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Question about single-shape aperiodic tiling
In plane discrete geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that
Einstein_problem
Logic puzzle
puzzle is often called Einstein's Puzzle or Einstein's Riddle because it is said[by whom?] to have been invented by Albert Einstein as a boy; it is also
Zebra_Puzzle
German-born theoretical physicist (1879–1955)
Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist best known for developing the known theory of relativity. Einstein also
Albert_Einstein
Tiling hobbyist
discoveries related to aperiodic monotiles that helped to solve the einstein problem. Smith discovered a 13-sided polygon in November 2022 whilst using
David Smith (amateur mathematician)
David_Smith_(amateur_mathematician)
American computer scientist and mathematician
that the tile discovered by hobbyist David Smith is a solution to the einstein problem, a single shape which aperiodically tiles the plane but cannot do so
Craig_S._Kaplan
Swiss-American engineer and educator
Hans Albert Einstein (May 14, 1904 – July 26, 1973) was a Swiss-American engineer, the second child and first son of physicists Albert Einstein and Mileva
Hans_Albert_Einstein
Family of physicist Albert Einstein
The Einstein family is the family of physicist Albert Einstein (1879–1955). Einstein's fourth-great-grandfather, Jakob Weil, was his oldest recorded relative
Einstein_family
Chinese mathematician (born 1958)
Kähler-Einstein surfaces. The case of Kähler surfaces was revisited by Tian in 1990, claiming a complete resolution of the Kähler-Einstein problem in that
Tian_Gang
Field-equations in general relativity
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution
Einstein_field_equations
Wife and cousin of Albert Einstein (1876–1936)
Elsa Einstein (18 January 1876 – 20 December 1936) was the second wife and cousin of Albert Einstein. Their mothers were sisters, making them maternal
Elsa_Einstein
who concerns himself with fates and actions of human beings". Einstein believed the problem of God was the "most difficult in the world"—a question that
Religious and philosophical views of Albert Einstein
Religious_and_philosophical_views_of_Albert_Einstein
Topics referred to by the same term
Look up Einstein or einstein in Wiktionary, the free dictionary. Albert Einstein (1879–1955) was a German-born theoretical physicist. Einstein may also
Einstein_(disambiguation)
Type of metric in Riemannian geometry
The most important problem for this area is the existence of Kähler–Einstein metrics for compact Kähler manifolds. This problem can be split up into
Kähler–Einstein_metric
Preserved brain of the scientist
The brain of Albert Einstein has been a subject of much research and speculation. Albert Einstein's brain was removed shortly after his death. His apparent
Brain_of_Albert_Einstein
Newspaperman, sportswriter, and novelist (1926–2007)
and well-handled problem in construction. Stroby, Wallace (March 12, 2007). "Charles Einstein 1926-2007". Blog post. Charles Einstein (April 6, 2004).
Charles_Einstein
State of matter
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities
Bose–Einstein_condensate
Series of public disputes between physicists Niels Bohr and Albert Einstein
Bohr decades later in an article titled, "Discussions with Einstein on Epistemological Problems in Atomic Physics". Based on the article, the philosophical
Bohr–Einstein_debates
Riemannian metrics, complex manifolds
'right-hand side' of the Kähler–Einstein problem depends on the 'unknown' metric, thereby placing the Kähler–Einstein problem outside the domain of prescribing
Calabi_conjecture
Albert Einstein's hypothetical situations to argue scientific points
A hallmark of Albert Einstein's career was his use of visualized thought experiments (German: Gedankenexperiment) as a fundamental tool for understanding
Einstein's thought experiments
Einstein's_thought_experiments
{\displaystyle C^{4}} (Brendan Guilfoyle and Wilhelm Klingenberg, 2025) Einstein problem (David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
On lattices and sphere packing in Euclidean space
1935. The einstein problem, where "einstein" means "one stone" in German's word play, is the natural extension of Hilbert's eighteenth problem's second question
Hilbert's_eighteenth_problem
Form of plane tiling without repeats at scale
David Smith is an aperiodic monotile, i.e., a solution to the einstein problem, a problem that seeks the existence of any single shape aperiodic tile.
Aperiodic_tiling
Wife of Albert Einstein (1875–1948)
Mileva Marić-Einstein (Милева Марић-Ајнштајн, Mileva Marić-Ajnštajn), was a Serbian mathematician. She also was the first wife of Albert Einstein from 1903
Mileva_Marić
1919 observations which confirmed Einstein's theory of general relativity
field and atmospheric electricity. In 1925, Einstein stated to the Brazilian press about the results, "The problem conceived by my brain was solved by the
Eddington_experiment
1939 letter to U.S. president Franklin D. Roosevelt
The Einstein–Szilard letter was a letter written by Leo Szilard and signed by Albert Einstein on August 2, 1939, that was sent to President of the United
Einstein–Szilard_letter
already been done using gases. But Einstein was the first to successfully solve the problem using liquids. Einstein obtained a respectable estimate for
List of scientific publications by Albert Einstein
List_of_scientific_publications_by_Albert_Einstein
Two interrelated physics theories by Albert Einstein
The theory of relativity comprises two physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and
Theory_of_relativity
Physics concept expressed as E = mc²
units of measurement. The principle is described by the physicist Albert Einstein's formula: E = m c 2 {\displaystyle E=mc^{2}} . In a reference frame where
Mass–energy_equivalence
Theory of gravitation as curved spacetime
theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in May 1916 and is the accepted
General_relativity
Aspect of general relativity
Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity.
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
American actor (born 1947)
Albert Lawrence Einstein (born July 22, 1947), known professionally as Albert Brooks, is an American actor, comedian, director, and screenwriter. He received
Albert_Brooks
Animated children's TV series
Out Problem". KET. Retrieved December 25, 2017. "The Cold Camel Problem/The Einstein Problem". KET. Retrieved December 25, 2017. "The T-Ball Problem/The
Peg_+_Cat
2008 television film directed by Philip Martin
Newton's laws, he writes to Einstein despite the ban to inquire into his view on the problem. On receiving Eddington's letter, Einstein starts work on this new
Einstein_and_Eddington
Hypothetical topological feature of spacetime
points in time, or both). Wormholes are based on a special solution of the Einstein field equations, and are consistent with the general theory of relativity
Wormhole
American animated children's television series
problem, helping someone, or finding something. Little Einsteins was developed after The Walt Disney Company acquired and purchased The Baby Einstein
Little_Einsteins
Exact gravitational-wave solution to Einstein's field equations
cylindrical gravitational waves. Einstein first predicted the existence of gravitational waves in 1916. He returned to the problem 20 years later, working with
Einstein–Rosen_metric
French mathematician, physicist and engineer (1854–1912)
However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically
Henri_Poincaré
Historical critique of quantum mechanics
The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen, which argues
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Basic shape(s) used in a tessellation
monotile, i.e. a solution to a longstanding open einstein problem. In higher dimensions, the problem had been solved earlier: the Schmitt-Conway-Danzer
Prototile
Value representing energy density of space
letter lambda: Λ), alternatively called Einstein's cosmological constant, is a coefficient that Albert Einstein initially added to his field equations
Cosmological_constant
German-born scientist Albert Einstein was best known during his lifetime for his development of the theory of relativity, his contributions to quantum
Political views of Albert Einstein
Political_views_of_Albert_Einstein
Tensor used in general relativity
In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature
Einstein_tensor
Description of the behaviour of bosons
In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting identical
Bose–Einstein_statistics
Sister of Albert Einstein (1881–1951)
"Maja" Einstein Winteler (18 November 1881 - 25 June 1951) was a German Romanist and the younger sister of the physicist Albert Einstein. Einstein was born
Maja_Einstein
Process of achieving a goal by overcoming obstacles
theory of relativity: "The creator of the problem possesses the solution." Einstein said that he did his problem solving without words, mostly in images
Problem_solving
Observatory
The Einstein Tower (German: Einsteinturm) is an astrophysical observatory in the Albert Einstein Science Park in Potsdam, Germany. The Tower was built
Einstein_Tower
Albert Einstein and J. Robert Oppenheimer were twentieth century physicists who made pioneering contributions to physics. From 1947 to 1955 they had been
Einstein–Oppenheimer relationship
Einstein–Oppenheimer_relationship
Model of the Universe proposed 1932
The Einstein–de Sitter universe is a model of the universe proposed by Albert Einstein and Willem de Sitter in 1932. On first learning of Edwin Hubble's
Einstein–de_Sitter_universe
German mathematician (1862–1943)
religion, but scientific results prove themselves in due time." Like Albert Einstein, Hilbert had closest contacts with the Berlin Group, whose leading founders
David_Hilbert
Alleged flaw in the United States Constitution
told Albert Einstein about it at the time, but Morgenstern, in his recollection of the incident in 1971, never mentioned the exact problem as Gödel saw
Gödel's_Loophole
Mathematics book
good (and bad) approaches to the topic. The notes also identify unsolved problems, point out areas of potential application, and provide connections to other
Tilings_and_patterns
Concept in general relativity
The Einstein–Hilbert action in general relativity yields the Einstein field equations through the principle of stationary action. With the ( − , + , +
Einstein–Hilbert_action
Geometry and crystallography point array
lattices split into enantiomorphic pairs. Crystal habit Crystal system einstein problem Geometrical crystallography before X-rays Miller index Reciprocal lattice
Bravais_lattice
American pathologist (1912–2007)
pathologist who conducted the autopsy on Albert Einstein in 1955. Harvey afterwards preserved Einstein's brain on the condition that it would be studied
Thomas_Stoltz_Harvey
Hypothesis that inertial and gravitational masses are equivalent
trajectories and landing at identical times. The extended form by Albert Einstein requires special relativity to also hold in free fall and requires the
Equivalence_principle
Debate about credit for general relativity
tensor as the key for the solution of the problem posed by Einstein. This was followed by several attempts of Einstein to find valid field equations for this
General relativity priority dispute
General_relativity_priority_dispute
Blackboard used by Albert Einstein on 16 May 1931 lectures at the University of Oxford
Einstein's Blackboard is a blackboard which physicist Albert Einstein (1879–1955) used on 16 May 1931 during his lectures while visiting the University
Einstein's_Blackboard
Classical physics prediction that black body radiation grows unbounded with frequency
constant, exp denotes the exponential function. In 1905, Albert Einstein solved the problem physically by postulating that Planck's quanta were real physical
Ultraviolet_catastrophe
theoretical physicist Albert Einstein has been the subject of (or inspiration for) many works of popular culture. Einstein is a favorite model for depictions
Albert Einstein in popular culture
Albert_Einstein_in_popular_culture
Quadrilateral symmetric across a diagonal
tiles the plane only aperiodically, key to a claimed solution of the einstein problem. In non-Euclidean geometry, a kite can have three right angles and
Kite_(geometry)
Thought experiment in quantum mechanics
Schrödinger in 1935, in a discussion with Albert Einstein, to illustrate what Schrödinger saw as the problems of Niels Bohr and Werner Heisenberg's philosophical
Schrödinger's_cat
Application of the theory of relativity to the universe as a whole
Einstein's static universe, a.k.a. the Einstein universe or the Einstein static eternal universe, is a relativistic model of the universe proposed by Albert
Einstein's_static_universe
Model of a crystalline solid
mechanics could solve the specific heat problem in classical mechanics. The original theory proposed by Einstein in 1907 has great historical relevance
Einstein_solid
Concept of absolute rotation
theories, Mach's principle (or Mach's conjecture) is the name given by Albert Einstein to an imprecise hypothesis often credited to the physicist and philosopher
Mach's_principle
Attraction of masses and energy
Gravity is described by the general theory of relativity, proposed by Albert Einstein in 1915, which describes gravity in terms of the curvature of spacetime
Gravity
Friedmann–Einstein model can be discerned on Einstein's blackboard. Einstein–de Sitter universe Einstein, Albert (1931). "Zum kosmologischen Problem der allgemeinen
Friedmann–Einstein_universe
Compact astronomical body
its gravity prevents anything, including light, from escaping. Albert Einstein's theory of general relativity, which describes gravitation as the curvature
Black_hole
Mathematical model combining space and time
to assess one's state of acceleration in an absolute sense. Einstein resolved this problem through the principle of equivalence. The equivalence principle
Spacetime
Aspect of relativity in physics
propagate away at the speed of light. They were first predicted by Albert Einstein as a consequence of his general theory of relativity, appearing as "ripples
Gravitational_wave
Description of physical properties at the atomic and subatomic scale
1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper, which explained the photoelectric
Quantum_mechanics
Thought experiment in special relativity
Sommerfeld (1913), Einstein (1918) or Max Born (1921) in order specifically point out that there is an asymmetry between the clocks. Neither Einstein nor Langevin
Twin_paradox
Hypothetical object of spacetime
addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past. This region does not
White_hole
1949 article by Albert Einstein
written by Albert Einstein in May 1949 that appeared in the first issue of the socialist journal Monthly Review. It addresses problems with capitalism,
Why_Socialism?
Differential geometry conjecture
due to Obata (1971): Every solution to the Yamabe problem on a closed Einstein manifold is Einstein. Obata then went on to prove that, except in the case
Yamabe_problem
Concept in cosmology
problem in physics Why is the vacuum energy density much smaller than a zero-point energy suggested by quantum field theory? More unsolved problems in
Cosmological_constant_problem
Israeli-American physicist (1909–1995)
Bibcode:1935PhRv...47..777E. doi:10.1103/PhysRev.47.777. Einstein, Albert & Rosen, Nathan (1935). "The Particle Problem in the General Theory of Relativity". Physical
Nathan_Rosen
Israeli musical artist
Arieh Lieb "Arik" Einstein (Hebrew: אָרִיק אַייְנְשְׁטֵייְן [ˈʔaʁik ˈʔajnʃtejn]; (3 January 1939 – 26 November 2013) was an Israeli singer, songwriter
Arik_Einstein
Class of axisymmetric solutions to Einstein's field equations
'outer' problem, a boundary value problem for vacuum Einstein's field equations whose solution determines the external field, and the 'inner' problem, whose
Relativistic_disk
Concept that simultaneity depends on choice of reference frame
relativity. According to the special theory of relativity introduced by Albert Einstein, it is impossible to say in an absolute sense that two distinct events
Relativity_of_simultaneity
Investigations by Albert Einstein
1918, Felix Klein had found a similar problem in the coordinates of Einstein–de Sitter universe, but Einstein dismissed the idea. In 1922, when asked
Einstein's unsuccessful investigations
Einstein's_unsuccessful_investigations
Japanese mathematician
to the Kähler-Einstein problem, due to the fact that constant scalar curvature metrics in such a Kähler class must be Kähler-Einstein. Owing to the second
Toshiki_Mabuchi
Convention for synchronising clocks
Einstein synchronisation (or Poincaré–Einstein synchronisation) is a convention for synchronising clocks at different places by means of signal exchanges
Einstein_synchronisation
American mathematician
work on Heesch's problem, to which he contributed a polygon with Heesch number 5. This problem is closely related to the einstein problem, of whether there
Casey_Mann
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies
Two-body problem in general relativity
Two-body_problem_in_general_relativity
Hypothetical quantum cosmological effect
yet been detected. Modern black holes were first predicted using Albert Einstein's general theory of relativity. Evidence of the astrophysical objects termed
Hawking_radiation
British astrophysicist (1882–1944)
helium. Eddington wrote a number of articles that announced and explained Einstein's theory of general relativity to the English-speaking world. World War
Arthur_Eddington
German physicist (1873–1916)
and astronomer. Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single
Karl_Schwarzschild
Equations in physical cosmology
relativity. They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker
Friedmann_equations
Criticism of the theory of relativity of Albert Einstein was mainly expressed in the early years after its publication in the early twentieth century,
Criticism of the theory of relativity
Criticism_of_the_theory_of_relativity
Hypothetical physical concept
combined by James Clerk Maxwell's theory of electromagnetism and Albert Einstein's theory of relativity explained how they are connected. By the 1930s, Paul
Theory_of_everything
Dutch physicist (1853–1928)
research. He initially asked Albert Einstein to succeed him as Professor of Theoretical Physics at Leiden. However, Einstein did not accept, because he had
Hendrik_Lorentz
English mathematician, mathematical physicist (born 1931)
Penrose was awarded the Albert Einstein Medal for outstanding work related to the work of Albert Einstein by the Albert Einstein Society (Switzerland). In
Roger_Penrose
Hypothetical FTL transportation by warping space
laws. Although the metric proposed by Alcubierre is consistent with the Einstein field equations, construction of such a drive is not necessarily possible
Alcubierre_drive
Field theory in physics that aims to unify the fundamental forces and particles
coined by Albert Einstein, who attempted to unify his general theory of relativity with electromagnetism since the 1920s. Einstein attempted to create
Unified_field_theory
Light bending by mass between source and observer
observer. The amount of gravitational lensing is described by Albert Einstein's general theory of relativity. If light is treated as corpuscles travelling
Gravitational_lens
Tensor describing energy momentum density in spacetime
energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source
Stress–energy_tensor
Measured time difference as explained by relativity theory
of clocks. In the context of special relativity it was shown by Albert Einstein (1905) that this effect concerns the nature of time itself, and he was
Time_dilation
Exact solution for the Einstein field equations
quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear
Kerr_metric
General-relativistic effect
increases (the clock moving away from the source of gravitation). Albert Einstein originally predicted this in his theory of relativity, and it has since
Gravitational_time_dilation
Issue in science history
Albert Einstein presented the theories of special relativity and general relativity in publications that either contained no formal references to previous
Relativity_priority_dispute
EINSTEIN PROBLEM
EINSTEIN PROBLEM
Surname or Lastname
English
English : unexplained.Possibly an Americanized spelling of French Imbert or a translation of German and Jewish Bernstein, which means ‘amber’.Muslim (widespread throughout the Muslim world) : from the Arabic personal name ‛Anbar, literally ‘perfume’, ‘ambergris’, figuratively ‘good’, ‘pleasant’, ‘agreeable’.
Girl/Female
Indian, Telugu
Destroyer of Problems
Surname or Lastname
English
English : habitational name from any of various places called Burston, in Buckinghamshire, Norfolk, and Staffordshire, which have different origins. The Buckinghamshire place name is from an Old English personal name Briddel + Old English þorn ‘thorn tree’; the place in Norfolk is named with Old English byrst ‘rough ground’, ‘landslip’ + tÅ«n ‘farmstead’; the Staffordshire place name has the same second element, the first being an Old English personal name Burgwine or Burgwulf.English : possibly from an unrecorded Old English personal name, BurgstÄn.Jewish (American) : Americanized spelling of Burstein (see Bernstein).
Boy/Male
Norse
Lucky.
Boy/Male
Norse
Rock or hard spear.
Boy/Male
Hindu, Indian
Problem
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Muslim
Problem solver
Surname or Lastname
English
English : from an Old English personal name composed of the elements wynn ‘joy’ + stÄn ‘stone’.English : habitational name from any of various places called Winston or Winstone, from various Old English personal names + Old English tÅ«n ‘enclosure’, ‘settlement’, or, in the case of Winstone in Gloucestershire, Old English stÄn ‘stone’.Americanized form of Jewish Weinstein.
Boy/Male
Norse
Lucky.
EINSTEIN PROBLEM
EINSTEIN PROBLEM
Boy/Male
American, Australian, British, English
Darling; Beloved; Variant of Darrell
Girl/Female
Indian
Thankful one
Boy/Male
Indian, Telugu
Belongs to Lord Shiva
Girl/Female
English
Star.
Girl/Female
Arthurian Legend
Mother of Boore.
Girl/Female
Tamil
Name of a indian music Raagini
Female
Greek
(ἌÏτεμις) Greek name derived from the word artémes, ARTEMIS means "safe and sound." In mythology, this is the name of a daughter of Zeus and Lêtô and twin sister to Apollo.Â
Girl/Female
Arabic, Australian, Muslim
Happy; Joyful; Cheerful; Glad
Boy/Male
Scandinavian
Thief of peace.
Girl/Female
Tamil
Mahika means earth in Sanskrit (Celebrity Name: Arjun Rampal)
EINSTEIN PROBLEM
EINSTEIN PROBLEM
EINSTEIN PROBLEM
EINSTEIN PROBLEM
EINSTEIN PROBLEM
n.
To cause to stick; to bring to a stand; to pose; to puzzle; as, to stick one with a hard problem.
n.
A problem of more than usual difficulty added to another on an examination paper.
n.
To begin to deal with; as, to tackle the problem.
a.
Questionable; equivocal; indefinite; problematical.
a.
Alt. of Problematical
a.
Liable to question; subject to be doubted or called in question; problematical; doubtful; suspicious.
n.
A problem to be solved, or an example to be wrought out.
v. i.
To work, as at a puzzle; as, to puzzle over a problem.
n.
The quality, condition, or degree of being soluble or solvable; as, the solubility of a salt; the solubility of a problem or intricate difficulty.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.
n.
The act of solving, or the state of being solved; the disentanglement of any intricate problem or difficult question; explanation; clearing up; -- used especially in mathematics, either of the process of solving an equation or problem, or the result of the process.
n.
An instrument of the ancients for finding two mean proportionals between two given lines, required in solving the problem of the duplication of the cube.
a.
Having the nature of a problem; not shown in fact; questionable; uncertain; unsettled; doubtful.
v. t.
To propose problems.
a.
Single; not complex; not infolded or entangled; uncombined; not compounded; not blended with something else; not complicated; as, a simple substance; a simple idea; a simple sound; a simple machine; a simple problem; simple tasks.
v. t.
To explain; to resolve; to unfold; to clear up (what is obscure or difficult to be understood); to work out to a result or conclusion; as, to solve a doubt; to solve difficulties; to solve a problem.
a.
Susceptible of being solved; as, a soluble algebraic problem; susceptible of being disentangled, unraveled, or explained; as, the mystery is perhaps soluble.
v. t.
To have just and adequate ideas of; to apprehended the meaning or intention of; to have knowledge of; to comprehend; to know; as, to understand a problem in Euclid; to understand a proposition or a declaration; the court understands the advocate or his argument; to understand the sacred oracles; to understand a nod or a wink.
n.
The quality or state of being solvable; as, the solvability of a difficulty; the solvability of a problem.
n.
One who proposes problems.