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In geometry, a set of lines is called equiangular if all the lines intersect at a single point, and every pair of lines makes the same angle. Computing
Equiangular_lines
Polygon with equally angled vertices
angles θ. An equiangular polygon can be constructed from a regular polygon or regular star polygon where edges are extended as infinite lines. Each edges
Equiangular_polygon
Topics referred to by the same term
Look up equiangular in Wiktionary, the free dictionary. Equiangular may refer to: Equiangular lines, a set of lines where every pair of lines makes the
Equiangular
two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite
Two-graph
Natural number
seven-dimensional vectors have a cross product, and the number of equiangular lines possible in seven-dimensional space is anomalously large. The lowest
7
Natural number
.. 276 is the size of the largest set of equiangular lines in 23 dimensions. The maximal set of such lines, derived from the Leech lattice, provides
276_(number)
Natural number
symmetry group of the largest possible set of equiangular lines in 22 dimensions, which contains 176 lines. "Sloane's A005153 : Practical numbers". The
176_(number)
Quadrilateral with four right angles
with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°);
Rectangle
Self-similar growth curve
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic
Logarithmic_spiral
Describing a family of graphs by excluding certain (sub)graphs
Subgraphs for Graphs of Bounded Spectral Radius, with Applications to Equiangular Lines". Israel Journal of Mathematics. 236 (1): 393–421. arXiv:1708.02317
Forbidden graph characterization
Forbidden_graph_characterization
Type of measurement in quantum mechanics
Bibcode:2010JMP....51d2203S. doi:10.1063/1.3374022. S2CID 115159554. TY Chien. Equiangular lines, projective symmetries and nice error frames. PhD thesis University
SIC-POVM
Award for advancements in discrete mathematics
Jiang, Jonathan Tidor, Yuan Yao, Shengtong Zhang, and Yufei Zhao for Equiangular lines with a fixed angle Nathan Keller and Noam Lifshitz for The junta method
Fulkerson_Prize
Probability distribution in quantum mechanics
|X|\leq \dim(\operatorname {Hom} (U(d),s,s-1))} Spherical design Equiangular lines Welch bounds Dankert, Christoph; Cleve, Richard; Emerson, Joseph;
Quantum_t-design
Theorem on equilateral triangles
necessarily have opposite sides parallel. If a polygon is regular (both equiangular and equilateral), the sum of the distances to the sides from an interior
Viviani's_theorem
Shape with three equal sides
the median and angle bisector being equal in length, considering those lines as their altitude depending on the base's choice. The equilateral triangle
Equilateral_triangle
{\displaystyle \mathbb {CP} ^{n-1}} . Spherical design Quantum t-design Equiangular lines Welch, L. (1974-05-01). "Lower bounds on the maximum cross correlation
Welch_bounds
spherical 2-designs exist. Maximally sized collections of equiangular lines (up to identification of lines as antipodal points on the sphere) are examples of
Spherical_design
_{\text{min}}}{90}}\right]}} Another common measure of quality is based on equiangular skew. Equiangle Skew = max [ θ max − θ e 180 − θ e , θ e − θ min θ
Types_of_mesh
Time-telling device
better by a watch. A dial is said to be equiangular if its hour-lines are straight and spaced equally. Most equiangular sundials have a fixed gnomon style
Sundial
as SIC-POVMs or SICs, which correspond to maximal sets of complex equiangular lines. Some of the known SICs—those in vector spaces of 2 and 3 dimensions
Exceptional_object
Arc crossing all meridians of longitude at the same angle
the two edges. On a stereographic projection map, a loxodrome is an equiangular spiral whose center is the north or south pole. All loxodromes spiral
Rhumb_line
Plane figure bounded by line segments
star-shaped. Equiangular: all corner angles are equal. Equilateral: all edges are of the same length. Regular: both equilateral and equiangular. Cyclic: all
Polygon
(Tetrad) Greek school of Pythagoreanism The tetractys is an equidistant and equiangular arrangement of ten points inside a triangle, akin to the fourth triangle
List_of_occult_symbols
Book by the Scottish D'Arcy Wentworth Thompson 1917
logarithmic spiral, which has the property of never changing its shape: it is equiangular and is continually self-similar. Shells as diverse as Haliotis, Triton
On_Growth_and_Form
Shape with six sides
regular hexagon is defined as a hexagon that is both equilateral and equiangular. Its internal angle is one-third of a circle, equal to 120°. The Schläfli
Hexagon
Mathematical symbol of equality
left-hand side is an estimator for the right-hand side) ≚ (U+225A ≚ EQUIANGULAR TO) ≛ (U+225B ≛ STAR EQUALS) ≜ (U+225C ≜ DELTA EQUAL TO) (used to define
Equals_sign
Points on a common circle
p. 77, ISBN 9780883857632. De Villiers, Michael (March 2011). "95.14 Equiangular cyclic and equilateral circumscribed polygons". The Mathematical Gazette
Concyclic_points
Four-sided polygon
that is not a rhombus. Rectangle: all four angles are right angles (equiangular). An equivalent condition is that the diagonals bisect each other, and
Quadrilateral
Regular non-convex polygon
stars. A regular star polygon is a self-intersecting, equilateral, and equiangular polygon. A regular star polygon is denoted by its Schläfli symbol {p/q}
Star_polygon
Cyclic polygon Equiangular polygon Equilateral polygon Regular polygon Penrose tile Polyform Balbis Gnomon Golygon Star without crossing lines Star polygon
List_of_mathematical_shapes
Shape with five sides
pentagon is unique up to similarity, because it is equilateral and it is equiangular (its five angles are equal). A cyclic pentagon is one for which a circle
Pentagon
If and only if relation
not mean that P and Q need to have the same meaning (e.g., P could be "equiangular trilateral" and Q could be "equilateral triangle"). When phrased as a
Logical_biconditional
Quadrilateral symmetric across a diagonal
opposite sides are equal). All equilateral kites are rhombi, and all equiangular kites are squares. When classified partitionally, rhombi and squares
Kite_(geometry)
Plane spiral projected onto the surface of a cone
constant!}}} ). Because of this property a conchospiral is called an equiangular conical spiral. The length of an arc of a conical spiral can be determined
Conical_spiral
Special orthogonal group
just two, and all half-lines from O are displaced through the same angle. Such rotations are called isoclinic or equiangular rotations, or Clifford displacements
Rotations in 4-dimensional Euclidean space
Rotations_in_4-dimensional_Euclidean_space
Property of objects which are scaled or mirrored versions of each other
proportional. It can be shown that two triangles having congruent angles (equiangular triangles) are similar, that is, the corresponding sides can be proved
Similarity_(geometry)
Polygon whose four sides all touch a circle
(PDF) on 2013-06-16, retrieved 2012-05-09. De Villiers, Michael (2011), "Equiangular cyclic and equilateral circumscribed polygons", Mathematical Gazette
Tangential_quadrilateral
Visible regularity of form found in the natural world
Trochoidea liebetruti Water droplets fly off a wet, spinning ball in equiangular spirals In mathematics, a dynamical system is chaotic if it is (highly)
Patterns_in_nature
4th-century Greek mathematician (c. 290–350)
Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method
Pappus_of_Alexandria
Machine that uses steam to rotate a shaft
_{1}-\rho ^{2}\right)(1+kc)={\frac {1}{2}}\cos ^{2}\alpha _{1}(1+kc)} . For equiangular blades, β 1 = β 2 {\displaystyle \beta _{1}=\beta _{2}} , therefore c
Steam_turbine
Process of projecting a 3D object onto a 2D plane
and does not represent what the eye actually sees: in particular parallel lines remain parallel and distant objects are not reduced in size. It can be considered
Axonometry
Wide-angle photographic lens with strong barrel distortion
proven useful for scientific purposes because of their equidistant (equiangular) projection, in which distance along the radius of the circular image
Fisheye_lens
Peerless Brass to meet customer demand. A horizontal dial, takes the equiangular hour lines of an equatorial dial and projects them onto a plane oblique to
London_dial
Digital 3D representation of the outcrop surface
additional mesh editing and optimization is often required to improve equiangularity, solve topology problems or reorient inverted surface normals. Image
Digital_outcrop_model
Canadian mathematician
274–276. doi:10.1006/jctb.1999.1938. D. De Caen (2000). "Large Equiangular Sets of Lines in Euclidean Space". The Electronic Journal of Combinatorics.
Dominique_de_Caen
EQUIANGULAR LINES
EQUIANGULAR LINES
Girl/Female
Indian, Tamil
Music Lines; Lyrics
Girl/Female
Indian
Lines of Short Poem
Girl/Female
Tamil
Padmarekha | பதà¯à®®à®°à¯‡à®•à®¾
Lotus like lines on palm
Padmarekha | பதà¯à®®à®°à¯‡à®•à®¾
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lotus-like Lines on Palm
Surname or Lastname
English
English : metronymic from Line.
Boy/Male
Arabic, Muslim, Pashtun
Piercing Lines; Fighter
Girl/Female
Hindu, Indian, Malayalam, Marathi
Three Lines
Girl/Female
Tamil
Gunrekha | கà¯à®¨à¯à®°à¯‡à®•à®¾
Useful lines of life
Gunrekha | கà¯à®¨à¯à®°à¯‡à®•à®¾
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from any of various places, for example in Aisne and Calvados, so called from Old French pierre ‘stone’ + pont ‘bridge’.All the New England Pierpont lines seem to be descended from James and his sons John and Robert, who came to America about 1640. James also may have had a brother Robert who was part of that group. The southern Pierpo(i)nt family are descended from Henry, who came to the VA–MD region in 1635.
Boy/Male
Hindu, Indian, Jain, Marathi, Sanskrit, Sindhi, Tamil
Lines on Any Particular Raaga from Sanskrit; Permutations and Combinations of Parents; Aarya Cost King Ashoka's Birth
Surname or Lastname
English
English : habitational name from any of various places, for example in Derbyshire, Dorset, and Suffolk, so called from Old English hol ‘hollow’, ‘sunken’ + brÅc ‘stream’. The name has probably absorbed the Dutch surname van Hoobroek, found in London in the early 17th century, and possibly a similar Low German surname (Holbrock or Halbrock). Several American bearers of the name in the 1880 census give their place of birth as Oldenburg or Hannover, Germany.This name was first taken to America by the brothers Thomas and John Holbrook, who emigrated to MA in the 17th century; their line can be traced back to Dundry, Somerset, England, in the first half of the 16th century. Other English bearers who started early lines of descent in the New World are Joseph Ho(u)lbrook of Warrington, Lancashire, who emigrated to MD as an indentured servant in the later 17th century; Randolph Holbrook, who was in VA in the 1720s but later returned to Nantwich, Cheshire; and Rev. John Holbrook, who emigrated from Handbury, Staffordshire, to NJ in about 1723. The spelling Haulbrook originated in GA in the 1870s, reflecting the southern U.S. pronunciation of the name.
Girl/Female
Indian
Useful lines of life
Boy/Male
Indian
Poetic Lines
Girl/Female
Indian, Marathi
Lines in Vedic Verse or Shloka
EQUIANGULAR LINES
EQUIANGULAR LINES
Girl/Female
African, American, Arabic, Bengali, Gujarati, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Oriya, Russian, Sanskrit, Sindhi, Swedish, Tamil, Telugu
Inexhaustible; Gracious; Graceful; Resurrection; Favour; Form of Anna; Beautiful; Something Unexpected; Grace of God
Boy/Male
Hindu
Beloved
Surname or Lastname
English
English : southwestern dialect variant of Bridge, from a metathesized form of Old English brycg. Compare Burge.
Girl/Female
Russian
Grace.
Girl/Female
Indian
Break of dawn
Girl/Female
Spanish
Fruitful orchard' as Mount Carmel in Palestine.
Girl/Female
Australian, British, Christian, English, Latin
Precious; A Gem of the Sea
Girl/Female
Muslim
Smiling
Girl/Female
Bengali, Hindu, Indian, Marathi, Sanskrit
Holy Leaf Offered to Lord Shiva; Auspicious Fruit; A Sacred Leaf
Boy/Male
Arabic, French
Helper
EQUIANGULAR LINES
EQUIANGULAR LINES
EQUIANGULAR LINES
EQUIANGULAR LINES
EQUIANGULAR LINES
n.
A short poem or stanza of eight lines, in which the first line is repeated as the fourth and again as the seventh line, the second being, repeated as the eighth.
a.
Equiangular.
a.
Having equal angles; equiangular.
v. t.
An appearance of diagonal lines or ribs produced in textile fabrics by causing the weft threads to pass over one and under two, or over one and under three or more, warp threads, instead of over one and under the next in regular succession, as in plain weaving.
v. t.
To form or work, as by inlaying, with irregular lines or impressions resembling the tracks of worms, or appearing as if formed by the motion of worms.
n.
The point in any figure opposite to, and farthest from, the base; the terminating point of some particular line or lines in a figure or a curve; the top, or the point opposite the base.
a.
Waving or wavy; -- applied to ordinaries, or division lines.
a.
Of, pertaining to, or included by, three lines; as, trilinear coordinates.
n.
The color green, represented in a drawing or engraving by parallel lines sloping downward toward the right.
v. i.
To weave, as cloth, so as to produce the appearance of diagonal lines or ribs on the surface.
prep.
A large and handsome American butterfly (Basilarchia, / Limenitis, archippus). Its wings are orange-red, with black lines along the nervures and a row of white spots along the outer margins. The larvae feed on willow, poplar, and apple trees.
a.
Made or marked with irregular wavy lines or impressions; vermiculate.
a.
Wormlike in shape; covered with wormlike elevations; marked with irregular fine lines of color, or with irregular wavy impressed lines like worm tracks; as, a vermiculate nut.
a.
Not ruled or marked with lines; as, unruled paper.
n.
A figure bounded by three lines, and containing three angles.
v. i.
To ascend in spiral lines about a support; to climb spirally; as, many plants twine.
a.
Having equal angles; as, an equiangular figure; a square is equiangular.
n.
An ancient French song, or short poem, wholly in two rhymes, and composed in short lines, with a refrain.