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Circle
In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. The points can only be those that are part of a conic section; within the set of a plane normal to the axis of a right cone. Circles are simple closed curves, dividing the plane into an interior and exterior. Sometimes the word circle is used to mean the interior, with the circle itself called the circumference(C). Usually, however, the circumference means the length of the circle, and the interior of the circle is called a disk. final version: 05.11.2006 22:16, |
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Cone
A cone is a three dimensional geometric shape. It is the locus of all line segments between a simply connected region of a plane (the base) and a point (the apex) outside the plane. There are four types of cones; circular, elliptical, right and oblique all of which are conic solids. All pyramids are also cones, in otherwords it is the generalization of a pyramid to non-polygonal bases. In common usage and elementary geometry, a cone refers to a right circular cone. The boundary of a conic solid is a conic surface. A cone with its apex cut off by a plane parallel to its base is called a truncated cone or frustum. final version: 01.10.2007 01:05, |
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Cuboid
In geometry, a cuboid is a solid figure bounded by six rectangular faces: a rectangular box. All angles are right angles, and opposite faces of a cuboid are equal. It is also a right rectangular prism. The term "rectangular or oblong prism" is ambiguous. Also the term rectangular parallelepiped is used. The square cuboid, square box or right square prism (also ambiguously called square prism) is a special case of the cuboid in which at least two faces are squares. The cube is a special case of the square prism in which all faces are squares. If the dimensions of a cuboid are a, b and c, then its volume is abc and its surface area is [FORMEL...]. The length of the space diagonal is [FORMEL...] . the volume is [FORMEL...] final version: 23.01.2007 16:25, |
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Cylinder
In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: [FORMEL...] This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). Even more general is the generalized cylinder: the cross-section can be any curve. The cylinder is a degenerate quadric because at least one of the coordinates (in this case z) does not appear in the equation. By some definitions the cylinder is not considered to be a quadric at all. In common usage, a cylinder is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by [FORMEL...] and its surface area is [FORMEL...] final version: 16.03.2008 21:02, |
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Rectangle
In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. From this definition, it follows that a rectangle has two pairs of parallel sides of equal length; that is, a rectangle is a parallelogram. A square is a special kind of rectangle where all four sides have equal length; that is, a square is both a rectangle and a rhombus. A rectangle that is not a square is colloquially known as an oblong. final version: 03.11.2006 18:38, |
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Sphere
A sphere is a perfectly symmetrical, three-dimensional geometrical object. In mathematics, the term refers to the surface or boundary of a ball, but in non-mathematical usage, the term is used to refer either to a three-dimensional ball or to its surface. final version: 03.11.2006 18:51, |
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Spherical cap
In geometry, a spherical cap is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere. final version: 28.11.2006 16:44, |
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Triangle - Pythagorean theorem
A central theorem is the Pythagorean theorem stating that in any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides. If side C is the hypotenuse, we can write this as c² = a² + b² final version: 04.11.2007 19:37, |
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