Geometry Topics
- 2D
- Having both width and length, but no thickness.
- 3D
- Having length, width, and thickness i.e. space.
- Acute Angle
- A positive angle that is less than 90 degrees.
- Acute Triangle
- A triangle in which all of the angles are less than 90 degrees.
- Adjacent Angles
- Two angles are adjacent if they share a common vertex and have a common side between them.
- Alternate Exterior Angles
- Exterior angles on alternate sides of the transversal ie not on the same parallel line.
- Alternate Interior Angles
- Interior angles on alternate sides of the transversal ie not on the same parallel line.
- Altitude of a Triangle
- The perpendicular segment from a vertex to the line containing the opposite side of a triangle.
- Angle Bisector
- A ray that divides an angle into two congruent angles.
- Angles
- The inclination of one line to another.
- Arc
- Part of a circle.
- Axis of Rotation
- Centre line about which rotation occurs.
- Central Angle
- Angle whose vertex is placed at the center of a circle.
- Cevian
- A line segment extending from a vertex of a triangle to the opposite side.
- Chord
- A line segment that connects two points of a curve or circle.
- Circle
- The set of points equidistant from a given point.
- Complementary Angles
- Two angles whose sum is 90°.
- Concentric Circles
- Circles that have the same center and varying radii.
- Corresponding Angles
- Two angles in the same relative position on two lines when those lines are cut by a transversal.
- Coterminal Angles
- Two angles that have the same terminal side.
- Cube
- A solid figure bounded by 6 congruent squares.
- Cyclic Polygon
- A polygon whose vertices lie on a circle.
- Decagon
- A polygon with ten sides.
- Degree
- A unit describing a plane angle, 1 degree = 1/90 right angle.
- Diagonal
- In a polygon, the line segment joining a vertex with another (non-adjacent) vertex is called a diagonal.
- Dihedral Angle
- The angle formed by two planes meeting in space.
- Dodecagon
- A polygon with 12 sides.
- Dodecahedron
- A solid figure with 12 faces.
- Domino
- Two congruent squares joined along an edge.
- Ellipsoid
- A solid figure whose equation is x2/a2+y2/b2+z2/c2=1.
- Enneagon
- A nine-sided polygon.
- Equiangular Polygon
- A polygon all of whose interior angles are equal.
- Equichordal Point
- A point inside a closed convex curve in the plane is called an equichordal point if all chords through that point have the same length.
- Equilateral Polygon
- A polygon all of whose sides are equal.
- Equilateral Triangle
- A triangle with three equal sides.
- Escribed Circle
- An escribed circle of a triangle is a circle tangent to one side of the triangle and to the extensions of the other sides.
- Euler Line
- The Euler line of a triangle is the line connecting the centroid and the circumcentre.
- Excentre
- The centre of an excircle.
- Excircle
- An escribed circle of a triangle.
- Face Angle
- The plane angle formed by adjacent edges of a polygonal angle in space.
- Fermat′s Spiral
- A parabolic spiral.
- Focal Chord
- A chord of a conic that passes through a focus.
- Focal Radius
- A line segment from the focus of an ellipse to a point on the perimeter of the ellipse.
- Foot of Altitude
- The intersection of an altitude of a triangle with the base to which it is drawn.
- Foot of Line
- The point of intersection of a line with a line or plane.
- Frustum
- For a given solid figure, a related figure formed by two parallel planes meeting the given solid. For a cone or pyramid, a frustum is determined by the plane of the base and a plane parallel to the base.
- Geometry Books
- Lists all Books in the Encyclopaedia
- Geometry Calculations
- Lists all Calculations in the Encyclopaedia
- Geometry Conversions
- Lists all Conversions in the Encyclopaedia
- Geometry Weblinks
- Lists all Weblinks in the Encyclopaedia
- Great Circle
- A circle on the surface of a sphere whose centre is the centre of the sphere.
- Half Plane
- The part of a plane that lies on one side of a given line.
- Helical
- Having the shape of a helix, or screw.
- Helix
- A path formed as a point advances uniformly around a cylinder, as the thread on a screw or the flutes on a drill.
- Hemisphere
- Half of a sphere.
- Heptadecagon
- A 17 sided polygon.
- Heptagon
- A polygon with 7 sides.
- Heronian Triangle
- A triangle with integer sides and integer area.
- Hexadecagon
- A 16 sided polygon.
- Hexagon
- A polygon with 6 sides.
- Hexagonal Prism
- A prism with a hexagonal base.
- Hexahedron
- A polyhedron having 6 faces.
- Hexomino
- A polygon in the plane made of 6 equal-sized squares connected edge-to-edge.
- Icosahedron
- A 20 sided solid.
- Incentre
- The incentre of a triangle is the center of its inscribed circle.
- Incircle
- The circle inscribed in a given figure.
- Included Angle
- The angle made by two sides of a polygon.
- Inscribed Angle
- The angle formed by two chords of a curve that meet at the same point on the curve.
- Interior of a Circle
- The set of points whose distance from the center of the circle is less than that of the radius.
- Isogonal Conjugate
- Isogonal lines of a triangle are cevians that are symmetric with respect to the angle bisector. Two points are isogonal conjugates if the corresponding lines to the vertices are isogonal.
- Isosceles Tetrahedron
- A tetrahedron in which each pair of opposite sides have the same length.
- Isosceles Triangle
- A triangle with two equal sides.
- Isotomic Conjugate
- Two points on the side of a triangle are isotomic if they are equidistant from the midpoint of that side. Two points inside a triangle are isotomic conjugates if the corresponding cevians through these points meet the opposite sides in isotomic points.
- Kite
- A quadrilateral which has two pairs of adjacent sides equal.
- Knot
- A curve in space formed by interlacing a piece of string and then joining the ends together.
- Latus Rectum
- A chord of an ellipse passing through a focus and perpendicular to the major axis of the ellipse.
- Loxodrome
- On a sphere, a curve that cuts all parallels under the same angle.
- L-tetromino
- A tetromino in the shape of the letter L.
- Malfatti Circles
- Three equal circles that are mutually tangent and each tangent to two sides of a given triangle.
- Medial Triangle
- The triangle whose vertices are the midpoints of the sides of a given triangle.
- Midpoint
- The point M is the midpoint of line segment AB if AM=MB. That is, M is halfway between A and B.
- Molecular Geometry
- Shape of a molecule, based on the relative positions of the atoms.
- Nagel Point
- In a triangle, the lines from the vertices to the points of contact of the opposite sides with the excircles to those sides meet in a point called the Nagel point.
- Nine Point Centre
- In a triangle, the circumcenter of the medial triangle is called the nine point centre.
- Nine Point Circle
- In a triangle, the circle that passes through the midpoints of the sides is called the nine point circle.
- Nonagon
- A nine sided polygon.
- Oblique Angle
- An angle that is not a right angle.
- Oblique Triangle
- A triangle that is not a right triangle.
- Obtuse Angle
- An angle larger than 90° but smaller than 180°.
- Obtuse Triangle
- A triangle that contains an obtuse angle.
- Octadecagon
- An 18 sided polygon.
- Octagon
- A polygon with 8 sides.
- Octahedron
- A polyhedron with 8 faces.
- One Dimensional
- Having length, but no width e.g. a line.
- Orthic Triangle
- The triangle whose vertices are the feet of the altitudes of a given triangle.
- Pedal Triangle
- The pedal triangle of a point P with respect to a triangle ABC is the triangle whose vertices are the feet of the perpendiculars dropped from P to the sides of triangle ABC.
- Pentadecagon
- A 15 sided polygon.
- Pentagon
- A polygon with five sides.
- Pentomino
- A five-square polyomino.
- Perfect Cube
- An integer is a perfect cube if it is of the form m3 where m is an integer.
- Plane Angle
- The plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius is 1 radian.
- Polygon
- A shape of multiple sides. Regular polygons have sides of equal length.
- Polyomino
- A planar figure consisting of congruent squares joined edge-to-edge.
- Primitive Pythagorean Triangle
- A right triangle whose sides are relatively prime integers.
- Pythagorean Triangle
- A right triangle whose sides are integers.
- Quadrangle
- A four-sided polygon.
- Quadrangular Prism
- A prism whose base is a quadrilateral.
- Quadrangular Pyramid
- A pyramid whose base is a quadrilateral.
- Quadrature
- The quadrature of a geometric figure is the determination of its area.
- Quadridecagon
- A 14 sided polygon.
- Radical Axis
- The locus of points of equal power with respect to two circle.
- Radical Centre
- The radical centre of three circles is the common point of interesection of the radical axes of each pair of circles.
- Rectangle
- A quadrilateral with 4 right angles.
- Reflex Angle
- An angle between 180deg; and 360deg;.
- Regular Polygon
- A polygon in which all of the angles and all of the sides are equal.
- Right Angle
- right angle = π/2 radians = 90°
- Right Triangle
- A triangle that contains a right angle.
- Same Side Exterior Angles
- Angles located outside a set of parallel lines and on the same side of the transversal.
- Same Side Interior Angles
- Angles located inside a set of parallel lines and on the same side of the transversal.
- Scalene Triangle
- A triangle in which no two sides are of equal length.
- Septagon
- A seven-sided polygon.
- Similar Figures
- Two geometric figures are similar if their sides are in proportion and all their angles are the same.
- Small Circle
- The circle formed by the intersection of a sphere and a plane that doesn't contain the centre of the sphere.
- Solid Geometry
- The study of figures in three-dimensional space.
- Sphere
- Basic calculations of the properties of a sphere.
- Spherical Triangles
- A triangle on the surface of a unit sphere.
- Square
- A number raised to the power 2 ie 2 x 2 = 22 = 4. Also, a 2 dimensional figure with the height and width having the same lengths,and at right angles to each other.
- Straight Angle
- An angle whose measure is 180 degrees.
- Supplementary Angles
- Two angles are supplementary if they add up to 180°.
- Surface Contour
- The outline or profile of a surface.
- Symmedian
- Reflection of a median of a triangle about the corresponding angle bisector.
- Tangential
- Having the characteristics of a tangent - a straight line touching a circle at one point and forming a right angle with the radius connecting this point with the center of the circle.
- Tetragon
- A four-sided polygon.
- Tetromino
- A four-square polyomino.
- Three Dimensional
- Having length, width, and thickness i.e. space.
- Toroidal
- Having the specific geometrical shape of a torus.
- Trapezium
- A quadrilateral in which no sides are parallel.
- Triangle
- A three sided shape.
- Triclinic
- Having three axes of any length with none of the included angles being equal to one another or 90 degrees.
- Tridecagon
- A 13 sided polygon.
- Trigon
- A three-sided polygon - a triangle.
- Tromino
- A three-square polyomino.
- Truncated Pyramid
- A section of a pyramid between its base and a plane parallel to the base.
- Two Dimensional
- Having both width and length, but no thickness.
- Undecagon
- An eleven sided polygon.
- Unit Circle
- A circle with radius 1.
- Unit Cube
- A cube with edge length 1.
- Unit Square
- A square of side length 1.
- Vertical Angles
- Two angles that share a common vertex and whose sides form 2 lines.
- X-pentomino
- A pentomino in the shape of the letter X.
- Zero Angle
- An angle whose measure is 0.
- Zero Dimensional
- Having no dimension; a point.
Subjects: Mathematics