Search results
Results from the WOW.Com Content Network
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...
In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem[1] or the upside down Pythagorean theorem[2]) is as follows: [3] Let A, B be the endpoints of the hypotenuse of a right triangle ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space[1][2]) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in . Inner products allow formal definitions of intuitive ...
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]
Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius ...
In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides and opposite respective angles and (see Fig. 1), the law of cosines states: The law of cosines generalizes the Pythagorean theorem, which holds only ...
The triangle inequality is a defining property of norms and measures of distance. This property must be established as a theorem for any function proposed for such purposes for each particular space: for example, spaces such as the real numbers, Euclidean spaces, the L p spaces (p ≥ 1), and inner product spaces.