Math in the Modern World

• According to Ian Stewart in his book Nature by Numbers, when we hear the word “mathematics”, the first thing that springs to mind is numbers.
• “Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of Mathematics resides precisely in the fact that it is an art; by informing us of the nature of own minds it informs us of much that depends on our minds.” John William Navin Sullivan (1886-1937), Aspects of Science, 1925.
• Mathematics comes from the ancient Greek word “Mathema” means “that which I learnt” or “to learn” in the modern Greek.
• 6 TYPES OF PATTERNS IN NATURE

  1. Symmetry2. Fractals3. Spirals4. Spots and stripes5. Flower Petals6. Number Patterns and Sequences
• Symmetry is an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis. It indicates that you can draw an imaginary line across an object and the resulting parts are mirror images of each other.
• Reflection Symmetry – It is also called mirror symmetry or line symmetry. It is made with a line going through an object which divides it into two pieces which are mirror images of each other. This is often termed as bilateral symmetry as it divides the object into two (“bi “ means two) mirror images.
• Rotational Symmetry – It is also called radial symmetry. Note that if you rotate the given images below by several degrees, you can still achieve the same appearance as the original position.
• Translational Symmetry – This kind of symmetry is exhibited by objects which do not change its size and shape even if it moved to another location. Note that the movement does not involve with reflection or rotation.
• Fractals are never-ending patterns that are self-similar across different scales. The image just reappears over and over again no matter how many times the object is magnified.
• Spirals are curved patterns made by series of circular shapes revolving around a central point.
• Spots and Stripes - Patterns are also exhibited in the external appearances of animals.
• Flowers Petals are easily considered as things of beauty. Their vibrant colors and fragrant odors make them very appealing as gifts or decorations. The flowers below have different number of petals. Flowers with 5 petals are said to be the most common.
• Number Patterns and Sequences - Patterns in which a list number that follows a certain sequence.
• This number sequence was developed in the Middle Ages, and it was named after Leonardo Pisano Bigollo, a famous Italian mathematician who also happened to discover Fibonacci. He is the greatest European mathematician of the middle ages. He was born in 1170 and died in 1250.
• Fibonacci is a short term for the latin filius bonacci, which means “the son of Bonacci”
• FIBONACCI SEQUENCE FORMULA: F_n=F_(n-1)+F_(n-2)
• BINET'S FORMULA: F_n=(((1+√5)/2)^n-((1-√5)/2)^n)/√5
• GOLDEN RATIO IS = 1.618 also known as "Phi"