Problem-solving in mathematics[ change change source ] Mathematics solves problems by using logic. One of the main tools of logic used by mathematicians is deduction.
Argand diagram[ edit ] Argand diagram. A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram The complex plane is sometimes called the Argand plane because it is used in Argand diagrams.
These are named after Jean-Robert Argand —although they were first described by Norwegian-Danish land surveyor and mathematician Caspar Wessel — The concept of the complex plane allows a geometric interpretation of complex numbers.
Under additionthey add like vectors. The multiplication of two complex numbers can Mathematic english expressed most easily in polar coordinates — the magnitude or modulus of the product is the product of the two absolute valuesor moduli, and the angle or argument of the product is the sum of the two angles, or arguments.
In particular, multiplication by a complex number of modulus 1 acts as a rotation. Butterfly diagram Butterfly diagram[ edit ] In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms DFTs into a larger DFT, or vice versa breaking a larger DFT up into subtransforms.
The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The same structure can also be found in the Viterbi algorithmused for finding the most likely sequence of hidden states.
The butterfly diagram show a data-flow diagram connecting the inputs x left to the outputs y that depend on them right for a "butterfly" step of a radix-2 Cooley—Tukey FFT algorithm. This diagram resembles a butterfly as in the morpho butterfly shown for comparisonhence the name.
A commutative diagram depicting the five lemma Main article: Mathematic english diagram In mathematics, and especially in category theorya commutative diagram is a diagram of objectsalso known as vertices, and morphismsalso known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
Commutative diagrams play the role in category theory that equations play in algebra.
Hasse diagrams[ edit ] A Hasse diagram is a simple picture of a finite partially ordered setforming a drawing of the partial order's transitive reduction.
In this case, we say y covers x, or y is an immediate successor of x. In a Hasse diagram, it is required that the curves be drawn so that each meets exactly two vertices: Any such diagram given that the vertices are labeled uniquely determines a partial order, and any partial order has a unique transitive reduction, but there are many possible placements of elements in the plane, resulting in different Hasse diagrams for a given order that may have widely varying appearances.
Knot diagrams[ edit ] In Knot theory a useful way to visualise and manipulate knots is to project the knot onto a plane—;think of the knot casting a shadow on the wall. A small perturbation in the choice of projection will ensure that it is one-to-one except at the double points, called crossings, where the "shadow" of the knot crosses itself once transversely  At each crossing we must indicate which section is "over" and which is "under", so as to be able to recreate the original knot.
This is often done by creating a break in the strand going underneath. If by following the diagram the knot alternately crosses itself "over" and "under", then the diagram represents a particularly well-studied class of knot, alternating knots.
Venn diagram[ edit ] A Venn diagram is a representation of mathematical sets: The principle of these diagrams is that classes be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram.
That is, the diagram initially leaves room for any possible relation of the classes, and the actual or given relation, can then be specified by indicating that some particular region is null or is notnull. Voronoi diagram[ edit ] A Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.
This diagram is named after Georgy Voronoialso called a Voronoi tessellationa Voronoi decomposition, or a Dirichlet tessellation after Peter Gustav Lejeune Dirichlet. In the simplest case, we are given a set of points S in the plane, which are the Voronoi sites.
Each site s has a Voronoi cell V s consisting of all points closer to s than to any other site. The segments of the Voronoi diagram are all the points in the plane that are equidistant to two sites.
The Voronoi nodes are the points equidistant to three or more sites Wallpaper group diagram. Wallpaper group diagrams[ edit ] A wallpaper group or plane symmetry group or plane crystallographic group is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern.
Such patterns occur frequently in architecture and decorative art. There are 17 possible distinct groups. Wallpaper groups are two-dimensional symmetry groupsintermediate in complexity between the simpler frieze groups and the three-dimensional crystallographic groupsalso called space groups.
Wallpaper groups categorize patterns by their symmetries. Subtle differences may place similar patterns in different groups, while patterns which are very different in style, color, scale or orientation may belong to the same group.Supreme Mathematic African Ma'At Magic [African Creation Energy] on iridis-photo-restoration.com *FREE* shipping on qualifying offers.
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Numbers and Symbols for Maths. The short form of mathematics in British English is maths and in American English it's math. Can you add, subtract and do your multiplication tables in English?
Before you can do the math you need to understand the question. Learning English for math means learning numbers, words, and symbols. mathematics definition: 1. the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organizing them2.
the science of numbers, forms, amounts, and their relationships. Learn more. Mathematic definition, of, relating to, or of the nature of mathematics: mathematical truth. See more.
The importance of teaching academic vocabulary. Vocabulary instruction is essential to effective math instruction. Not only does it include teaching math-specific terms such as "percent" or "decimal," but it also includes understanding the difference between the mathematical definition of a word and other definitions of that word.