
• Euclid - pentagram/golden star
• Plato - 5 solid figures
• 5 solid figures - tetrahedron, octahedron, icosahedron, dodecahedron, cubes
• Leonardo Di Ser Piero Da Vinci - vitruvian man, last supper, monalisa
• Alessandro Di Mariano Di Vanni Filipepi - birth of venus
• Rembrandt Van Rijn - dutch painter and known sa self portrait
• Great Pyramid of Giza - 4700 BC in Ahmes Papyrus Egypt is proportional. the side of pyramid is 756 ft and the height is 481 ft and the total is 1.5717
• Notre Dame - gothic cathedral built in paris between 1163 and 1250