Pizza theorem
In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because it mimics a traditional pizza slicin
Heilbronn triangle problem
In discrete geometry and discrepancy theory, the Heilbronn triangle problem is a problem of placing points in the plane, avoiding triangles of small area. It is named after Hans Heilbronn, who conject
Schwarz lantern
In mathematics, the Schwarz lantern is a polyhedral approximation to a cylinder, used as a pathological example of the difficulty of defining the area of a smooth (curved) surface as the limit of the
Square trisection
In geometry, a square trisection is a type of dissection problem which consists of cutting a square into pieces that can be rearranged to form three identical squares.
Surface area
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerabl
Mrs. Miniver's problem
Mrs. Miniver's problem is a geometry problem about the area of circles. It asks how to place two circles and of given radii in such a way that the lens formed by intersecting their two interiors has e
Hyperbolic sector
A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a) and (b, 1/b) on the rectangular hyperbola xy = 1,
One-seventh area triangle
In plane geometry, a triangle ABC contains a triangle having one-seventh of the area of ABC, which is formed as follows: the sides of this triangle lie on cevians p, q, r where p connects A to a point
Dividing a circle into areas
In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes ca
Osgood curve
In mathematical analysis, an Osgood curve is a non-self-intersecting curve that has positive area. Despite its area, it is not possible for such a curve to cover a convex set, distinguishing them from
Surface integral
In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of
Shoelace formula
The shoelace formula, shoelace algorithm, or shoelace method (also known as Gauss's area formula and the surveyor's formula) is a mathematical algorithm to determine the area of a simple polygon whose
Bernoulli quadrisection problem
In triangle geometry, the Bernoulli quadrisection problem asks how to divide a given triangle into four equal-area pieces by two perpendicular lines. Its solution by Jacob Bernoulli was published in 1
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose
Base (geometry)
In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom"
Dot planimeter
A dot planimeter is a device used in planimetrics for estimating the area of a shape, consisting of a transparent sheet containing a square grid of dots. To estimate the area of a shape, the sheet is
Area of a circle
In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Square–cube law
The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's s
Quadratrix
In geometry, a quadratrix (from Latin quadrator 'squarer') is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are th
Arpent
An arpent (French pronunciation: [aʁpɑ̃], sometimes called arpen) is a unit of length and a unit of area. It is a pre-metric French unit based on the Roman actus. It is used in Quebec, some areas of
Area (graph drawing)
In graph drawing, the area used by a drawing is a commonly used way of measuring its quality.
Brahmagupta's formula
In Euclidean geometry, Brahmagupta's formula is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides; its generalized version (Brets
Pappus's centroid theorem
In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes
Dissection puzzle
A dissection puzzle, also called a transformation puzzle or Richter Puzzle, is a tiling puzzle where a set of pieces can be assembled in different ways to produce two or more distinct geometric shapes
Planimeter
A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape.
Heron's formula
In geometry, Heron's formula (or Hero's formula) gives the area A of a triangle in terms of the three side lengths a, b, c. If is the semiperimeter of the triangle, the area is, It is named after firs
Pappus's area theorem
Pappus's area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. The theorem, which can also be thought of as a generalizati
Vector area
In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions. Every bounded surface in
Biggest little polygon
In geometry, the biggest little polygon for a number n is the n-sided polygon that has diameter one (that is, every two of its points are within unit distance of each other) and that has the largest a
Pick's theorem
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was
Routh's theorem
In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The theorem states that if in triangle points
Cavalieri's principle
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows:
* 2-dimensional case: Suppose two regions in a plane are i
Body surface area
In physiology and medicine, the body surface area (BSA) is the measured or calculated surface area of a human body. For many clinical purposes, BSA is a better indicator of metabolic mass than body we
Quadratrix of Hippias
The quadratrix or trisectrix of Hippias (also quadratrix of Dinostratus) is a curve which is created by a uniform motion. It is one of the oldest examples for a kinematic curve (a curve created throug
Area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface a
Goat problem
The goat problem is either of two related problems in recreational mathematics involving at least figuratively a tethered goat (horse, bull) grazing a circular area: the interior grazing problem and t
Bretschneider's formula
In geometry, Bretschneider's formula is the following expression for the area of a general quadrilateral: Here, a, b, c, d are the sides of the quadrilateral, s is the semiperimeter, and α and γ are a
Geometric mean theorem
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line s
Blaschke–Lebesgue theorem
In plane geometry the Blaschke–Lebesgue theorem states that the Reuleaux triangle has the least area of all curves of given constant width. In the form that every curve of a given width has area at le
Rod (unit)
The rod, perch, or pole (sometimes also lug) is a surveyor's tool and unit of length of various historical definitions, often between approximately 3 and 8 meters (9 ft 10 in and 26 ft 2 in). In moder
Filling area conjecture
In differential geometry, Mikhail Gromov's filling area conjecture asserts that the hemisphere has minimum area among the orientable surfaces that fill a closed curve of given length without introduci