T puzzle
The T puzzle is a tiling puzzle consisting of four polygonal shapes which can be put together to form a capital T. The four pieces are usually one isosceles right triangle, two right trapezoids and an
Square trisection
In geometry, a square trisection is a type of dissection problem which consists of cutting a square into pieces that can be rearranged to form three identical squares.
Dehn invariant
In geometry, the Dehn invariant is a value used to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another, and whether a polyhedron or its dissections can t
Ostomachion
Ostomachion, also known as loculus Archimedius (Archimedes' box in Latin) and also as syntomachion, is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arab
Wallace–Bolyai–Gerwien theorem
In geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and , is a theorem related to dissections of polygons. It answers the question when one polygon can be forme
The Banach–Tarski Paradox (book)
The Banach–Tarski Paradox is a book in mathematics on the Banach–Tarski paradox, the fact that a unit ball can be partitioned into a finite number of subsets and reassembled to form two unit balls. It
Geometric magic square
A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. A traditional magic square is a square array of numbers (almost al
Banach–Tarski paradox
The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite numb
Missing square puzzle
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only tex
Paradoxical set
In set theory, a paradoxical set is a set that has a paradoxical decomposition. A paradoxical decomposition of a set is two families of disjoint subsets, along with appropriate group actions that act
Hinged dissection
In geometry, a hinged dissection, also known as a swing-hinged dissection or Dudeney dissection, is a kind of geometric dissection in which all of the pieces are connected into a chain by "hinged" poi
Squaring the square
Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous a
Monsky's theorem
In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square does not have an odd equidissection. The proble
Dissection puzzle
A dissection puzzle, also called a transformation puzzle or Richter Puzzle, is a tiling puzzle where a set of pieces can be assembled in different ways to produce two or more distinct geometric shapes
Dissection into orthoschemes
In geometry, it is an unsolved conjecture of Hugo Hadwiger that every simplex can be dissected into orthoschemes, using a number of orthoschemes bounded by a function of the dimension of the simplex.
Tangram
The tangram (Chinese: 七巧板; pinyin: qīqiǎobǎn; lit. 'seven boards of skill') is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective
Dissection problem
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this
Equidissection
In geometry, an equidissection is a partition of a polygon into triangles of equal area. The study of equidissections began in the late 1960s with Monsky's theorem, which states that a square cannot b
Tarski's circle-squaring problem
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equ
Chessboard paradox
The chessboard paradox or paradox of Loyd and Schlömilch is a falsidical paradox based on an optical illusion. A chessboard or a square with a side length of 8 units is cut into four pieces. Those fou
Hilbert's third problem
The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it al
Hooper's paradox
Hooper's paradox is a falsidical paradox based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwards get assembled into a rectangle with an