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A more formal definition states that two subsets A and B of Euclidean space R n are called congruent if there exists an isometry f : R n → R n (an element of the Euclidean group E(n)) with f(A) = B. Congruence is an equivalence relation.
CPCTC (triangle geometry) Cameron–Erdős theorem (discrete mathematics) Cameron–Martin theorem (measure theory) Cantor–Bernstein–Schroeder theorem (set theory, cardinal numbers) Cantor's intersection theorem (real analysis) Cantor's isomorphism theorem (order theory) Cantor's theorem (set theory, Cantor's diagonal argument)
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H.M. – harmonic mean. HOL – higher-order logic. Hom – Hom functor. hom – hom-class. hot – higher order term. HOTPO – half or triple plus one. hvc – havercosine function. (Also written as havercos.) hyp – hypograph of a function.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Project Mathematics! (stylized as Project MATHEMATICS! ), is a series of educational video modules and accompanying workbooks for teachers, developed at the California Institute of Technology to help teach basic principles of mathematics to high school students. [ 1 ]
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
Consider a triangle ABC.Let the angle bisector of angle ∠ A intersect side BC at a point D between B and C.The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC: