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Chord Theorem
The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's ''Elements''. More precisely, for two chords ''AC'' and ''BD'' intersecting in a point ''S'' the following equation holds: :, AS, \cdot, SC, =, BS, \cdot, SD, The converse is true as well, that is if for two line segments ''AC'' and ''BD'' intersecting in S the equation above holds true, then their four endpoints ''A'', ''B'', ''C'' and ''D'' lie on a common circle. Or in other words if the diagonals of a quadrilateral ''ABCD'' intersect in ''S'' and fulfill the equation above then it is a cyclic quadrilateral. The value of the two products in the chord theorem depends only on the distance of the intersection point ''S'' from the circle's center a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the mainstream of 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, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord Theorem Power
Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a particular tuning * Chord (geometry), a line segment joining two points on a curve * Chord (astronomy), a line crossing a foreground astronomical object during an occultation which gives an indication of the object's size and/or shape * Chord (graph theory), an edge joining two nonadjacent nodes in a cycle * Chord in truss construction – an outside member of a truss, as opposed to the inner "webbed members" * Chord (aeronautics), the distance between the front and back of a wing, measured in the direction of the normal airflow. The term chord was selected due to the curved nature of the wing's surface * Chord (peer-to-peer), a peer-to-peer protocol and algorithm for distributed hash tables (DHT) * Chord (concurrency), a concurrency construct in some object-oriented programming languages * In British railway terminology, a chor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord Theorem Proof
Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a particular tuning * Chord (geometry), a line segment joining two points on a curve * Chord (astronomy), a line crossing a foreground astronomical object during an occultation which gives an indication of the object's size and/or shape * Chord (graph theory), an edge joining two nonadjacent nodes in a cycle * Chord in truss construction – an outside member of a truss, as opposed to the inner "webbed members" * Chord (aeronautics), the distance between the front and back of a wing, measured in the direction of the normal airflow. The term chord was selected due to the curved nature of the wing's surface * Chord (peer-to-peer), a peer-to-peer protocol and algorithm for distributed hash tables (DHT) * Chord (concurrency), a concurrency construct in some object-oriented programming languages * In British railway terminology, a chor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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