Circles of Apollonius
The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for exampl ...
Brocard circle
In geometry, the Brocard circle for a triangle is a circle defined from a given triangle. It passes through the circumcenter and symmedian of the triangle, and is centered at the midpoint of the line segment joining them.
Circular sector
A circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle in radians, r {\displ ...
Circular segment
In geometry, a circular segment is a region of a circle which is "cut off" from the rest of the circle by a secant or a chord. More formally, a circular segment is a region of twodimensional space that is bounded by an arc of a circle and by the ...
Extouch triangle
The vertices of the extouch triangle are given in trilinear coordinates by: T A = 0: csc 2 B / 2: csc 2 C / 2 {\displaystyle T_{A}=0:\csc ^{2}{\leftB/2\right}:\csc ^{2}{\leftC/2\right}} T B = csc 2 A / 2: 0: csc 2 C / 2 {\displaystyle T_{ ...
Fuhrmann circle
In geometry, the Fuhrmann circle of a triangle, named after the German Wilhelm Fuhrmann, is the circle with a diameter of the line segment between the orthocenter H {\displaystyle H} and the Nagel point N {\displaystyle N}. This circle is identic ...
Johnson circles
In geometry, a set of Johnson circles comprises three circles of equal radius r sharing one common point of intersection H. In such a configuration the circles usually have a total of four intersections: the common point H that they all share, an ...
Malfatti circles
In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies of the problem of ...
Schinzel circle
Schinzel circles are a set of circles with a given number of integer points on the circumference of the circle. If the number n of points on the circumference of the circle is even, n = 2 k, then a Schinzel circle is given by: x − 1 2 + y 2 = 1 4 ...
Spieker circle
In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19thcentury German geometer Theodor Spieker. Its center, the Spieker center, in addition to being the incenter of the medial triangle, is the cente ...
Tangent circles
In geometry, tangent circles are circles in a common plane that intersect in a single point. There are two types of tangency: internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often h ...
Tangent lines to circles
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circles interior. Tangent lines to circles form the subject of several theorems, and play an important role in many ...
Van Lamoen circle
In Euclidean plane geometry, the van Lamoen circle is a special circle associated with any given triangle T {\displaystyle T}. It contains the circumcenters of the six triangles that are defined inside T {\displaystyle T} by its three medians. Sp ...
Prince Ruperts cube
In geometry, Prince Ruperts cube is the largest cube that can pass through a hole cut through a unit cube, i.e. through a cube whose sides have length 1, without splitting the cube into two pieces. Its side length is approximately 6% larger than ...
5Con triangles
In geometry, two triangles are said to be 5Con or almost congruent if they are not congruent triangles but they are similar triangles and share two side lengths. The 5Con triangles are important examples for understanding the solution of triang ...
Calabi triangle
The Calabi triangle is a special triangle found by Eugenio Calabi and defined by its property of having three different placements for the largest square that it contains. It is an obtuse isosceles triangle with an irrational but algebraic ratio ...
Right triangle
A right triangle or rightangled triangle is a triangle in which one angle is a right angle. The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse s ...
Archimedean circle
In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes twin circles. The radius ρ of such a circle is given by ρ = 1 2 r 1 − r, {\displaystyle \rho ={\frac {1}{2}}r\left1r\righ ...
Archimedes quadruplets
In geometry, Archimedes quadruplets are four congruent circles associated with an arbelos. Introduced by Frank Power in the summer of 1998, each have the same area as Archimedes twin circles, making them Archimedean circles.
Schoch circles
In 1979, Thomas Schoch discovered a dozen new Archimedean circles; he sent his discoveries to Scientific American s "Mathematical Games" editor Martin Gardner. The manuscript was forwarded to Leon Bankoff. Bankoff gave a copy of the manuscript to ...
Schoch line
In geometry, the Schoch line is a line defined from an arbelos and named by Peter Woo after Thomas Schoch, who had studied it in conjunction with the Schoch circles.
Twin circles
In geometry, the twin circles are two special circles associated with an arbelos. An arbelos is determined by three collinear points A, B, and C, and is the curvilinear triangular region between the three semicircles that have AB, BC, and AC as t ...
Straightedge and compass construction
Straightedge and compass construction, also known as rulerandcompass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass. The idealized ruler, kno ...
Compass equivalence theorem
The compass equivalence theorem is an important statement in compass and straightedge constructions. The tool advocated by Plato in these constructions is a divider or collapsing compass, that is, a compass that "collapses" whenever it is lifted ...
360gon
A regular 360gon is represented by Schlafli symbol {360} and also can be constructed as a truncated 180gon, t{180}, or a twicetruncated enneacontagon, tt{90}, or a thricetruncated tetracontapentagon, ttt{45}. One interior angle in a regular 3 ...
Apothem
The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word "apothem" can also refer ...
Bicentric quadrilateral
In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and center of these circles are called inradius and circumradius, and incenter and circumcenter respectively. From ...
Concave polygon
A simple polygon that is not convex is called concave, nonconvex or reentrant. A concave polygon will always have at least one reflex interior angle  that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive. Some l ...
Dual polygon
Regular polygons are selfdual. The dual of an isogonal vertextransitive polygon is an isotoxal edgetransitive polygon. For example, the isogonal rectangle and isotoxal rhombus are duals. In a cyclic polygon, longer sides correspond to larger e ...
Enneacontagon
In geometry, an enneacontagon or enenecontagon or 90gon is a ninetysided polygon. The sum of any enneacontagons interior angles is 15840 degrees. A regular enneacontagon is represented by Schlafli symbol {90} and can be constructed as a truncat ...
Enneadecagon
As 19 is a Pierpont prime but not a Fermat prime, the regular enneadecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or an angle trisector. Another animation of an approximate construction. ...
Equiangular polygon
In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths.
Equilateral pentagon
In geometry an equilateral pentagon is a polygon with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. The requirement is that all angles must add ...
Equilateral polygon
In geometry, three or more than three straight lines make a polygon and an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it doesn’t need to be equiangular, but if it does then it is a regula ...
Extangential quadrilateral
In Euclidean geometry, an extangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral. It has also been called an exscriptible quadrilateral. The circle is called ...
Golygon
A golygon is any polygon with all right angles whose sides are consecutive integer lengths. Golygons were invented and named by Lee Sallows, and popularized by A.K. Dewdney in a 1990 Scientific American column. Variations on the definition of gol ...
Hendecagon
A regular hendecagon is represented by Schlafli symbol {11}. A regular hendecagon has internal angles of 147. 27 degrees =147 3 11 {\displaystyle {\tfrac {3}{11}}} degrees. The area of a regular hendecagon with side length a is given by A = 11 4 ...
Heptacontagon
In geometry, a heptacontagon or 70gon is a seventysided polygon. The sum of any heptacontagons interior angles is 12240 degrees. A regular heptacontagon is represented by Schlafli symbol {70} and can also be constructed as a truncated triaconta ...
Icosidigon
As 22 = 2 × 11, the icosidigon can be constructed by truncating a regular hendecagon. However, the icosidigon is not constructible with a compass and straightedge, since 11 is not a Fermat prime. Consequently, the icosidigon cannot be constructed ...
Icosihexagon
In geometry, an icosihexagon or 26gon is a twentysixsided polygon. The sum of any icosihexagons interior angles is 4320 degrees.
Icosioctagon
In geometry, an icosioctagon or 28gon is a twenty eight sided polygon. The sum of any icosioctagons interior angles is 4680 degrees.
Infinite skew polygon
In geometry, an infinite skew polygon or skew apeirogon is an infinite 2polytope has vertices that are not all colinear. Infinite zigzag skew polygons are 2dimensional infinite skew polygons with vertices alternating between two parallel lines ...
Isosceles trapezoid
In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both ...
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Isothetic polygon 

Lemoine hexagon 

Megagon 

Midpoint polygon 

Midpointstretching polygon 

Myriagon 

Octadecagon 

Parallelogon 

Pentacontagon 

Rectilinear polygon 

Regular polygon 

Simple polygon 

Skew polygon 

Tangential polygon 

Tetracontadigon 

Tetradecagon 

Tridecagon 

Zonogon 
Quadrilaterals 

Ailles rectangle 

Altitude (triangle) 

Automedian triangle 

Brocard points 

Central line (geometry) 

Exsymmedian 

Fuhrmann triangle 

Isogonal conjugate 
Isotomic conjugate 

Lemoines problem 

Mandart inellipse 

Ninepoint hyperbola 

Orthocentric system 

Orthocentroidal circle 

Orthopole 

Pedal triangle 

Polar circle (geometry) 

Semiperimeter 

Simson line 

Splitter (geometry) 

Symmedian 
Thomson cubic 

Trilinear polarity 

Ballbot 
Twowheeled balancing robots 
Threewheeled balancing robots 
Trimer (chemistry) 
Natural phenol trimers 
Natural phenol tetramers 
Central Rook openings 
Double Ranging Rook openings 
Fourth File Rook openings 
Opposing Rook openings 
Static Rook vs Ranging Rook openings 
Third File Rook openings 
Double Static Rook openings 
Fortress openings 

Cayleys sextic 
Coble curve 

Quadrifolium 
Wimans sextic 
Wirtinger sextic 
Spiric sections 
Burkhardt quartic 

Consani–Scholten quintic 
Klein cubic threefold 
Koras–Russell cubic threefold 
Quartic threefold 
Segre cubic 
Algebraic surface 

Barth surface 
Campedelli surface 
Castelnuovo surface 
Castelnuovos contraction theorem 
Catanese surface 

Chatelet surface 

Clebsch surface 
Coble surface 

Cubic surface 
Del Pezzo surface 
Dolgachev surface 

Endrass surface 
Fake projective plane 
Fano surface 
Godeaux surface 
Hilbert modular variety 
Hirzebruch surface 
Horikawa surface 
Hyperelliptic surface 
Irregularity of a surface 

Kummer surface 
Plucker surface 
Quartic surface 
Raynaud surface 

Sarti surface 
Segre surface 
Supersingular K3 surface 
Todorov surface 
Weddle surface 

White surface 
Zeuthen–Segre invariant 
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