BROWSE ALPHABETICALLY LEVEL:    Elementary    Advanced    Both INCLUDE TOPICS:    Basic Math    Algebra    Analysis    Biography    Calculus    Comp Sci    Discrete    Economics    Foundations    Geometry    Graph Thry    History    Number Thry    Phys Sci    Statistics    Topology    Trigonometry triangle – whole number triangle   Geometry: A closed plane figure with three straight sides meeting at three vertices. If one side of a triangle is chosen as the base, then the height of the triangle is the perpendicular distance to the base from the vertex opposite the base.Triangles are classified by their angle measures:Acute – all angles less than 90°.Obtuse – one angle greater than 90°.Right – one angle exactly 90°.Scalene – all angles and sides unequal.Isosceles – two angles equal (equivalently, two sides equal).Equilateral – all angles equal (equivalently, all sides equal).On a right triangle, the sides adjacent to the right angle are called the legs, and the side opposite is called the hypotenuse.Cf. Pythagorean Theorem.Graph Theory: A cycle with three vertices. trigonometric function   The “trig” functions are transcendental functions defined on angles. They include the sine, cosine, tangent, secant, cosecant, and cotangent functions. See the related article for a complete description. Related article: Trig Functions and Identities trigonometry   The mathematical subject concerned with trigonometric functions, which are defined on angles. They include the sine, cosine, tangent, secant, cosecant, and cotangent functions. Related article: Trig Functions and Identities trivial   The smallest, simplest, and usually least interesting example of any object or construction. Every field has a specific definition of what is considered the trivial object of study in that field. The following entries provide examples.Logic: A conclusion is trivial if it is so obvious that no proof or demonstration is required to establish its truth. tuple   An ordered list of elements from a set, usually represented as (a1, a2, a3, ... ,an). (Sometimes angle brackets are used in place of parentheses.) A tuple with only two elements is called an ordered pair, and tuples with 3, 4, and 5 elements are called ordered triples, quadruples, and quintuples, respectively. In general, a tuple with n elements is called an n-tuple. A relation on a family of sets is represented by a set of tuples.Cf. flat pair. union   The union of two sets A and B is the set consisting of those elements which are in A or in B or in both, and is denoted byIf the union is taken over a family of sets {Ai}i = 1, 2, ..., n, then it is the set consisting of those elements that are in at least one of the sets in the collection.Sometimes the word “union” is used to indicate the sumset of a set A, and is then loosely described as “union A.” In this latter case the union is understood to be the union over the elements of A, and is denoted byWhen considering an algebra of sets, the union of two or more sets is sometimes called the join of the sets.Cf. intersection. unit circle   A circle with radius 1. unit interval   The interval on the real number line from 0 to 1, inclusive. unit square   The set of points of the Cartesian plane with domain and range values in the unit interval, that is the square region with vertices (0, 0), (0, 1), (1, 0), and (1, 1), including its boundary. universal quantifier   upper bound   An upper bound of a set with an order relation (such as “ < ”) defined on it is an element which is greater than or equal to every element in the set.Cf. least upper bound. vector   A quantity having two components; a magnitude component and a direction component. In n-dimensional Euclidean space, a vector is representable by an ordered tuple (a1, a2, a3, ... an) whose elements are called the components of the vector. In this case the magnitude of the vector is given by the square root of the sum of the squares of the components of the vector. vertex   Geometry: In a plane figure, a point which is a common end-point for two or more lines or curves.Graph Theory: One of two kinds of entities in a graph.Cf. edge. vertex set   The set of vertices of some graph. For a graph G, the vertex set of G is denoted by V(G), or, if there is no ambiguity as to the graph in question, simply by V. well-founded   In set theory, a collection is well-founded if every subcollection has a least member under the membership relation. For example, the set of natural numbers is well-founded. In ZFC, the foundation axiom asserts this property of all sets. A set which is not well-founded is sometimes called a hyperset. whole number   An element of the set consisting of the number 0 together with the counting numbers, 1, 2, 3, etc.; i.e., the set N of natural numbers with 0 included. Sometimes the term “whole” is meant to refer to negative integers also; the intended meaning should be clear from the context. triangle – whole number
 HOME | ABOUT | CONTACT | AD INFO | PRIVACYCopyright © 1997-2013, Math Academy Online™ / Platonic Realms™. Except where otherwise prohibited, material on this site may be printed for personal classroom use without permission by students and instructors for non-profit, educational purposes only. All other reproduction in whole or in part, including electronic reproduction or redistribution, for any purpose, except by express written agreement is strictly prohibited. Please send comments, corrections, and enquiries using our contact page.