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Contents. Kite (geometry) A kite, showing its pairs of equal-length sides and its inscribed circle. In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, [ 1 ] but the word ...
Molecular geometry. Appearance. Geometry of the water molecule with values for O-H bond length and for H-O-H bond angle between two bonds. Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any ...
Cyclic quadrilateral. In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the ...
In the 19th century, the internal development of geometry (pure mathematics) led to definition and study of non-Euclidean geometries, spaces of dimension higher than three and manifolds. At this time, these concepts seemed totally disconnected from the physical reality, but at the beginning of the 20th century, Albert Einstein developed the ...
Solid. v. t. e. A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge.
The sum of the internal angle and the external angle on the same vertex is π radians (180°). The sum of all the internal angles of a simple polygon is π (n −2) radians or 180 (n –2) degrees, where n is the number of sides. The formula can be proved by using mathematical induction: starting with a triangle, for which the angle sum is 180 ...
A Newman projection is a drawing that helps visualize the 3-dimensional structure of a molecule. [1] This projection most commonly sights down a carbon-carbon bond, making it a very useful way to visualize the stereochemistry of alkanes. A Newman projection visualizes the conformation of a chemical bond from front to back, with the front atom ...
As with any simple polygon, the sum of the internal angles of a concave polygon is π × (n − 2) radians, equivalently 180× (n − 2) degrees (°), where n is the number of sides. It is always possible to partition a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex ...