a mathematics reviewer/cheatsheet, Cheat Sheet of Mathematics

Download a mathematics reviewer/cheatsheet and more Cheat Sheet Mathematics in PDF only on Docsity! MATHEMATICS IN THE MODERN WORLD (Reviewer) Definition of Terms Module I Nature of Mathematics PATTERNS -regular, repeated or recurring forms or designs. -helps us identify relationships and find local connections to form generalizations and make predictions. TYPES OF PATTERNS -Patterns of Visuals -Patterns of Flow -Patterns of Movement -Patterns of Rhythm -Patterns of Texture -Geometric Patterns SEQUENCE -Sequences are ordered collections of elements, and they can take various forms and serve different purposes. Here are some common types of sequences: 1. Arithmetic Sequence: - An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference. The general form of an arithmetic sequence is: a, a + d, a + 2d, a + 3d, ... 2. Geometric Sequence: - A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The general form of a geometric sequence is: a, a * r, a * r^2, a * r^3, ... 3. Fibonacci Sequence: - The Fibonacci sequence is a famous sequence in which each term is the sum of the two preceding ones. It starts with 0 and 1, and then each subsequent term is the sum of the two previous terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, ... 4. Harmonic Sequence: - A harmonic sequence is a sequence of numbers in which the reciprocals of the terms form an arithmetic sequence. The general form of a harmonic sequence is: 1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d), ... 5. Quadratic Sequence: - A quadratic sequence is a sequence of numbers in which the difference between consecutive terms forms an arithmetic sequence. The general form of a quadratic sequence is: a, a + b, a + 2b, a + 3b, ... SYMMETRY -an imaginary line across an object and the resulting parts are mirror images of each other. Symmetrical -same BILATERAL SYMMETRY -left and the right portions are exactly the same. Leonardo d Vinci’s Vitruvian Man -shows the proportion and symmetry of the human body. ROTATIONAL SYMMETRY -same appearance as the original position after a rotation. ANGLE OF ROTATION -smallest measure of angle that a figure can be rotated while still preserving the original position ORDER OF ROTATION -rotational symmetry of order n (n- fold rotational symmetry). HONEYCOMB -made by bees in hexagon (The reason is that more area will be covered). ALLAN TURING -British mathematician - “reaction- diffusion equations” – system that governed the formation of hyena’s spot and tiger stripes. GOLDEN RATIO -Geometrically visualized as a rectangle perfectly formed by a square and another rectangle which can be repeated infinitely inside each section. PHYSICAL BEAUTY -the proportions of the length of the nose, the position of the eyes and the length of the chin all conform to some aspect of the Golden Ratio. GREEK GOLDEN RATIO OF BEAUTY PHI -secret formula of perfection. AESTHETICALLY PLEASING- Shapes and figures that bear the Golden Ratio. VARIABLE - represented by a letter, like x or y - symbol for a value we don’t know yet. - temporary name to what you were seeking so that you can perform concrete computations with it to help discover its possible values. Chapter 2 MATHEMATICAL LANGUAGE AND SYMBOLS MATHEMATICAL LANGUAGE -the system used to communicate mathematical ideas. -This language consists of some natural language using technical terms (mathematical terms) and grammatical conventions that are uncommon to mathematical discourse, supplemented by a highly specialized symbolic notation for mathematical formulas. -The mathematical notation used for formulas has its own grammar and shared by mathematicians anywhere in the globe. THE LANGUAGE OF SETS -math with "things". SET -collection of objects. Elements -objects contained in a set.