Equilateral

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Equilateral

In geometry

Geometry

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....
, an equilateral polygon is a polygon

Polygon

In geometry a polygon is traditionally a plane Shape that is bounded by a closed curve path or circuit, composed of a finite sequence of straight line segments ....
which has all sides of the same length.

For instance, an equilateral triangle

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
is a triangle of equal edge lengths. All equilateral triangles are similar

Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape. Equivalently and more precisely, one is congruence to the result of a uniform Scaling of the other....
to each other, and have 60 degree internal angle

Internal angle

In geometry, an interior angle is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon....
s.

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Encyclopedia

In geometry

Geometry

Polygon

Triangle

Similarity (geometry)

Internal angle

In geometry, an interior angle is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon....
s.

Any equilateral quadrilateral

Quadrilateral

In geometry, a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on....
is a rhombus

Rhombus

In geometry, a rhombus , or rhomb is an equilateral polygon parallelogram. In other words, it is a four-sided polygon in which every side has the same length....
, which includes the square

Square (geometry)

In Euclidean geometry, a square is a regular polygon with four equal sides and four equal angles . A square with vertices ABCD would be denoted ....
.

An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon

Regular polygon

A regular polygon is a polygon which is Equiangular polygon and equilateral . Regular polygons may be convex or Star polygon....
. Not all equilateral polygons are convex

Convex polygon

In geometry, a polygon can be either convex or concave....
: all equilateral polygons with more than four sides, such as the pentagon

Pentagon

In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
, can be concave

Convex polygon

In geometry, a polygon can be either convex or concave....
.

Viviani's theorem

Viviani's theorem

Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from a point to the sides of an equilateral triangle equals the length of the triangle's Altitude ....
holds for equiangular polygons (and also holds for equilateral ones):

The sum of distances from a point to the side lines of an equiangular [or equilateral] polygon does not depend on the point and is that polygon's invariant.

External links

With interactive animation
a discussion of Viviani's theorem at Cut-the-knot
Cut-the-knot

Cut-the-knot is an educational website maintained by Alexander Bogomolny and devoted to popular exposition of a great variety of topics in mathematics....
.
With Java animations.
A family of pieces resembling lenses tiling
Tiling

Tiling may refer to:* The physical act of laying tiles* The mathematics of tessellations* The compiler optimization of loop tiling* People with the surname Tiling...
the plane.

Equilateral

See also

External links