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2004 video by R.E.M.
Perfect Square is a 2004 concert film of the alternative rock band R.E.M., filmed on July 19, 2003, at the Bowling Green in Wiesbaden, Germany. It was
Perfect_Square
Product of an integer with itself
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with
Square_number
Topics referred to by the same term
perfect square is an element of algebraic structure that is equal to the square of another element. Square number, a perfect square integer. Perfect Square
Perfect_square
Mathematical problem
square into n {\displaystyle n} squares of one or two different sizes. A "perfect" squared square is a square such that each of the smaller squares has
Squaring_the_square
Algorithms for calculating square roots
S {\displaystyle S} . Since all square roots of natural numbers, other than of perfect squares, are irrational, square roots can usually only be computed
Square_root_algorithms
(Mathematical) decomposition into a product
any field, where either –1, 2 or –2 is a square. In a finite field, the product of two non-squares is a square; this implies that the polynomial x 4 +
Factorization
A perfect rectangle is a rectangle that can be divided into squares of different sizes. If a perfect rectangle is specifically a square, it is analogously
Perfect_rectangle
Polynomial equation of degree 4
has a pair of folded perfect squares, one on each side of the equation. The two perfect squares balance each other. If two squares are equal, then the
Quartic_equation
Mathematical proof technique
divides a2 + b2. Prove that a2 + b2/ab + 1 is a perfect square. Fix some value k that is a non-square positive integer. Assume there exist positive integers
Vieta_jumping
American entertainment company
††† - Yen Press has the rights to series' digital release due to being a Square Enix title. 2001 Nights A, A Prime A.D. Police: Dead End City Abara Act-Age
Viz_Media
Integer side lengths of a right triangle
{\displaystyle {\tfrac {(c-a)(c-b)}{2}}} is always a perfect square; in fact it is equal to the square of the inradius of the associated right triangle.[citation
Pythagorean_triple
Two-dimensional packing problem
allows the packing of n {\displaystyle n} unit squares is known when n {\displaystyle n} is a perfect square (in which case it is n {\displaystyle {\sqrt
Square_packing
Positive integer that is an integer power of another positive integer
a perfect power is a natural number that is a product of equal natural factors, or, in other words, an integer that can be expressed as a square or a
Perfect_power
Data
A most-perfect magic square of order n is a magic square containing the numbers 1 to n2 with two additional properties: Each 2 × 2 subsquare sums to 2s
Most-perfect_magic_square
Quadrilateral with four right angles
squaring.net. The lowest number of squares need for a perfect tiling of a rectangle is 9 and the lowest number needed for a perfect tilling a square is
Rectangle
Square of numbers with equal row, column and diagonal totals
of squares. Except for n ≤ 5, the enumeration of higher-order magic squares is still an open challenge. The enumeration of most-perfect magic squares of
Magic_square
Unique positive real number which when multiplied by itself gives 2
lemma can be used to show that two identical perfect squares can never be added to produce another perfect square. Suppose the contrary that 2 {\displaystyle
Square_root_of_2
Number whose square is a given number
the square root of numbers having many digits. It was known to the ancient Greeks that square roots of positive integers that are not perfect squares are
Square_root
Product of a number by itself
to squaring is quadratic. The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often
Square_(algebra)
Triangle whose side lengths and area are integers
Heronian triangles with perfect square sides are connected to the Perfect cuboid problem. The existence of a solution to the Perfect cuboid problem is equivalent
Heronian_triangle
Mathematical identity of polynomials
difference of two squares is one squared number (the number multiplied by itself) subtracted from another squared number. Every difference of squares may be factored
Difference_of_two_squares
Number, product of consecutive integers
nth pronic number is at a radius of n and n + 1 from a perfect square, and the nth perfect square is at a radius of n from a pronic number. The nth pronic
Pronic_number
Four basic unsolved problems about prime numbers
one prime between consecutive perfect squares? Are there infinitely many primes p such that p − 1 is a perfect square? In other words: Are there infinitely
Landau's_problems
"Top Music Videos". Billboard. Vol. 115, no. 46. November 15, 2003. Perfect Square: "Top Music Video". Billboard. Vol. 116, no. 14. April 3, 2004. When
R.E.M._discography
Number equal to the sum of its proper divisors
of a perfect number (whether even or odd) must be even, because N cannot be a perfect square. From these two results it follows that every perfect number
Perfect_number
Method for solving quadratic equations
{\displaystyle x^{2}+10x+28.} This quadratic is not a perfect square, since 28 is not the square of 5: ( x + 5 ) 2 = x 2 + 10 x + 25. {\displaystyle (x+5)^{2}\
Completing_the_square
Greatest integer less than or equal to square root
{y}}} run forever on each input y {\displaystyle y} which is not a perfect square. Algorithms that compute ⌊ y ⌋ {\displaystyle \lfloor {\sqrt {y}}\rfloor
Integer_square_root
unlike the flags of Switzerland and the Vatican City, it is not a perfect square. In 1830, the flag, at that time non-officially, consisted of three
Flag_of_Belgium
Visualization of the prime numbers formed by arranging the integers into a spiral
than the square spiral used by Ulam, and are spaced so that one perfect square occurs in each full rotation. (In the Ulam spiral, two squares occur in
Ulam_spiral
Figurate number
to just check if 24x + 1 is a perfect square. For non-generalized pentagonal numbers, in addition to the perfect square test, it is also required to check
Pentagonal_number
Natural number
only square number that is the sum of two consecutive, positive cubes: 3 2 = 9 = 1 3 + 2 3 {\displaystyle 3^{2}=9=1^{3}+2^{3}} If an odd perfect number
9
Natural number
triangular numbers. Three is the only prime which is one less than a perfect square. Any other number which is n 2 {\displaystyle n^{2}} − 1 for some integer
3
Formula that provides the solutions to a quadratic equation
\end{aligned}}} Because the left-hand side is now a perfect square, we can easily take the square root of both sides: x + b 2 a = ± b 2 − 4 a c 2 a .
Quadratic_formula
Place of worship in Hinduism
around which is formed a perfect square in the space available. The circle of the mandala circumscribes the square. The square is considered divine for
Hindu_temple
Integer that is a perfect square modulo some integer
an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x such that x 2 ≡ q (
Quadratic_residue
Numbers obtained by adding the two previous ones
{\displaystyle 5x^{2}+4} or 5 x 2 − 4 {\displaystyle 5x^{2}-4} is a perfect square. This is because Binet's formula, which can be written as F n = ( φ
Fibonacci_sequence
Open space surrounded by covered walks or open galleries
neighboring site by Abbot Richbold (784–804) the cloister was made a perfect square, against the south flank of the new church, precisely as in the plan
Cloister
Type of motion which combines translation and rotation with respect to a surface
with the surface. The construction of a specific surface allows even a perfect square wheel to roll with its centroid at constant height above a reference
Rolling
Classical averages studied in ancient Greece
product is a perfect square, esp. a natural perfect square number. However, the mean is irrational when the product is not a perfect square, esp. when the
Pythagorean_means
Concept in number theory
intuitively that there are more positive integers than perfect squares, because every perfect square is already positive and yet many other positive integers
Natural_density
Function whose actual domain of definition may be smaller than its apparent domain
) {\displaystyle f(n)} is only defined if n {\displaystyle n} is a perfect square (that is, 0 , 1 , 4 , 9 , 16 , … {\displaystyle 0,1,4,9,16,\ldots }
Partial_function
Square of a triangular number
JSTOR 2688231. Stroeker, R. J. (1995), "On the sum of consecutive cubes being a perfect square", Compositio Mathematica, 97 (1–2): 295–307, MR 1355130. Toeplitz, Otto
Squared_triangular_number
Measure of readability
syllables in three 10-sentence samples, estimate the count's square root (from the nearest perfect square), and add 3. A 2010 study published in the Journal of
SMOG
around which is formed a perfect square in the space available. The circle of mandala circumscribes the square. The square is considered divine for its
Hindu_temple_architecture
Drawing by Leonardo da Vinci, c. 1490
breadth will be found to be the same as the height, as in the case of a perfect square. — Vitruvius in De architectura, book three, chapter one 19th-century
Vitruvian_Man
Number raised to the third power
minimum perfect cube, since the cube of a negative integer is negative. For example, (−4) × (−4) × (−4) = −64. Unlike perfect squares, perfect cubes do
Cube_(algebra)
Crocheted block assembled to make larger textiles
colors. The small blocks can be sewn or drawn together, so as to make a perfect square, this joining being done on the wrong side. The idea is to have the
Granny_square
Number that is not a ratio of integers
the golden ratio φ, and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like all real
Irrational_number
Mathematical proof expressed visually
sum of all positive odd numbers up to 2n − 1 is a perfect square—more specifically, the perfect square n2—can be demonstrated by a proof without words.
Proof_without_words
Treatise by Archimedes
contains accurate approximations to the square root of 3 (one larger and one smaller) and other larger non-perfect square roots; however, Archimedes gives no
Measurement_of_a_Circle
Words can be read horizontally and vertically
9-square in 1897; and the 10-square in 2023. Here are examples of English word squares up to order eight: The following is one of several "perfect" nine-squares
Word_square
Mathematical problem of square numbers which are also square-pyramidal
a perfect square, would have N = 8, yielding a total of (14 × 14 = ) 196 cannonballs. The only numbers that are simultaneously triangular and square pyramidal
Cannonball_problem
Geographical quadrant
[clarification needed] Originally, the District of Columbia was a near-perfect square but contained more than one settlement; the Capitol was to be the center
Quadrants_of_Washington,_D.C.
Traditional Japanese wrapping cloth
chirimen, cotton, rayon, and nylon. The cloth is typically square, although not a perfect square, to facilitate the wrap. Sizes vary, from 45 by 45 centimetres
Furoshiki
Number that remains the same when its digits are reversed
below: There are many palindromic perfect powers nk, where n is a natural number and k is 2, 3 or 4. Palindromic squares: 0, 1, 4, 9, 121, 484, 676, 10201
Palindromic_number
Type of Diophantine equation
a perfect square, Pell's equation has infinitely many distinct integer solutions. These solutions may be used to accurately approximate the square root
Pell's_equation
American-Canadian animated web and television series
with Bravest Warriors being one of the titles announced under their Perfect Square imprint. They were announced to be released in 2014. The series was
Bravest_Warriors
Unsolved problem in mathematics
{n(n-1)}{2}}n^{n}(n-1)^{n-1}t^{n-1}(1-t),} and this is not in general a perfect square. Solutions for alternating groups must be handled differently for odd
Inverse_Galois_problem
1992 single by R.E.M.
been studio-recorded. The song is also included on the 2003 live DVD Perfect Square, the 2007 live CD/DVD R.E.M. Live, and the 2009 live CD Live at the
Drive_(R.E.M._song)
Unofficial holiday
2081. Square Root Days fall upon the same nine dates each century. Notably, May 5, 2025, which also coincided with Cinco de Mayo, is a perfect Square Root
Square_Root_Day
Shape with four equal sides and angles
subdivision with distinct smaller squares is called a perfect squared square. Another variant of squaring the square called "Mrs. Perkins's quilt" allows
Square
Natural number
{\displaystyle n^{n}} , where n = 4 {\displaystyle n=4} . 256 is a perfect square (162). 256 is the only 3-digit number that is zenzizenzizenzic. It is
256_(number)
In mathematics, when is n!+1 a square
of n {\displaystyle n} such that n ! + 1 {\displaystyle n!+1} is a perfect square, where n ! {\displaystyle n!} is the factorial. Only three values of
Brocard's_problem
Size of a set in mathematics
perfect squares as there are square roots. However, every number is a square root, since it can be squared, but not every number is a perfect square.
Cardinality
Natural number
expressed as (8+9)2. 289 is a perfect square being equal to 172. It is also the 7th number to only have 3 factors because it is a square of a prime number. 289
289_(number)
1967 painting by David Hockney
both times by auction at Sotheby's in London). The canvas – almost a perfect square – is dominated by the strong vertical and horizontal lines of the trees
A_Bigger_Splash
Unit of area
A perfect rectangle of these dimensions would be (855/1000) × (589/1000) = 0.504 km2. Parks come in all sizes; a few are almost exactly one square kilometre
Square_kilometre
Italian-French scientist (1736–1813)
an integer n which is not a perfect square, to find a number x such that nx2 + 1[verification needed] is a perfect square; and the general differential
Joseph-Louis_Lagrange
Boutique hotel in Penang, Malaysia
tiles made of encaustic clay in geometric pieces all shaped to fit to a perfect square, Glasgow cast iron works by MacFarlane's & Co. and Art Nouveau stained
Cheong_Fatt_Tze_Mansion
Arithmetic operation, inverse of nth power
simplified form, we can proceed as follows. First, look for a perfect square under the square root sign and remove it: 32 5 = 16 ⋅ 2 5 = 16 ⋅ 2 5 = 4 2 5
Nth_root
Natural number
positive integers that is simultaneously two more than a perfect square and two less than a perfect cube (123 = 112 + 2 = 53 - 2). In numerology, the sequence
123_(number)
Arithmetic function
{\displaystyle n} is the characteristic function of the squares: ∑ d | n λ ( d ) = { 1 if n is a perfect square, 0 otherwise. {\displaystyle \sum _{d|n}\lambda
Liouville_function
Figurate number
hdl:1893/29437. Beldon, Tom; Gardiner, Tony (2002). "Triangular Numbers and Perfect Squares". The Mathematical Gazette. 86 (507): 423–431. doi:10.2307/3621134
Triangular_number
Natural number
composite number. 285 is the 9th square pyramidal number. That means it is the sum of a number of consecutive perfect squares starting with 1. For 285, it
285_(number)
Park in Fountain Valley, California, US
effort to create the park. The park derives its name from the near-perfect square of land that it occupies, bounded by Edinger and Warner Avenues on the
Mile_Square_Regional_Park
Probabilistic primality testing algorithm
147755149. If n is a perfect square, then step 3 will never yield a D with (D/n) = −1; this is not a problem because perfect squares are easy to detect
Baillie–PSW_primality_test
Mathematical inequality relating inner products and norms
helpful when the inequality involves fractions where the numerator is a perfect square. The real vector space R 2 {\displaystyle \mathbb {R} ^{2}} denotes
Cauchy–Schwarz_inequality
Japanese manga series by Noriyki Konishi
April 2023. Viz Media publishes the series in North America under their Perfect Square imprint, whereas Shogakukan Asia publishes the series in Singapore and
Yo-kai_Watch_(manga)
2003 video by R.E.M.
the Rain" (Buck, Mills, Stipe) (David Weir) – 4:38 Recorded at Trafalgar Square on April 29, 2001: "Imitation of Life" (Buck, Mills, Stipe) "Losing My Religion"
In View: The Best of R.E.M. 1988–2003
In_View:_The_Best_of_R.E.M._1988–2003
Unsolved problem in mathematics
question on the differences between perfect squares and perfect cubes. It asserts that a perfect square y2 and a perfect cube x3 that are not equal must lie
Hall's_conjecture
Integer that is both a perfect square and a triangular number
In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words
Square_triangular_number
Dukedom of Spain
Susana, Bishop of Sigüenza, and confessor to the King. The Dukedom was a perfect square of twenty-five leagues on a side, extending towards the west from the
Duke_of_Veragua
Cuboid whose edges and face diagonals have integer lengths
(2000). "Perfect Cuboids and Perfect Square Triangles". Mathematics Magazine, 73(5), 400–401. Sharipov R.A. (2012). "Perfect cuboids and irreducible polynomials"
Euler_brick
Probabilistic test for the primality of an integer
in this case, n+1 = (p+1)2 is a perfect square. One can quickly detect perfect squares using Newton's method for square roots. By combining a Lucas pseudoprime
Lucas_pseudoprime
Natural number
preceding 112. 111 is the fourth non-trivial nonagonal number, and the seventh perfect totient number. 111 is furthermore the ninth number such that its Euler
111_(number)
Providing control of layout during building
a suitable coordinate system selected for the project. The nearly perfect squareness and north–south orientation of the Great Pyramid of Giza, built c
Construction_surveying
Anonymous commentary on a work of Plato
principles used to find square and oblong numbers can be further applied to perfect square numbers can be extended to finding perfect cubes,Pythagorean triples
Anonymous Commentary on Plato's Theaetetus
Anonymous_Commentary_on_Plato's_Theaetetus
2013 role-playing video game
December 15, 2012. This series has been licensed by Viz Media under its Perfect Square imprint. The series went on to earn awards for best Children's Manga
Yo-kai_Watch_(video_game)
Generalisation of Fourier transform to any ring
{\displaystyle F_{q}} , then one must ensure q {\displaystyle q} is a perfect square or extend to F q 2 {\displaystyle F_{q^{2}}} in order to define the
Discrete Fourier transform over a ring
Discrete_Fourier_transform_over_a_ring
Natural number
). "Sequence A359013 (Numbers k that can be written as the sum of a perfect square and a factorial in exactly 3 distinct ways)". The On-Line Encyclopedia
40,000
German mathematician (1894–1967)
Sprague–Grundy theorem and for being the first mathematician to find a perfect squared square. With two mathematicians, Thomas Bond Sprague and Hermann Amandus
Roland_Sprague
Famous mathematical optimization problem
Thus when we have u2 + v2, we can add the middle term −2uv to get a perfect square. We have x + a b x . {\displaystyle x+{\frac {ab}{x}}.} If we regard
Regiomontanus' angle maximization problem
Regiomontanus'_angle_maximization_problem
French mathematician (1811–1832)
Lagrange can be deduced. If r > 1 is a rational number that is not a perfect square, then r = [ a 0 ; a 1 , a 2 , … , a 2 , a 1 , 2 a 0 ¯ ] . {\displaystyle
Évariste_Galois
Convex polytope, the n-dimensional analogue of a square and a cube
For example, the exponent 2 will yield a square number or "perfect square", which can be arranged into a square shape with a side length corresponding to
Hypercube
lines of the rectangle from where the lower angles begin results in a perfect square. Arms under the House of Castile The Habsburg arms, with half-arches
Coat of arms of the Dominican Republic
Coat_of_arms_of_the_Dominican_Republic
Natural number
definition) with 9801 9801 = 992, the largest 4 digit perfect square, centered octagonal number, square pentagonal number, member of a Ruth-Aaron pair (first
9000_(number)
Natural number
C. J. Bouwkamp, and A. J. W. Duijvestijn, "Catalogue of Simple Perfect Squared Squares of Orders 21 Through 25." Eindhoven University of Technology, Nov
21_(number)
Mechanical measurement
engine with a displacement of 2793 cubic centimeters is an example of a perfect square engine with an 84.0 mm × 84.0 mm (3.31 in × 3.31 in) bore and stroke
Stroke_ratio
Relation between sides of a right triangle
a hypotenuse is related to the unit by the square root of a positive integer that is not a perfect square, it is a realization of a length incommensurable
Pythagorean_theorem
Unsolved problem in mathematics
same difference between terms as the other two, the terms are all perfect squares, and the middle terms of the three arithmetic progressions themselves
Magic_square_of_squares
PERFECT SQUARE
PERFECT SQUARE
Girl/Female
Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Perfect
Boy/Male
Hindu
Perfect
Boy/Male
Tamil
Perfect
Boy/Male
Tamil
Perfect
Girl/Female
Arabic, Muslim, Pakistani
Perfect
Boy/Male
Muslim
Perfect
Girl/Female
Hindu, Indian, Japanese, Kannada, Malayalam, Marathi, Telugu
Perfect
Girl/Female
Indian, Telugu
Perfect
Surname or Lastname
English (Bristol)
English (Bristol) : variant of Parrott 1.
Girl/Female
Hindu, Indian, Marathi, Tamil, Telugu
Perfect
Girl/Female
Tamil
Surasti | ஸà¯à®°à®¸à¯à®¤à¯€
Perfect
Surasti | ஸà¯à®°à®¸à¯à®¤à¯€
Boy/Male
French
Perfect.
Girl/Female
Hindu
Perfect
Girl/Female
Tamil
Nicika | நீஸீகா  Â
Perfect
Nicika | நீஸீகா  Â
Girl/Female
Tamil
Perfect
Surname or Lastname
English
English : variant of Parfitt.
Surname or Lastname
French
French : from a pet form of the personal name P(i)erre, French form of Peter.English (Bristol) : variant of Parrott
Girl/Female
Spanish
Perfect.
Boy/Male
Muslim
Perfect
Girl/Female
Arabic
Perfect.
PERFECT SQUARE
PERFECT SQUARE
Boy/Male
Tamil
Ramsagar | ராமஸாகர
Male
Welsh
Old Welsh form of Celtic Orbogen, URBGEN means "privileged birth."
Boy/Male
American, Anglo, Australian, British, Christian, English, French, German
Will; Desire; Fortress; Dearly Loved Stronghold; Resolute; Brilliant; Wild Boar; Walled Stronghold
Girl/Female
Muslim
(Daughter of a scholar from baghdad)
Surname or Lastname
Greek and Turkish
Greek and Turkish : nickname for a rich man, from Turkish gani ‘rich’, of Arabic origin.English : unexplained.
Girl/Female
Hindu, Indian, Sanskrit
Title; Headline; Important
Girl/Female
Tamil
Debadrita | தேபதà¯à®°à®¿à®¤à®¾
Girl/Female
Muslim
Able, Worthy
Boy/Male
Indian, Modern
Power; Strength
Girl/Female
Indian, Sikh
Blessing
PERFECT SQUARE
PERFECT SQUARE
PERFECT SQUARE
PERFECT SQUARE
PERFECT SQUARE
n.
Power to produce results; efficiency; force; importance; account; as, to speak with effect.
a.
Liable to defect; imperfect.
a.
Well informed; certain; sure.
a.
Producing mathematically perfect harmony or concord; sweetly or perfectly harmonious.
a.
Not perfect; not complete in all its parts; wanting a part; deective; deficient.
n.
A Roman officer who controlled or superintended a particular command, charge, department, etc.; as, the prefect of the aqueducts; the prefect of a camp, of a fleet, of the city guard, of provisions; the pretorian prefect, who was commander of the troops guarding the emperor's person.
a.
To make perfect; to finish or complete, so as to leave nothing wanting; to give to anything all that is requisite to its nature and kind.
a.
Perfect.
a.
Perfect.
a.
Imperfect.
a.
Brought to consummation or completeness; completed; not defective nor redundant; having all the properties or qualities requisite to its nature and kind; without flaw, fault, or blemish; without error; mature; whole; pure; sound; right; correct.
n.
The imperfect tense; or the form of a verb denoting the imperfect tense.
n.
Execution; performance; realization; operation; as, the law goes into effect in May.
v. t.
To make imperfect.
imp. & p. p.
of Perfect
n.
Failing; fault; imperfection, whether physical or moral; blemish; as, a defect in the ear or eye; a defect in timber or iron; a defect of memory or judgment.
adv.
In a perfect manner or degree; in or to perfection; completely; wholly; throughly; faultlessly.
n.
One who, or that which, makes perfect.
a.
Hermaphrodite; having both stamens and pistils; -- said of flower.
n.
The perfect tense, or a form in that tense.