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In metric geometry, comparison triangles are constructions used to define higher bounds on curvature in the framework of locally geodesic metric spaces
Comparison_triangle
Shape with three sides
Euclid. Equilateral triangle Isosceles triangle Scalene triangle Right triangle Acute triangle Obtuse triangle All types of triangles are commonly found
Triangle
Type of metric space in mathematics
\mathbf {\operatorname {\textbf {CAT}} } (k)} inequality if there is a comparison triangle Δ ′ {\displaystyle \Delta '} in the model space M k {\displaystyle
CAT(k)_space
Geometry concept
the lower curvature bound is defined via comparison of geodesic triangles in the space to geodesic triangles in standard constant-curvature Riemannian
Alexandrov_space
Index of articles associated with the same name
Lichnerowicz comparison theorem Eigenvalue comparison theorem Cheng's eigenvalue comparison theorem Comparison triangle There exist various comparisons between
Comparison_theorem
Curved triangle with constant width
A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed
Reuleaux_triangle
Property of geometry, also used to generalize the notion of "distance" in metric spaces
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length
Triangle_inequality
1986 song by New Order
"Bizarre Love Triangle" is a song by English rock band New Order, released as a single in November 1986 from their fourth studio album, Brotherhood (1986)
Bizarre_Love_Triangle
Perpendicular line segment from a triangle's side to opposite vertex
In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge opposite
Altitude_(triangle)
Symbol of anti-fascism
The red triangle, also known as the red wedge, was a required accessory worn by left-wing dissidents incarcerated in Nazi concentration camps during World
Red_triangle_(badge)
between points on the boundary of a geodesic triangle are less than or equal to the comparison triangle in the hyperbolic upper half plane or equivalently
Busemann_function
Model of the constraints of project management
The project management triangle (called also the triple constraint, iron triangle and project triangle) is a model of the constraints of project management
Project_management_triangle
same side lengths as this triangle (see comparison triangle). Consider the angle at the vertex of the flat triangle corresponding to p. The limit of this
Tits_metric
Japanese manga series by Kentaro Yabuki
Ayakashi Triangle (Japanese: あやかしトライアングル, Hepburn: Ayakashi Toraianguru) sometimes abbreviated as AyaTri, (あやトラ, Ayatora) is a Japanese fantasy romantic
Ayakashi_Triangle
Basketball offensive strategy
The triangle offense is an offensive strategy used in basketball. Its basic ideas were initially established by Hall of Fame coach Sam Barry at the University
Triangle_offense
Triangle comparison theorem in Riemannian geometry
(named after Victor Andreevich Toponogov) is a triangle comparison theorem. It is one of a family of comparison theorems that quantify the assertion that a
Toponogov's_theorem
Unique ellipse tangent to all 3 midpoints of a given triangle's sides
triangle is the unique ellipse inscribed in the triangle and tangent to the sides at their midpoints. It is an example of an inellipse. By comparison
Steiner_inellipse
Trilateral partnership in Eastern Europe
The Lublin Triangle (Lithuanian: Liublino trikampis; Polish: Trójkąt Lubelski; Ukrainian: Люблінський трикутник, romanized: Liublinskyi trykutnyk) is a
Lublin_Triangle
extends to the category of geodesic metric spaces, where one can use comparison triangles to quantify the curvature of a space; in this context, non-positively
Non-positive_curvature
Relation between sides of a right triangle
fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the
Pythagorean_theorem
Architecture features MOperations/s MPixels/s MTexels/s MTri/s GRays/s (triangles) GRays/s (voxels or boxes) TOPS (INT8) TOPS (INT4) Size (MiB) Clock (MHz)
List of AMD graphics processing units
List_of_AMD_graphics_processing_units
Subtractive color model used in printing
Comparison of printing separations: CMY (left) vs CMYK (right).
CMYK_color_model
Triangular motif formed of three interlaced arcs or loops
triquetra bears a resemblance to the valknut, a design of three interlacing triangles, found in the same context. The triquetra is often found in insular art
Triquetra
footwear industry Comparison of 3D computer graphics software Comparison of CAD, CAM, and CAE file viewers Comparison of EDA software Comparison of free software
Comparison of computer-aided design software
Comparison_of_computer-aided_design_software
Circumellipse of a triangle whose center is the triangle's centroid
By comparison the circumcircle of a triangle is another circumconic that touches the triangle at its vertices, but is not centered at the triangle's centroid
Steiner_ellipse
Pattern of stars in the Northern Hemisphere
The Spring Triangle is an astronomical asterism involving an imaginary triangle drawn upon the celestial sphere, with its defining vertices at Arcturus
Spring_Triangle
Polygonal curve made from right triangles
composed of right triangles, placed edge-to-edge. It was named after Theodorus of Cyrene. The spiral is started with an isosceles right triangle, with each leg
Spiral_of_Theodorus
Rivalries Rosters TV shows Wrestling families Related topics Combat sport Comparison of professional wrestling and mixed martial arts Martial arts Mock combat
2025 in professional wrestling
2025_in_professional_wrestling
Interpolation method in computer graphics
used to achieve continuous lighting on triangle meshes by computing the lighting at the corners of each triangle and linearly interpolating the resulting
Gouraud_shading
Geometric shape
that further includes all the interior points. By Thales' theorem, any triangle inscribed in a semicircle with a vertex at each of the endpoints of the
Semicircle
geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain
List_of_triangle_inequalities
1893 painting by Franz Stuck
its half-visible breasts. Nipples and navel form a downward stretched triangle with their points in the composition of the painting. An enlarged dark
The_Sin_(Stuck)
Relationship between two figures of the same shape and size, or mirroring each other
the two triangles. Sufficient evidence for congruence between two triangles in Euclidean space can be shown through the following comparisons: SAS (side-angle-side):
Congruence_(geometry)
Type of metric geometry
satisfied as in general triangles with two taxicab-congruent sides and a taxicab-congruent angle between them are not congruent triangles. In any metric space
Taxicab_geometry
Vector distance function
same formula does not define a metric because it fails to satisfy the triangle inequality. For example, distance between ( 0 , 0 ) {\displaystyle (0,0)}
Minkowski_distance
Shape that is the intersection of two circles with the same radius
isogonic centers of a triangle are the intersections of three vesicae piscis whose paired vertices are the vertices of the triangle Comparison of associated Reuleaux
Vesica_piscis
Region of the body between the genitals and anus
into two triangles: The anterior urogenital triangle contains the penis and scrotum (males) or vulva (females) The posterior anal triangle contains the
Perineum
American musician (born 2003)
noted for its blend of indie pop and alternative R&B, often drawing comparisons to artists like Steve Lacy and Dominic Fike. Malcolm Todd Hobert was
Malcolm_Todd_(musician)
Quadrilateral with two pairs of parallel sides
orange triangles. The area of the rectangle is K rect = ( B + A ) × H {\displaystyle K_{\text{rect}}=(B+A)\times H\,} and the area of a single triangle is
Parallelogram
Length of a line segment
} This can be seen by applying the Pythagorean theorem to a right triangle with horizontal and vertical sides, having the line segment from p {\displaystyle
Euclidean_distance
1989 NES game
Brett Alan Weiss (AllGame) put Cobra Triangle in the lineage of the 1982 River Raid for the Atari 2600. In comparison, both games have vehicular boat combat
Cobra_Triangle
Similarity measure for number sequences
exhibit the triangle inequality property — or, more formally, the Schwarz inequality — and it violates the coincidence axiom. To repair the triangle inequality
Cosine_similarity
Mathematical space with a notion of distance
from y to x: d ( x , y ) = d ( y , x ) {\displaystyle d(x,y)=d(y,x)} The triangle inequality holds: d ( x , z ) ≤ d ( x , y ) + d ( y , z ) {\displaystyle
Metric_space
Geographic region in southern Alberta and Saskatchewan
Palliser's Triangle (French: Triangle de Palliser), or the Palliser Triangle, is a semi-arid steppe occupying a substantial portion of the Canadian Prairies
Palliser's_Triangle
Mathematical metric
Comparison of Chebyshev, Euclidean and Manhattan ('taxicab') distances for the hypotenuse of a 3-4-5 triangle on a chessboard
Chebyshev_distance
Encyclopædia describes the style of the Cook Islands, a pattern formed by small triangles and squares entirely covering a surface and sometimes varied by a band
History_of_wood_carving
Body hair in the genital region
Triangle or American wax (pubic hair is shortened from the sides to form a triangle so that pubic hair is hidden while wearing swimwear. The triangle
Pubic_hair
Reading a text on a computer or smart device screen
and was dubbed the Google Golden Triangle. A 2014 Meditative blog showed evidence of the decline of the Golden Triangle phenomenon since 2005 as users view
Screen_reading
2009 studio album by Perfume
Triangle (published as ⊿) is the second studio album by Japanese girl group Perfume. It was released on July 8, 2009, through Tokuma Japan. Triangle builds
Triangle_(Perfume_album)
Fictional video game character
Thing" (レッドピラミッドシング, Reddo Piramiddo Shingu), "Red Triangle Head" (赤い三角頭, Akai Sankakutō) or "Triangle Head" (三角頭, Sankakuatama), is a character from the
Pyramid_Head
Affluent area of southeast England
d'Abernon at the southern corner of the triangle in 2007. This has brought it into comparison with other "golden triangles" such as that of Cheshire, which many
Golden_Triangle_(Surrey)
1618–1651 theater of war
JSTOR 41559848. "Intelligence-gathering" episodes in the "Manila-Macao-Taiwan Triangle" during the Dutch Wars". scholar.google.com. Retrieved 2025-12-17. Villiers
Thirty Years' War outside Europe
Thirty_Years'_War_outside_Europe
Relationship between two numbers of the same kind
meaning by themselves), a triangle analysis using barycentric or trilinear coordinates applies regardless of the size of the triangle. Cross ratio Dilution
Ratio
Possessiveness and inability to accept disinterest or rejection
relationship Intimacy Limerence Love addiction Love at first sight Love triangle Lovesickness Lovestruck Obsessive love Parental love Passion Passionate
Obsessive_love
War Post Second Comparison of Nazism and Stalinism Totalitarianism Pro-Americanism Pro-ROC sentiment Red Scare Red-baiting Red triangle U.S. policy towards
Anti–North_Korean_sentiment
Paper size of 8.5 by 11 inches
Letter paper tiled with almost equilateral triangles. (Perfectly equilateral triangles require the aspect ratio to be 3⁄4√3 ≈ 1.299.)
Letter_(paper_size)
Species of sea snail
vivid pearlescent interior. This marine species is found within the Coral Triangle in the tropical Western Pacific. Known populations are located off: The
Calliostoma_vilvensi
Tabular arrangement of the chemical elements
as spirals (Otto Theodor Benfey's pictured to the right), circles and triangles. Alternative periodic tables are often developed to highlight or emphasize
Periodic_table
Part of the body between the chest and pelvis
Side-by-side comparison of quadrants and regions
Abdomen
Type of microscope
A comparison microscope is a device used to analyze side-by-side specimens. It consists of two microscopes connected by an optical bridge, which results
Comparison_microscope
Non-Euclidean geometry
Euclidean plane geometry. For example, the sum of the interior angles of any triangle is always greater than 180°. Elliptic geometry may be derived from spherical
Elliptic_geometry
GPL, BSD, Creative Commons, zlib, MIT, Artistic License or other (see Comparison of free and open-source software licenses). Only the game engines in this
List of commercial video games with later released source code
List_of_commercial_video_games_with_later_released_source_code
Triangulation method
triangulation of a set of points in the plane subdivides their convex hull into triangles whose circumcircles do not contain any of the points; that is, each circumcircle
Delaunay_triangulation
Polyhedron with four faces
the base to a common point. In the case of a tetrahedron, the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is
Tetrahedron
History of the quarter of the Neukölln borough in Berlin, Germany
Klein-Beirut (Little Beirut); Sa′ed Atshan, Katharina Galor, The Moral Triangle: Germans, Israelis, Palestinians, Durham 2020, p. 131; Gunda Bartels, "
History_of_Neukölln
the Play for Today series on BBC1. 5 January – Debut of the BBC1 soap Triangle, a twice-weekly series set aboard a North Sea ferry, and filmed on location
Timeline_of_BBC_One
Canadian retail loyalty program
form introduced as Canadian Tire Money Advantage, rebranded in 2018 as Triangle Rewards. Issuance of paper Canadian Tire Money ended in 2020. Canadian
Canadian_Tire_money
Prime Minister of India since 2014
University Press. ISBN 978-1-78738-294-7. Madan, Tanvi (2020). Fateful Triangle: How China Shaped US-India Relations During the Cold War. Penguin Random
Narendra_Modi
the genuine one is much denser and heavier. According to Incredible Comparisons (©1996) by Russell Ash, gold has a density of roughly 11 ounces per cubic
List of The Patty Duke Show episodes
List_of_The_Patty_Duke_Show_episodes
Future airport in Badgerys Creek, New South Wales, Australia
acquired an adjacent 1.363-hectare (3.37-acre) portion of the Leppington Triangle for A$149,000; a land value 22 times less per hectare than that paid by
Western_Sydney_Airport
Female genital piercing
Clitoris Clitoral hood Fourchette Isabella Labia Nefertiti Princess Albertina Triangle Male genital piercings Ampallang Apadravya Deep shaft Dydoe Fibula Foreskin
Labia_piercing
confer (cf.) compare The abbreviation cf. is used in text to suggest a comparison with something else (cf. citation signal). Congregatio Sanctissimi Redemptoris
List_of_Latin_phrases_(full)
Algorithm for generating contour lines on a 2D scalar field
individual numerical values). A similar method can be used to contour 2D triangle meshes. The contours can be of two kinds: Isolines – lines following a
Marching_squares
1954 U.S. law criminalizing membership in communist organizations and supporting them
War Post Second Comparison of Nazism and Stalinism Totalitarianism Pro-Americanism Pro-ROC sentiment Red Scare Red-baiting Red triangle U.S. policy towards
Communist_Control_Act_of_1954
2001 film by Joel Gallen
life in 2018". YouTube. September 23, 2018. "Not another Teen Movie (Comparison: Theatrical Cut and Unrated Director's Cut)". movie-censorship.com. May
Not_Another_Teen_Movie
Operation in computer graphics
Lighting Global illumination Hidden-surface determination Polygon mesh (Triangle mesh) Shading Deferred Surface triangulation Wire-frame model Concepts
Alpha_compositing
Brand by Alfa Romeo
vehicles. The logo consists of a green four-leaf clover contained in a triangle. The four-leaf clover symbol appeared for the first time on one of the
Alfa_Romeo_Quadrifoglio
Leader of China since 2012
and became governor a year later. Xi proposed the concept of the Golden Triangle at Min River (Chinese: 闽江口金三角经济圈) and oversaw the construction of the Fuzhou
Xi_Jinping
American mixed martial artist (born 1987)
past the first two rounds, with Tate surviving an armbar attempt and a triangle attempt, Rousey finally submitted Tate via armbar in the third round to
Ronda_Rousey
South Korean cultural term for a trio of actresses
Korean media coverage discussing celebrity branding and generational comparisons. Media outlets have drawn parallels between this grouping and the "1970s
Tae-Hye-Ji
Polyhedral compromise map projection
(modeled as a sphere), and then the scale diminishes toward the middle of the triangle. The transformation process was formally mathematically defined in 1978
Dymaxion_map
Scholars debate whether this originated from a core area—often the "Golden Triangle" (northern Levant, northern Jezirah, southeastern Anatolia)—or through
Neolithic_in_the_Near_East
American actress (born 1949)
(also 1982), portraying a Polish survivor of Auschwitz caught in a love triangle between a young naïve writer (Peter MacNicol) and a Jewish intellectual
Meryl_Streep
Characteristic of human females
Nam YJ, "Comparison of body shape between USA and Korean women: {Hourglass, Bottom Hourglass, Top Hourglass, Spoon, Triangle, Inverted Triangle, Rectangle}"
Female_body_shape
Number divisible only by 1 and itself
two-dimensional grid so that no three are in a line, or so that every triangle formed by three of the points has large area. Another example is Eisenstein's
Prime_number
2025 video game
The Verge complimented that the battles were not like Fire Emblem or Triangle Strategy and had unique gameplay that "fills the gaping hole Fire Emblem
The Hundred Line: Last Defense Academy
The_Hundred_Line:_Last_Defense_Academy
indicator tube, 21 mmCH, top-viewing, showing a vertical line, a circle, a triangle and a three-winged star, for use in industrial control panels Z510M – 0
List of Mullard–Philips vacuum tubes
List_of_Mullard–Philips_vacuum_tubes
British television series
"engrossing" and "tremendous fun to watch", awarding it three stars and noting comparisons to Disney+ series Rivals. Charlotte O'Sullivan of The Independent, in
A Woman of Substance (2026 TV series)
A_Woman_of_Substance_(2026_TV_series)
Proposed U.S. bill
War Post Second Comparison of Nazism and Stalinism Totalitarianism Pro-Americanism Pro-ROC sentiment Red Scare Red-baiting Red triangle U.S. policy towards
Crucial Communism Teaching Act
Crucial_Communism_Teaching_Act
General elections in the United States
Campaign finance Citizens United v. FEC Lobbying Political corruption Iron triangle Super PACs Corporate personhood Dark money United States portal Politics
United States midterm election
United_States_midterm_election
Technique employed in sensory analysis
known, two unknown, test is which unknown is the known (X = A or Y = A) Triangle (XXY) – three unknowns, test is which is odd one out (Y = 1, Y = 2, or
Discrimination_testing
Portuguese football manager (born 1963)
Chelsea win Premier League titles. Mourinho explained: Look, if I have a triangle in midfield – Claude Makélélé behind and two others just in front – I will
José_Mourinho
Office skyscraper in Manhattan, New York
building. The mural's Art Deco style is manifested in characteristic triangles, sharp angles, slightly curved lines, chrome ornaments, and numerous patterns
Chrysler_Building
Special HTML tag
several different types of shapes...</p> <section> <h4>Triangles</h4> <p>Here is some info about triangles</p> </section> <section> <h4>Circles</h4> <p>These
Article_element
2025: Transmettre, tout simplement". "Music, Moods, Wanderlust and the Triangle of Peace: Interview with Clarisse Albrecht – Afropean: Your guide to the
List of artists influenced by Michael Jackson
List_of_artists_influenced_by_Michael_Jackson
The flag's design incorporates core Masonic elements: the equilateral triangle,representing equality and the Masonic trinity of liberty, fraternity, and
Freemasonry_in_Cuba
Relation between the side lengths and altitude of a right triangle
is as follows: Let A, B be the endpoints of the hypotenuse of a right triangle △ABC. Let D be the foot of a perpendicular dropped from C, the vertex of
Inverse_Pythagorean_theorem
Concept in geometry
of n equal triangles with height h and base s, thus equals nhs/2. But since h < r and ns < c, the polygon area must be less than the triangle area, cr/2
Area_of_a_circle
Comparison used by AIDS activists
by AIDS activists to compare the AIDS epidemic to the Holocaust. The comparison was popularized by Larry Kramer and ACT-UP, especially the organization's
AIDS–Holocaust_metaphor
Greek philosopher (c. 570 – c. 495 BC)
[citation needed] a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the
Pythagoras
COMPARISON TRIANGLE
COMPARISON TRIANGLE
Boy/Male
Tamil
Without comparison
Girl/Female
Tamil
Comparison
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
Example; Comparison; Respectful; Brilliant
Girl/Female
Indian, Telugu
Compassion
Boy/Male
Hindu, Indian, Marathi, Punjabi, Sikh, Telugu
Compassion
Boy/Male
Arabic American Muslim
Companion.
Girl/Female
Muslim
Companion
Boy/Male
Gujarati, Indian
Compassion
Girl/Female
American, British, English, Latin
Compassion
Boy/Male
Arabic American
Companion.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Without Comparison
Girl/Female
Indian
Compassion.
Girl/Female
African, Indian, Swahili
Compassion
Boy/Male
Arabic American
Companion.
Girl/Female
Arabic
Compassion
Boy/Male
Hindu, Indian
Compassion
Boy/Male
Bengali, Celebrity, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sindhi, Telugu
Without Comparison; Incomparable; Unique
Boy/Male
Tamil
Compassion
Girl/Female
Gujarati, Indian, Kannada, Tamil
Compassion
Girl/Female
Hindu
Comparison
COMPARISON TRIANGLE
COMPARISON TRIANGLE
Girl/Female
Hindu, Indian
Slowly
Boy/Male
Tamil
An ancient king
Boy/Male
British, English
Violent
Girl/Female
Indian
Guardian
Boy/Male
Tamil
The God of silence
Girl/Female
Gaelic
Thin.
Girl/Female
Tamil
Dispeller of ignorance
Boy/Male
Hindu, Indian
Virtuous; Excellent
Boy/Male
Indian, Sanskrit
The Fulfiller of Desires
Boy/Male
Gaelic American Celtic Irish English Anglo Saxon
Servant.
COMPARISON TRIANGLE
COMPARISON TRIANGLE
COMPARISON TRIANGLE
COMPARISON TRIANGLE
COMPARISON TRIANGLE
n.
The state of being compared; a relative estimate; also, a state, quality, or relation, admitting of being compared; as, to bring a thing into comparison with another; there is no comparison between them.
n.
A wooden hood or penthouse covering the companion way; a companion hatch.
n.
The modification, by inflection or otherwise, which the adjective and adverb undergo to denote degrees of quality or quantity; as, little, less, least, are examples of comparison.
n.
A comparison; parable; proverb.
n.
The faculty of the reflective group which is supposed to perceive resemblances and contrasts.
n.
Illustration by comparison; simile.
v. t.
To qualify as a companion; to make equal.
v. t.
To be a companion to; to attend on; to accompany.
n.
Similitude; comparison.
n.
The act of comparing; an examination of two or more objects with the view of discovering the resemblances or differences; relative estimate.
n.
Mutual comparison of corresponding parts.
n.
Comparison.
a.
Of or pertaining to comparison.
n.
A figure by which one person or thing is compared to another, or the two are considered with regard to some property or quality, which is common to them both; e.g., the lake sparkled like a jewel.
n.
Comparison or illustration by contraries.
v. i.
To be equal; to hold comparison.
n.
A knight of the lowest rank in certain orders; as, a companion of the Bath.
n.
A comparison; a simile.
n.
That to which, or with which, a thing is compared, as being equal or like; illustration; similitude.
v. t.
To compare.