math

• This activity is worth 15 points.
• Mathematics (from Greek: máthēma, 'knowledge, study, learning') is an area of knowledge, which includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).
• The origin of counting can be traced back to patterns of movement.
• Mathematics is a tool to quantify, organize and control the world, control phenomena and makes life easier.
• Mathematics helps unravel the puzzles of nature, organize patterns and regularities, predict the behavior of nature and phenomena, and provides tools for calculations.
• Mathematics is the science of patterns and relationships, providing a sense of order, and allowing one to make an educated guess.
• Investigating the patterns that one finds in numbers, shapes and expressions would lead to making mathematical discoveries.
• Patterns, relationships and functions constitute a unifying theme in mathematics.
• Mathematics is depicted in nature in shapes, symmetry, and patterns.
• Geometry, a branch of Mathematics that describes shapes and establishes relationships between them, is relatively more common in nature.
• Shapes that appear relatively more common in nature include spheres, hexagons, cones, and parallel lines.
• Symmetry is the quality of being made up of exactly similar parts facing each other or around an axis.
• Bilateral Symmetry is present when an object has two sides that are mirror images of each other.
• Radial Symmetry is present when an object has a center point and numerous lines of symmetry could be drawn.
• Art historians have found other examples of the golden ratio in the Mona Lisa, and the Great Pyramid of Giza.
• Maynard James Keenan, the lead singer of Tool, began with the seventh number of the Fibonacci sequence (13), implying a missing verse in between, and descended back down with the following pattern; 13-8-5-3.
• Pacioli's book, "De Divina Proportione", has been a source of inspiration for many enthusiasts who claim that the number is naturally pleasing to the eye, a mathematical distillation of beauty, and that golden ratio line segments, golden rectangle side lengths, and golden triangles are represented throughout art history.
• In 2001, American prog-metal band Tool released “Lateralus,” a song with Fibonacci-inspired time signatures.
• Le Corbusier, a famous mid-century modern architect, based a good deal of his architectural system around the golden ratio.
• The Parthenon in Athens, built by the ancient Greeks from 447 to 438 BC, is regarded by many to illustrate the application of the Golden Ratio in design.
• Salvador Dali, the surrealist painter, intentionally used a canvas shaped like a golden rectangle for his painting, The Sacrament of the Last Supper.
• The second verse of the song adds the missing line to complete the sequence; "There is (2), so (1), much (1), more that (2), beckons me (3), to look through to these (5), infinite possibilities (8)."
• A few artists and designers have deliberately based their work around the golden ratio.
• There’s no evidence that use of the golden ratio is better than use of other proportions, but artists and designers are always in the business of creating balance, order, and interesting composition for their work.
• Mathematics helps organize patterns and regularities, as well as irregularities in the world, and provides tools for calculations.
• Mathematics helps predict the behavior of nature and phenomena in the world, and provides tools for calculations.
• Mathematics provides tools for calculations, which can be used in different fields such as mathematics, science, engineering, and daily life.
• Mathematics helps make the world a better place to live.
• Fractals are infinitely complex patterns that are self-similar across different scales and are created by repeating a simple process over and over in an ongoing feedback loop.
• In 1509, Italian mathematician Luca Pacioli published the book De Divina Proportione, which, alongside illustrations by Leonardo da Vinci, praised the ratio as representing divinely inspired simplicity and orderliness.
• Self-organization in cell biology is used to create highly structured tissues.
• Invoked organized patterns pertain to patterns formed with external intervention.
• The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618 and is usually written as the Greek letter phi.
• Mathematics is the study of numbers, symbols, notations, operations, equations and functions, proof, and more.
• The circulatory system of animals is similar to the network of veins that move fluids around inside a leaf, showing clear fractal structure.
• Because of Pacioli’s book and Leonardo’s illustrations, the golden ratio gained fame among mathematicians and artists.
• In self-organizing systems, pattern formation occurs through interactions internal to the system, without intervention by external directing influences.
• Lichtenberg figures, produced by high-voltage electricity discharging through a non-conductive material, show repetitive self-similar branching characteristic of a fractal.
• The first known mention of the golden ratio is from around 300 BCE in Euclid’s Elements, the Classical Greek work on mathematics and geometry.
• The Fibonacci numbers are named after Leonardo Fibonacci of Pisa, Italy, who introduced the sequence to Western European Mathematics through the use in his important book “Liber Abaci” (Book of Calculation) in 1202.