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Heron's formula. A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, the area is [1] It is named after first-century engineer Heron of Alexandria (or Hero) who ...
Archimedes could also find the volume of the cone using the mechanical method, since, in modern terms, the integral involved is exactly the same as the one for area of the parabola. The volume of the cone is 1/3 its base area times the height. The base of the cone is a circle of radius 2, with area , while the height is 2, so the area is ...
Given a triangle with sides of length a, b, and c, if a 2 + b 2 = c 2, then the angle between sides a and b is a right angle. For any three positive real numbers a, b, and c such that a 2 + b 2 = c 2, there exists a triangle with sides a, b and c as a consequence of the converse of the triangle inequality.
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...
In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes' theorem are the cases of a surface in or , and the divergence theorem is the case of a volume in . [2] Hence, the theorem is sometimes referred to as the fundamental theorem of multivariate calculus.
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero- dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of ...
Ceva's theorem. Geometric relation between line segments from a triangle's vertices and their intersection. Ceva's theorem, case 1: the three lines are concurrent at a point O inside ABC. Ceva's theorem, case 2: the three lines are concurrent at a point O outside ABC. In Euclidean geometry, Ceva's theorem is a theorem about triangles.