Fractals
Representing geometry in SecondLife Some comments on the suitability of SecondLife as a way of presenting fractal geometry Fractal forms found by using Google Earth Readers are encouraged to contribute their own findings. POVRay Fractal Raytracing Contest Rendering Wada-type basins of attraction Here's a party trick for over Christmas. Fractal Dimension and Self Similarity A particular box counting software package, Ruler or Compass Dimension, Lacunarity, Multifractal spectrum, Recurrence plots, Self Similarity. Time exists so that not everything happens at once. Natural Fractals in Grand Canyon National Park Fractals: A Symmetry Approach Gasket Photography Fractals and Computer Graphics Interface Magazine Article I wonder whether fractal images are not touching the very structure of our brains. Diffusion Limited Aggregation DLA in 3D Platonic solids Tropical leaf Random Attractors Marketing idea: A potato chip in the shape of the Sierpinski gasket! It would infinitely crispy but have zero calories. Lemon
Algebra
"Algebraist" redirects here. For the novel by Iain M. Banks, see The Algebraist. The quadratic formula expresses the solution of the degree two equation in terms of its coefficients , where is not equal to Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.[6] For example, in the letter is unknown, but the law of inverses can be used to discover its value: . , the letters and are variables, and the letter The word algebra is also used in certain specialized ways. A mathematician who does research in algebra is called an algebraist. How to distinguish between different meanings of "algebra" For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. Algebra as a branch of mathematics can be any numbers whatsoever (except that cannot be Etymology History Early history of algebra History of algebra
Philosophy
Study of general and fundamental questions Philosophy (from Greek: φιλοσοφία, philosophia, 'love of wisdom')[1][2] is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language.[3][4][5] Such questions are often posed as problems[6][7] to be studied or resolved. Some sources claim the term was coined by Pythagoras (c. 570 – c. 495 BCE),[8][9] although this theory is disputed by some.[10][11][12] Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation.[13][14][i] Historically, philosophy encompassed all bodies of knowledge and a practitioner was known as a philosopher.[15] From the time of Ancient Greek philosopher Aristotle to the 19th century, "natural philosophy" encompassed astronomy, medicine, and physics. For example, Newton's 1687 Mathematical Principles of Natural Philosophy later became classified as a book of physics. Definitions Western philosophy
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Subtraction
"5 − 2 = 3" (verbally, "five minus two equals three") An example problem Subtraction of numbers 0–10. Performing subtraction is one of the simplest numerical tasks. Basic subtraction: integers[edit] Imagine a line segment of length b with the left end labeled a and the right end labeled c. a + b = c. From c, it takes b steps to the left to get back to a. c − b = a. To subtract arbitrary natural numbers, one begins with a line containing every natural number (0, 1, 2, 3, 4, 5, 6, ...). The solution is to consider the integer number line (..., −3, −2, −1, 0, 1, 2, 3, ...). Subtraction as addition[edit] Algorithms for subtraction[edit] There are various algorithms for subtraction, and they differ in their suitability for various applications. For machine calculation, the method of complements is preferred, whereby the subtraction is replaced by an addition in a modular arithmetic. The teaching of subtraction in schools[edit] sj sj−1 ... s1 from minuend mk mk−1 ... m1, Example: 704 − 512. Example:
Logic
Logic (from the Ancient Greek: λογική, logike)[1] is the branch of philosophy concerned with the use and study of valid reasoning.[2][3] The study of logic also features prominently in mathematics and computer science. Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning. The study of logic[edit] The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Informal logic is the study of natural language arguments. Logical form[edit] Main article: Logical form Logic is generally considered formal when it analyzes and represents the form of any valid argument type. This is called showing the logical form of the argument. Second, certain parts of the sentence must be replaced with schematic letters. That the concept of form is fundamental to logic was already recognized in ancient times. Deductive and inductive reasoning, and abductive inference[edit]
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Addition
3 + 2 =5 with apples, a popular choice in textbooks[1] Addition of numbers 0-10. Line labels = addend. Performing addition is one of the simplest numerical tasks. Notation and terminology[edit] The plus sign Addition is written using the plus sign "+" between the terms; that is, in infix notation. (verbally, "one plus one equals two") (verbally, "two plus two equals four") (verbally, "three plus three equals six") (see "associativity" below) (see "multiplication" below) There are also situations where addition is "understood" even though no symbol appears: Columnar addition: 5 + 12 = 17 The numbers or the objects to be added in general addition are called the terms, the addends, or the summands; this terminology carries over to the summation of multiple terms. Redrawn illustration from The Art of Nombryng, one of the first English arithmetic texts, in the 15th century[5] "Sum" and "summand" derive from the Latin noun summa "the highest, the top" and associated verb summare. Interpretations[edit]
