Portal:Geometry
From Wikipedia, the free encyclopedia
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was 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.)
The Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras, who is traditionally credited with its discovery, although knowledge of the theorem almost certainly predates him.
The theorem is as follows:
-
- In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse).
This provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found. This theorem may have more known proofs than any other. The Pythagorean Proposition, a book published in 1940, contains 370 proofs of Pythagoras' theorem, including one by American President James Garfield.
In mathematics, an astroid is a particular type of curve: a hypocycloid with four cusps. It is also a super ellipse with n=2/3 and a=b. Its modern name comes from the Greek word for "star". The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle.
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.
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
Portal:Geometry/Quotes
Portal:Geometry/Did you know
- Fill in Quotes
- Fill in Did you know
Euclidean geometry: Combinatorial • Convex • Discrete • Plane geometry • Solid geometry
Non-Euclidean geometry: Elliptic • Parabolic • Hyperbolic • Symplectic • Spherical • Affine • Projective • Riemannian
Trigonometry • Lie groups • Algebraic geometry • Differential geometry • List of mathematical shapes • List of geometry topics • List of differential geometry topics
