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67 relations: Altitude (triangle), Angle, Angle trisection, Apothem, Archaeological site, Area, Barrow's inequality, Bisection, Centroid, Cevian, Circumscribed circle, Compass-and-straightedge construction, Complex plane, Congruence (geometry), Dihedral group, Dihedral group of order 6, Equiangular polygon, Erdős–Mordell inequality, Euclid's Elements, Euclidean geometry, Euclidean tilings by convex regular polygons, Euler line, Euler's theorem in geometry, Fermat number, Flag of Junqueirópolis, Flag of Nicaragua, Flag of the Philippines, Gateway Arch National Park, Geometry, If and only if, Incircle and excircles of a triangle, Integer triangle, Isoperimetric inequality, Isosceles triangle, Lepenski Vir, List of triangle inequalities, Median (geometry), Morley's trisector theorem, Nagel point, Napoleon's theorem, Optic equation, Perimeter, Platonic solid, Polyhedron, Pompeiu's theorem, Pythagorean theorem, Randhurst Village, Reflection symmetry, Regular polygon, Rotational symmetry, ..., Seal of the President of the Philippines, Semiperimeter, Steiner inellipse, Symmetry group, Tau Kappa Epsilon, Ternary plot, Tetrahedron, Traffic sign, Triangle, Triangle center, Triangle inequality, Triangular tiling, Trigonometry, Vesica piscis, Viviani's theorem, Weitzenböck's inequality, Yield sign. Expand index (17 more) »
Altitude (triangle)
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).
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Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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Angle trisection
Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.
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Apothem
The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides.
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Archaeological site
An archaeological site is a place (or group of physical sites) in which evidence of past activity is preserved (either prehistoric or historic or contemporary), and which has been, or may be, investigated using the discipline of archaeology and represents a part of the archaeological record.
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Area
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
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Barrow's inequality
In geometry, Barrow's inequality is an inequality relating the distances between an arbitrary point within a triangle, the vertices of the triangle, and certain points on the sides of the triangle.
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Bisection
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
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Centroid
In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape.
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Cevian
In geometry, a cevian is any line segment in a triangle with one endpoint on a vertex of the triangle and the other endpoint on the opposite side.
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Circumscribed circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
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Compass-and-straightedge construction
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Congruence (geometry)
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
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Dihedral group
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
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Dihedral group of order 6
In mathematics, the smallest non-abelian group has 6 elements.
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Equiangular polygon
In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal.
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Erdős–Mordell inequality
In Euclidean geometry, the Erdős–Mordell inequality states that for any triangle ABC and point P inside ABC, the sum of the distances from P to the sides is less than or equal to half of the sum of the distances from P to the vertices.
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Euclid's Elements
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
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Euclidean tilings by convex regular polygons
Euclidean plane tilings by convex regular polygons have been widely used since antiquity.
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Euler line
In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral.
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Euler's theorem in geometry
In geometry, Euler's theorem states that the distance d between the circumcentre and incentre of a triangle is given by.
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Fermat number
In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.
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Flag of Junqueirópolis
The flag of Junqueirópolis (bandeira de Junqueirópolis) is the official flag of the municipality of Junqueirópolis in the western region of the state of São Paulo, Brazil.
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Flag of Nicaragua
The flag of Nicaragua was first adopted on September 4, 1908, but not made official until August 27, 1971.
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Flag of the Philippines
The National Flag of the Philippines (Pambansang Watawat ng Pilipinas) is a horizontal flag bicolor with equal bands of royal blue and scarlet, and with a white, equilateral triangle at the hoist.
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Gateway Arch National Park
The Gateway Arch National Park, formerly known as the Jefferson National Expansion Memorial until 2018, is an American national park located in St. Louis, Missouri, near the starting point of the Lewis and Clark Expedition.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Incircle and excircles of a triangle
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.
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Integer triangle
An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers.
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Isoperimetric inequality
In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume.
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Isosceles triangle
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
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Lepenski Vir
Lepenski Vir (Лепенски Вир, "Lepena Whirlpool"), located in Serbia, is an important archaeological site of the Mesolithic Iron Gates culture of the Balkans.
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List of triangle inequalities
In geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions.
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Median (geometry)
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
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Morley's trisector theorem
In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle.
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Nagel point
In geometry, the Nagel point is a triangle center, one of the points associated with a given triangle whose definition does not depend on the placement or scale of the triangle.
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Napoleon's theorem
In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the centres of those equilateral triangles themselves form an equilateral triangle.
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Optic equation
In number theory, the optic equationDickson, L. E., History of the Theory of Numbers, Volume II: Diophantine Analysis, Chelsea Publ.
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Perimeter
A perimeter is a path that surrounds a two-dimensional shape.
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Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Pompeiu's theorem
Pompeiu's theorem is a result of plane geometry, discovered by the Romanian mathematician Dimitrie Pompeiu.
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Pythagorean theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
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Randhurst Village
Randhurst Village, previously known as Randhurst Mall and Randhurst Center or simply Randhurst, is a shopping mall located at the corner of Rand Road (U.S. Route 12) and Elmhurst Road (Illinois Route 83) in Mount Prospect, Illinois.
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Reflection symmetry
Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.
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Regular polygon
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
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Rotational symmetry
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.
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Seal of the President of the Philippines
The Seal of the President of the Philippines (Sagisag ng Pangulo ng Pilipinas) is a symbol used to represent the history and dignity of the President of the Philippines.
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Semiperimeter
In geometry, the semiperimeter of a polygon is half its perimeter.
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Steiner inellipse
In geometry, the Steiner inellipse,Weisstein, E. "Steiner Inellipse" — From MathWorld, A Wolfram Web Resource, http://mathworld.wolfram.com/SteinerInellipse.html.
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Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
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Tau Kappa Epsilon
Tau Kappa Epsilon (ΤΚΕ), commonly known as TKE or Teke, is an international all-male secret and social college fraternity founded on January 10, 1899, at Illinois Wesleyan University.
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Ternary plot
A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Traffic sign
Traffic signs or road signs are signs erected at the side of or above roads to give instructions or provide information to road users.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Triangle center
In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, i.e. a point that is in the middle of the figure by some measure.
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Triangle inequality
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 of the remaining side.
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Triangular tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.
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Trigonometry
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.
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Vesica piscis
The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other.
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Viviani's theorem
Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude.
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Weitzenböck's inequality
In mathematics, Weitzenböck's inequality, named after Roland Weitzenböck, states that for a triangle of side lengths a, b, c, and area \Delta, the following inequality holds: Equality occurs if and only if the triangle is equilateral.
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Yield sign
In road transport, a yield or give way sign indicates that each driver must prepare to stop if necessary to let a driver on another approach proceed.
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Redirects here:
Equalangular triangle, Equalateral triangle, Equiangular triangle, Equilateral, Equilateral Triangle, Equilateral Triangles, Equilateral triangles, Regular Triangle, Regular triangle.
References
[1] https://en.wikipedia.org/wiki/Equilateral_triangle
