Concept
Pythagorean theorem
Related concepts (74)
Euclid's Elements
Euclid's Elements (Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics.
John Wallis
John Wallis (ˈwɒlɪs; Wallisius; - ) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is credited with introducing the symbol ∞ to represent the concept of infinity. He similarly used 1/∞ for an infinitesimal. John Wallis was a contemporary of Newton and one of the greatest intellectuals of the early renaissance of mathematics. Cambridge, M.
Triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted . In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.
Spherical trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam.
Theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic.
Norm (mathematics)
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude of the vector.
Sign function
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that returns the sign of a real number. In mathematical notation the sign function is often represented as . The signum function of a real number is a piecewise function which is defined as follows: Any real number can be expressed as the product of its absolute value and its sign function: It follows that whenever is not equal to 0 we have Similarly, for any real number , We can also ascertain that: The signum function is the derivative of the absolute value function, up to (but not including) the indeterminacy at zero.
Trapezoid
In geometry, a trapezoid (ˈtɹæpəzɔɪd) in USA and Canadian English, or trapezium (trəˈpiːziəm) in British and other forms of English, is a quadrilateral that has at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases. A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast with the special cases below.
Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object.
Semicircle
In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, pi radians, or a half-turn). It has only one line of symmetry (reflection symmetry). In non-technical usage, the term "semicircle" is sometimes used to refer to either a closed curve that also includes the diameter segment from one end of the arc to the other or to the half-disk, which is a two-dimensional geometric region that further includes all the interior points.