Tromino
Encyclopedia
A tromino is a polyomino
of order 3, that is, a polygon
in the plane
made of three equal-sized square
s connected edge-to-edge. When rotation
s and reflection
s are not considered to be distinct shapes, there are only two different free trominoes: "I" and "L" (the "L" shape is also called "V").
Since both free trominoes have reflection symmetry
, they are also the only two one-sided trominoes (trominoes with reflections considered distinct). When rotations are also considered distinct, there are six fixed trominoes: two I and four L shapes. They can be obtained by rotating the above forms by 90°, 180° and 270°.
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling with a connected interior....
of order 3, that is, a polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
in the plane
Plane (mathematics)
In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...
made of three equal-sized square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
s connected edge-to-edge. When rotation
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
s and reflection
Reflection (mathematics)
In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as set of fixed points; this set is called the axis or plane of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection...
s are not considered to be distinct shapes, there are only two different free trominoes: "I" and "L" (the "L" shape is also called "V").
Since both free trominoes have reflection symmetry
Reflection symmetry
Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.In 2D there is a line of symmetry, in 3D a...
, they are also the only two one-sided trominoes (trominoes with reflections considered distinct). When rotations are also considered distinct, there are six fixed trominoes: two I and four L shapes. They can be obtained by rotating the above forms by 90°, 180° and 270°.
External links
- Golomb's inductive proof of a tromino theorem at cut-the-knotCut-the-knotCut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics. The site has won more than 20 awards from scientific and educational publications, including a Scientific American Web Award in 2003,...
- Tromino Puzzle at cut-the-knot
- Interactive Tromino Puzzle at Amherst CollegeAmherst CollegeAmherst College is a private liberal arts college located in Amherst, Massachusetts, United States. Amherst is an exclusively undergraduate four-year institution and enrolled 1,744 students in the fall of 2009...