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Unsolved problem about inscribing a square in a Jordan curve
Unsolved problem in mathematics Does every Jordan curve have an inscribed square? More unsolved problems in mathematics The inscribed square problem, also
Inscribed_square_problem
Square whose vertices lie on a triangle
triangle depicted, the square with horizontal and vertical sides is inscribed; the other two squares in the figure are not inscribed. This is a special case
Inscribed square in a triangle
Inscribed_square_in_a_triangle
Geometric figure which is "snugly enclosed" by another figure
alternative usage of the term "inscribed", see the inscribed square problem, in which a square is considered to be inscribed in another figure (even a non-convex
Inscribed_figure
Shape with four equal sides and angles
which no other regular polygon can be inscribed. For an inscribed square in a triangle, at least one side of the square lies on a side of the triangle. Every
Square
German mathematician (1881–1940)
1920. In 1911, Toeplitz proposed the inscribed square problem: Does every Jordan curve contain an inscribed square? This has been established for convex
Otto_Toeplitz
holyhedron? Inscribed square problem, also known as Toeplitz' conjecture and the square peg problem – does every Jordan curve have an inscribed square? The Kakeya
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Shape with three sides
extended). The inscribed squares tangent their vertices to the triangle's sides is the special case of inscribed square problem, although the problem asking for
Triangle
Curved triangle with constant width
an object has a circular cross-section. In connection with the inscribed square problem, Eggleston (1958) observed that the Reuleaux triangle provides
Reuleaux_triangle
Australian and American mathematician (born 1975)
Wai6 Laan4 Cramer conjecture Erdős discrepancy problem Goldbach's weak conjecture Inscribed square problem King Faisal Foundation – retrieved 11 January
Terence_Tao
Convex quadrilateral with at least one pair of parallel sides
diagonal intersection. Frustum, a solid having trapezoidal faces. Inscribed square problem#Curves without special trapezoids Trapezoid graph, an intersection
Trapezoid
American mathematician (born 1981)
lens space realization problem, while he and a co-author have made advances in the understanding of the inscribed square problem. Greene completed his
Joshua_Evan_Greene
Hedgehog (curve) [1] Hilbert's sixteenth problem Hyperelliptic curve cryptography Inflection point Inscribed square problem intercept, y-intercept, x-intercept
List_of_curves_topics
American mathematician (1871–1959)
1959) was an American mathematician, known for his work on the inscribed square problem. Emch received his Ph.D. in 1895 at the University of Kansas under
Arnold_Emch
Mathematical problem
problems in computational geometry, the inscribed square problem, semigroup of polynomials, etc. The problem was popularized in the article by Goodman
Mountain_climbing_problem
Problem of constructing equal-area shapes
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given
Squaring_the_circle
Type of plane curve
that is inscribed in any strictly convex curve, with its vertices in order along the curve, must be a convex polygon. The inscribed square problem is the
Convex_curve
Soviet mathematician (1905–1938)
— André Weil, The Apprenticeship of a Mathematician, p. 107-108 Inscribed square problem Schnirelmann density Schnirelmann's constant Schnirelmann's theorem
Lev_Schnirelmann
Concept in geometry
is greater than E, split each arc in half. This makes the inscribed square into an inscribed octagon, and produces eight segments with a smaller total
Area_of_a_circle
Roman-era word square with a Latin palindrome
archaeologist Matteo Della Corte [it] discovered a Sator square, also in ROTAS form, inscribed on a column in the Palestra Grande [it] (the gymnasium)
Sator_Square
Problem solving strategy
the area of a small square inscribed in a circle, which itself is inscribed in a large square. However, by rotating the small square by 90° and then drawing
Symmetry_in_problem_solving
Triangle with at least two sides congruent
These include the Calabi triangle (a triangle with three congruent inscribed squares), the golden triangle and golden gnomon (two isosceles triangles whose
Isosceles_triangle
Sum of inverse squares of natural numbers
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed
Basel_problem
Square of numbers with equal row, column and diagonal totals
normal progression of 1 to 8, the adjacent square is obtained. Around 12th-century, a 4×4 magic square was inscribed on the wall of Parshvanath temple in Khajuraho
Magic_square
Simple curve of Euclidean geometry
and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle
Circle
Mathematical constant regarding inscribed polygons
Inscribe a regular triangle in this circle. Inscribe a circle in this triangle. Inscribe a square in it. Inscribe a circle, regular pentagon, circle, regular
Kepler–Bouwkamp_constant
Vector used in astronomy
in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them; such problems are called
Laplace–Runge–Lenz_vector
Convex polyhedron with 16 triangular faces
basis for the bicapped square antiprismatic molecular geometry, and in mathematical optimization as a solution to the Thomson problem. Like other gyroelongated
Gyroelongated square bipyramid
Gyroelongated_square_bipyramid
Mathematical term for squaring a plane figure
sense, the modern term is squaring. For example, the quadrature of the circle, (or squaring the circle) is a famous old problem that has been shown, in
Quadrature_(mathematics)
Public space in Portland, Oregon, U.S.
Pioneer Square", a citizens' group led by city commissioners Charles Ray Jordan and Mike Lindberg, and $750,000 raised by the sale of 50,000 inscribed bricks
Pioneer_Courthouse_Square
Unsolved geometry problem
Lebesgue's universal covering problem is an unsolved problem in geometry that asks for the convex shape of smallest area that can cover every planar set
Lebesgue's universal covering problem
Lebesgue's_universal_covering_problem
Number, approximately 3.14
transcendence of π implies that it is impossible to solve the ancient problem of squaring the circle with a compass and straightedge. The decimal digits of
Pi
Quadrilateral symmetric across a diagonal
when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). The convex kites are exactly the quadrilaterals that are both
Kite_(geometry)
On reflection in a spherical mirror
triangle inscribed within the circle, with the two given points on two sides of this triangle. Another equivalent form of Alhazen's problem asks to construct
Alhazen's_problem
Chinese scientist and writer (1192–1279)
a collection of 170 problems, all related to the same example of a circular city wall inscribed in a right triangle and a square. They often involve two
Li_Ye_(mathematician)
Topological space defined by the union of circles Inscribed angle – Angle formed in the interior of a circle Inscribed angle theorem – Angle formed in the interior
List_of_circle_topics
System of measurement used in Ancient Egypt
strip square was surveyed using a length of 96 cubits rather than 100, although the aroura was still figured to compose 2,756.25 m2. A 36 square cubit
Ancient Egyptian units of measurement
Ancient_Egyptian_units_of_measurement
Shape with three equal sides
also equilateral. It is the only regular polygon aside from the square that can be inscribed inside any other regular polygon. Given a point P {\displaystyle
Equilateral_triangle
Four-dimensional analog of the dodecahedron
convex 4-polytope, it contains inscribed instances of its four predecessors (recursively). It also contains 120 inscribed instances of the first in the
120-cell
Solid with six equal square faces
three-dimensional sphere packing problem in a cube Cubing the cube, analogue to the two-dimensional problem of squaring the square Superellipsoid, a solid whose
Cube
Geometry problem about finding touching circles
surface and four planes, a problem first considered by Charles Dupin. By solving Apollonius's problem repeatedly to find the inscribed circle, the interstices
Problem_of_Apollonius
Relates the length of a median of a triangle to the lengths of its sides
that the sum of the squares of any two sides of any triangle equals twice the square on half the third side plus twice the square on the median bisecting
Apollonius's_theorem
Difficulties arising when analyzing data with many aspects ("dimensions")
experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. The curse generally refers to issues that arise
Curse_of_dimensionality
Domestic policy of U.S. President Theodore Roosevelt
and over it is inscribed square deal." In 1888, in "letters from the people" (letters to the editor), one writer signed off as "Square Deal". In 1890
Square_Deal
Principal square root of minus 1
distinct complex-valued square roots, which are additive inverses of each other, while zero has only zero as its (double) square root. Historically, the
Imaginary_unit
in the answer of Plato to the Delians. When they consulted him on the problem set them by the Oracle, namely, that of duplicating the cube, he replied
A History of Greek Mathematics
A_History_of_Greek_Mathematics
Solid with twenty equal triangular faces
809a.} A problem dating back to the ancient Greeks is determining which of two shapes has a larger volume: a regular icosahedron inscribed in a sphere
Regular_icosahedron
Fastest curve descent without friction
straight line, but the arc of a circle. . . . Consequently the nearer the inscribed polygon approaches a circle the shorter the time required for descent
Brachistochrone_curve
Geometrical structure
However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in
Sphere_packing
typically inscribed with the service, name and number of the unit flying it. The naval jack (bandera de proa) is not based on the triband. It is a square flag
Flag_of_Peru
Time ball in New York City's Times Square
pieces have been inscribed with messages of hope for the new year, which are submitted through a public "Wishing Wall" erected in Times Square (where visitors
Times_Square_Ball
Probabilistic problem-solving algorithm
the results. For example, consider a quadrant (circular sector) inscribed in a unit square. Given that the ratio of their areas is π/4, the value of π
Monte_Carlo_method
Covering by shapes without overlaps or gaps
pentagons. Squaring the square is the problem of tiling an integral square (one whose sides have integer length) using only other integral squares. An extension
Tessellation
United States historic place
Pioneer Square is a neighborhood in the southwest corner of downtown Seattle, Washington, US. It was once the heart of the city: Seattle's founders settled
Pioneer_Square,_Seattle
Geometric treatise by Archimedes
right. Each of these triangles is inscribed in its own parabolic segment in the same way that the blue triangle is inscribed in the large segment. In propositions
Quadrature_of_the_Parabola
Size of a two-dimensional surface
square kilometre = 1,000,000 square metres 1 square metre = 10,000 square centimetres = 1,000,000 square millimetres 1 square centimetre = 100 square
Area
Right triangle with a feature making calculations on the triangle easier
triangles allow one to quickly calculate some useful quantities in geometric problems without resorting to more advanced methods. Angle-based special right triangles
Special_right_triangle
{2}}}{3}}\approx 0.94.} Moreover, for any square inscribed in any triangle we have Area of triangle Area of inscribed square ≥ 2. {\displaystyle {\frac {\text{Area
List_of_triangle_inequalities
Number, approximately 1.618
Toronto Studies. p. 4. Just as a tetrahedron can be inscribed in a cube, so a cube can be inscribed in a dodecahedron. By reciprocation, this leads to
Golden_ratio
Church in Mozambique
church was laid on June 28, 1936, and is located inside the narthex and inscribed by the Bishop of Mozambique and Cape Verde, D. Rafael Maria da Asunção
Cathedral of Our Lady of the Immaculate Conception, Maputo
Cathedral_of_Our_Lady_of_the_Immaculate_Conception,_Maputo
Line which touches a circle at exactly one point
immediately that no rectangle can have an inscribed circle unless it is a square, and that every rhombus has an inscribed circle, whereas a general parallelogram
Tangent_lines_to_circles
required scale, on a 200 × 200 micron square of poly(methyl methacrylate) with a beam of electrons. The main problem he had before he could claim the prize
Tom_Newman_(scientist)
Triangle whose side lengths and area are integers
have a rational sine. Any square inscribed in a Heronian triangle has rational sides: For a general triangle the inscribed square on side of length a has
Heronian_triangle
Municipal building in Manchester, England
local government departments. The building faces Albert Square to the north and St Peter's Square to the south, with Manchester Cenotaph facing its southern
Manchester_Town_Hall
Wiki-based programming chrestomathy
various programming problems in many different programming languages. It is named for the Rosetta Stone, which has the same text inscribed on it in three languages
Rosetta_Code
Geometric shape
transform any rectangle into a square of the same area, a problem called the quadrature of a rectangle. The side length of the square is the geometric mean of
Semicircle
Magic word
an amulet around their neck that was made up of a piece of parchment inscribed with a triangular formula derived from this. It was believed that when
Abracadabra
Ancient Greek philosopher (341–270 BC)
non curo ("I was not; I have been; I am not; I do not mind."), which is inscribed on the gravestones of his followers and seen on many ancient gravestones
Epicurus
Quadrilateral whose vertices lie on a circle
In geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral (four-sided polygon) whose vertices all lie on a single circle, making
Cyclic_quadrilateral
Used to count, measure, and label
the square root of 2 ( 2 ) {\displaystyle \left({\sqrt {2}}\right)} , and pi (π), and complex numbers which extend the real numbers with a square root
Number
National museum in London, England
Greek dialect from Galaxidi, central Greece (500–475 BC) Bronze mitra inscribed on both sides in archaic Cretan script with the Spensithios Decree, Lyttos-Afrati
British_Museum
Mathematical instrument consisting of two hinged rulers
number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It is used for solving problems in proportion, multiplication
Sector_(instrument)
Methods of calculating definite integrals
has roots in the geometrical problem of finding a square with the same area as a given plane figure (quadrature or squaring), as in the quadrature of the
Numerical_integration
Triangle containing a 90-degree angle
the only triangle having two, rather than one or three, distinct inscribed squares. Given any two positive numbers h {\displaystyle h} and k {\displaystyle
Right_triangle
Greek mathematician and physicist (c. 287 – 212 BC)
times the area of a corresponding inscribed triangle as shown in the figure at right, expressing the solution to the problem as an infinite geometric series
Archimedes
Mathematical treatise by Euclid
propositions on inscribed angles (20 through 22), and on chords, arcs, and angles (23 through 30), including the inscribed angle theorem relating inscribed to central
Euclid's_Elements
Intersection of cylinders
bicylinder a similar statement is true: The relations of the volumes of the inscribed square pyramid ( a = 2 r , h = r , V = 4 3 r 3 ) , {\displaystyle (a=2r
Steinmetz_solid
cross-section morphs between these two honeycombs periodically. If a 3-sphere is inscribed in each hypercell of this tessellation, the resulting arrangement is the
24-cell_honeycomb
Cube that fits through hole in smaller cube
length 1 of the unit cube through which it passes. The problem of finding the largest square that lies entirely within a unit cube is closely related
Prince_Rupert's_cube
Ancient Greek mathematician (fl. 300 BC)
to "a third type of proposition—an intermediate between a theorem and a problem—the aim of which is to discover a feature of an existing geometrical entity
Euclid
Greek activist (1948–1970)
Hellenic Government after metapolitefsi. In his monument a plaque is inscribed with his words in Greek. The monument was created gratis by sculptor Dimitris
Kostas_Georgakis
Association football club in England
single cannon, pointing eastwards, with the club's nickname, The Gunners, inscribed alongside it; this crest only lasted until 1925, when the cannon was reversed
Arsenal_F.C.
Trapezoid whose sides are all tangent to the same circle
sides are all tangent to a circle within the trapezoid: the incircle or inscribed circle. It is the special case of a tangential quadrilateral in which
Tangential_trapezoid
Problem of minimizing sum of transport costs
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane
Weber_problem
Equation of the form 1/a + 1/b = 1/c
sum of the squared reciprocal of the side of one of the two inscribed squares and the squared reciprocal of the hypotenuse equals the squared reciprocal
Optic_equation
Polynomial equation of degree two
terms of a, b, and c. Completing the square is one of several ways for deriving the formula. Solutions to problems that can be expressed in terms of quadratic
Quadratic_equation
Magical practice involving evocation of spirits
incantations were inscribed on cuneiform clay tablets. Ancient Egyptians also employed magical practices, including incantations inscribed on amulets. The
Goetia
Relation between sides of a right triangle
includes a problem involving two squares whose areas sum to a third square, whose solution is the Pythagorean triple 6:8:10, but the problem does not mention
Pythagorean_theorem
Four-sided polygon
include rhombi. Tangential quadrilateral: the four sides are tangents to an inscribed circle. A convex quadrilateral is tangential if and only if opposite sides
Quadrilateral
Problem in trigonometry
The Snellius–Pothenot problem is a trigonometry problem first described in the context of planar surveying where known points are used to solve an unknown
Snellius–Pothenot_problem
First Lady of Virginia, wife of Thomas Jefferson (1748–1782)
inscribed with words written by Thomas, the closing of which read: "Torn from him by death. September 6, 1782. This monument of his love is inscribed"
Martha_Jefferson
Quadrilateral with four right angles
rectangle with four sides of equal length is a square. The term "oblong" is used to refer to a non-square rectangle. A rectangle with vertices ABCD would
Rectangle
Geometrical concept relating area and volume
outside the inscribed paraboloid. Therefore, the volume of the flipped paraboloid is equal to the volume of the cylinder part outside the inscribed paraboloid
Cavalieri's_principle
Plane curve
parameters x ∘ , y ∘ , r {\displaystyle x_{\circ },y_{\circ },r} uses the inscribed angle theorem for circles: For four points P i = ( x i , y i ) , i =
Ellipse
Public monument in Clifton, Karachi
located in Clifton, Karachi, Sindh, Pakistan. The three marble swords are inscribed with Quaid-e-Azam Mohammad Ali Jinnah's creeds Unity, Faith and Discipline
Teen_Talwar
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
named after him, where he works on a problem given to him by Theodorus of Cyrene to demonstrate that the square roots of several numbers from 3 to 17
Ancient_Greek_mathematics
American astrophysicist
unavoidable reduction of signal strength as distance squared and that information can be densely encoded (inscribed) in matter. The article also suggested that
Gregory Wright (astrophysicist)
Gregory_Wright_(astrophysicist)
Ancient lighthouse in Egypt
reported that Sostratus of Cnidus had a dedication to the "Saviour Gods" inscribed in metal letters on the lighthouse. Writing in the first century AD, Pliny
Lighthouse_of_Alexandria
1617 device for calculating products and quotients
each of the digits 0 to 9 are needed. If square rods are used, the 40 multiplication tables can be inscribed on 10 rods. Napier gave details of a scheme
Napier's_bones
Colonial federation from 1895 to 1958
issued their own postage stamps until 1943. In many cases the stamps were inscribed with the name of the federation "Afrique Occidentale Française" as well
French_West_Africa
Ancient Greek mathematician
exhibit: and besides this, he discovered a method of determining when a problem, whose investigation is sought for, is possible, and when it is impossible
Leon_(mathematician)
INSCRIBED SQUARE-PROBLEM
INSCRIBED SQUARE-PROBLEM
Male
English
French form of English Stewart, STUART means "house guard; steward." In use by the English and Scottish.
Boy/Male
Anglo Saxon American English Scottish
Steward.
Surname or Lastname
English
English : patronymic from Squire.
Surname or Lastname
English
English : status name from Middle English squyer ‘esquire’, ‘a man belonging to the feudal rank immediately below that of knight’ (from Old French esquier ‘shield bearer’). At first it denoted a young man of good birth attendant on a knight, or by extension any attendant or servant, but by the 14th century the meaning had been generalized, and referred to social status rather than age. By the 17th century, the term denoted any member of the landed gentry, but this is unlikely to have influenced the development of the surname.
Boy/Male
American, British, English
Shield Bearer
Boy/Male
Italian
Squire.
Boy/Male
English
Shieldbearer.
Male
Chinese
square, in the sense of correctness.
Surname or Lastname
English
English : variant of Spear.
Boy/Male
American, Australian, British, English
Shield Bearer; Knight's Companion
Male
Swedish
Swedish name derived from Old Norse stúra, STURE means "obstinate."
Boy/Male
English American
Shieldbearer.
Boy/Male
French Latin
A squire.
Surname or Lastname
English
English : variant of Squire.
Boy/Male
Indian
Cover
Boy/Male
British, English
Spear-man
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Girl/Female
British, English
Bless
Boy/Male
Indian, Telugu
Inherent; Inscribed into Something; Within Something
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, Danish, English, French, German, Scottish
Steward; Stewart is Clan Name of the Royal House of Scotland; Surname; House Guard
INSCRIBED SQUARE-PROBLEM
INSCRIBED SQUARE-PROBLEM
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Pure
Boy/Male
Hindu, Indian
Worship of God; One who Sings God's Praises
Boy/Male
Welsh
Dwells in the woods.
Girl/Female
Indian, Japanese, Telugu
Deer; Gentle; Top of Hill
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
A Flower; Tree Heaven; Name of Ganesha
Girl/Female
Hindu, Indian
Best Friend
Girl/Female
Hindu
Look, Blessed with beauty, Shape, Beauty
Girl/Female
Tamil
Devavarnini | தேவாவாரà¯à®¨à¯€à®¨à¯€
Daughter of sage bharadvaja
Girl/Female
Hindu, Indian
Gift of Sun
Boy/Male
Indian
Servant of the great, Revered, Servant of the exalted (Allah)
INSCRIBED SQUARE-PROBLEM
INSCRIBED SQUARE-PROBLEM
INSCRIBED SQUARE-PROBLEM
INSCRIBED SQUARE-PROBLEM
INSCRIBED SQUARE-PROBLEM
a.
Rendering equal justice; exact; fair; honest, as square dealing.
n.
To multiply by itself; as, to square a number or a quantity.
n.
Hence, anything which is square, or nearly so
n.
To place at right angles with the keel; as, to square the yards.
imp. & p. p.
of Inscribe
n.
An instrument having at least one right angle and two or more straight edges, used to lay out or test square work. It is of several forms, as the T square, the carpenter's square, the try-square., etc.
a.
Having four equal sides and four right angles; as, a square figure.
v. t.
To attend as a squire.
imp. & p. p.
of Square
n.
Having the toe square.
n.
A square piece or fragment.
v. t.
To imprint deeply; to impress; to stamp; as, to inscribe a sentence on the memory.
a.
Even; leaving no balance; as, to make or leave the accounts square.
n.
A square. See 1st Squire.
n.
The product of a number or quantity multiplied by itself; thus, 64 is the square of 8, for 8 / 8 = 64; the square of a + b is a2 + 2ab + b2.
a.
Forming a right angle; as, a square corner.
n.
To make even, so as leave no remainder of difference; to balance; as, to square accounts.
n.
A square; a measure; a rule.
n.
One who inscribes.
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.