MMW P1

• MATHEMATICS - Is the study of the relationships among numbers, quantities, and shapes.
• Mathematics came from the word “mathem” which means “knowledge or learning”,
• Patterns in nature are visible regularities found in the natural world.
• Symmetry - Identical
• Spiral - Rotational Symmetry but is a series of curve focuses on the center.
• Radial - Circular in pattern
• Tessellations - The tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
• Joseph Plateau - Examined soap fils, leading him to formulate the concept of minimal surface. (The bubbles in-betweens are 120 degrees)
• Ernst Haeckel (German Biologist and artist) - Painted hundreds of marine organisms to emphasize their symmetry.
• D’arcy Thompson (Scottish Biologist) - Pioneered the study of growth patterns in both plants and animals, showing the simple equations could explain spiral growth.
• Alan Turing (British Mathematician) - Predicted mechanism of morphogenesis which give rise to patterns of spots and stripes.
• W. Gary Smith - Adopts eight patterns in his landscape work, namely: scattered, fractured, mosaic, naturalistic drift, serpentine, spiral, radial, and dendritic.
• Aristid Lindemayer (Hungarian Biologist) & Benoit Maldenbrot (French American Mathematician) - Showed how the mathematics of fractals could create plant growth patterns.
• Leonardo Pisano Bigollo (1170-1250, Italy), his nickname, “Fibonacci” roughly means “Son of Bonacci.”
• Fibonacci Day is November 23
• Golden Ratio - ϕ=1.618033
• The Golden Ratio is a mathematical ratio. It is commonly found in nature, and when used in a design, it fosters organic and natural-looking compositions that are aesthetically pleasing to the eye.
• Fractal Patterns - Patterns that build into a simple repetitive shapes that are reduced in size every time they are repeated. Spiderweb, Lightning, Spiral etc.
• Spectacular Patterns - Rainbows, Water Waves, Cloud Formation, Tree Branching Patterns and etc.
• An image formed by an object in a plane mirror can be explained mathematically by the law of reflection.
• A free-falling object is an object that is falling under the sole influence of gravity.
• The mathematics of pendulum is quite complicated but harmonic. Its period or the time it takes to swing back to its original position is related to its length, but the relationship is not linear.
• A free-falling object is an object that is falling under the sole influence of gravity.
• An image formed by an object in a plane mirror can be explained mathematically by the law of reflection.
• The art of applying mathematics to compex real-world problems is called engineering mathematics.