Portal:Geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry is one of the two fields of pre-modern mathematics, the other being the study of numbers.
In modern times, geometric concepts have been extended. They sometimes show a high level of abstraction and complexity. Geometry now uses methods of calculus and abstract algebra, so that many modern branches of the field are not easily recognizable as the descendants of early geometry. (See areas of mathematics.) A geometer is one who works or is specialized in geometry.
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| A Platonic solid is a convex regular polyhedron. These are the three-dimensional analogs of the convex regular polygons. There are precisely five such figures (shown on the right). The name of each figure is derived from the number of its faces: respectively 4, 6, 8, 12 and 20. They are unique in that the sides, edges and angles are all congruent.
Due to their aesthetic beauty and symmetry, the Platonic solids have been a favorite subject of geometers for thousands of years. They are named after the ancient Greek philosopher Plato who claimed the classical elements were constructed from the regular solids. The Platonic solids have been known since antiquity. The five solids were certainly known to the ancient Greeks and there is evidence that these figures were known long before then. The neolithic people of Scotland constructed stone models of all five solids at least 1000 years before Plato. |
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| Tetrahedron | |
| Hexahedron | |
| Octahedron | |
| Dodecahedron | |
| Icosahedron |
| ...Archive | Image credits: User:Cyp | Read more... |
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Euclid (also referred to as Euclid of Alexandria) (Greek: Εὐκλείδης) (c. 325–c. 265 BC), a Greek mathematician, who lived in Alexandria, Hellenistic Egypt, almost certainly during the reign of Ptolemy I (323 BC–283 BC), is often considered to be the "father of geometry". His most popular work, Elements, is thought to be one of the most successful textbooks in the history of mathematics. Within it, the properties of geometrical objects are deduced from a small set of axioms, thereby founding the axiomatic method of mathematics.
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The above shows an example of doubly ruled surface – the hyperboloid of one sheet. Although the wires are straight lines, they are lying within the surface. Through any point on this surface pass two straight lines, so it is doubly ruled.
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Did you know?
- ...that the hyperboloid of one sheet is a doubly ruled surface?
- ...that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...that a regular heptagon is the regular polygon with the fewest number of sides which is not constructible with a compass and straightedge?
- ...that it is possible for a three-dimensional figure to have a finite volume but infinite surface area? An example of this is Gabriel's Horn.
Categories
Algebraic geometry • Classical geometry
Conformal geometry • Convex geometry
Coordinate systems • Differential geometry
Digital geometry • Dimension • Discrete geometry
Duality theories • Figurate numbers
Frames of reference • Geometers
Geometric algorithms • Geometric graph theory
Geometric group theory • Geometric shapes
Homogeneous spaces • Incidence geometry
Integral geometry • Metric geometry
Symmetry • Trigonometry
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Topics in Geometry
| Basic topics | Trigonometry | Euclidean geometry | Other geometries |
|---|---|---|---|
| Differential geometry | Riemannian geometry | Algebraic geometry | Other |
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