## Combinatorial game theory

Combinatorial game theory, also known as CGT is a branch of applied mathematics and theoretical computer science that studies combinatorial games, and is distinct from "traditional" or "economic" game theory. CGT arose in relation to the theory o ...

## Game theory)

A game in game theory is a mathematical model, which is used to describe a process, as follows: There are several actors This choice influences the state of the system, and the choices the other actors have Each actor can influence the state of t ...

## Game theory

Game theory is the study of how and why people make decisions. It helps people understand parts of science and politics. An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory. In the Cold War ...

## Zero-sum game

A zero-sum game is a term in game theory and economic theory. It is a mathematical representation of a situation. Each individuals gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the ...

## Geometry

Geometry is the part of mathematics that studies the size, shapes, positions and dimensions of things. We can only see or make shapes that are flat or solid, but mathematicians are able to study shapes that are 4D, 5D, 6D, and so on. Squares, cir ...

## 16-cell

In four dimensional geometry, a 16-cell, is a regular convex polychoron, or polytope existing in four dimensions. It is also known as the hexadecachoron. It is one of the six regular convex polychora first described by the Swiss mathematician Lud ...

## 5-demicube

In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube with alternated vertices removed. It was discovered by Thorold Gosset. Since it was the only semiregular 5-polytope made of mo ...

## Apothem

The apothem of a regular polygon is a line segment from the center of the polygon to the middle of one of its sides. It is also perpendicular to that side. The word "apothem" can also mean the length of that line segment. Regular polygons are the ...

## Area

Area is the amount of space a two dimensional surface takes up. It is useful because it is how much of a material is needed to make a hollow container. Area is the amount of surface covered by a close object or shape. Small areas can be measured ...

## Base (geometry)

In plane geometry, the base is the side on which a polygon rests on, and which is used as a referenced side for other measurements. The base of a triangle or quadrilateral is often written as b {\displaystyle b}. It is used in the calculation of ...

## Catenary

A catenary is a type of curve. An ideal chain hanging between two supports and acted on by a uniform gravitational force makes the shape of a catenary. The supports can be at different heights and the shape will still be a catenary. A catenary lo ...

## Congruence

In geometry, two figures or objects F {\displaystyle F} and F ′ {\displaystyle F} 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. More formally, two sets of points are ca ...

## Diagonal

is a kind of straight line. A diagonal line does not go straight up, down, or across. It is a line that connects two corners of a line In mathematics, "diagonal" has different meanings. For example, in geometry a diagonal is any line that goes be ...

## Diameter

In geometry, the diameter of a circle is a line from one side directly to the opposite side through the centre. It can also be defined as the longest chord of a circle. The same explanations can be also used to describe the diameter in a sphere. ...

## Differential geometry

Differential geometry is a field of mathematics. It uses differential and integral calculus as well as linear algebra to study problems of geometry. The theory of the plane, as well as curves and surfaces in Euclidean space are the basis of this ...

## Euclidean distance

In Euclidean geometry, the Euclidean distance is the usual distance between two points p and q. This distance is measured as a line segment. The Pythagorean theorem can be used to calculate this distance.

## Euclidean geometry

Euclidean geometry is a system in mathematics. People think Euclid was the first person who described it; therefore, it bears his name. He first described it in his textbook Elements. The book was the first systematic discussion of geometry as it ...

## Flexagon

In geometry, a flexagon is a flat model, usually made by folding a piece of paper, so that when flexed, one or more hidden faces will be revealed from within the model. Flexagons are usually square or rectangular tetraflexagons or hexagonal hexaf ...

## Ham sandwich theorem

The ham sandwich theorem is a math theorem that says that a number of objects in the same number of dimension can be cut into two equal parts with a cut that is one dimension less.

## Hyperbolic geometry

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry isnt true. On a hyperbolic plane, lines that started out parallel will become further and further apart. Replacing this rul ...

## Hypotenuse

The hypotenuse is the side opposite the 90 degrees angle in a right triangle. It is always the longest side. For example: In this triangle, if angle C is 90 degrees, then the opposite side, "c", is the hypotenuse. The hypotenuse is important in t ...

## Improper rotation

An improper rotation can be understood as an inversion followed by a proper rotation. Equivalently it is the combination of a rotation and an inversion in a point on the axis. Therefore it is also called a rotoinversion or rotary inversion. A sim ...

## Klein bottle

The Klein bottle is a geometrical object, named after the German mathematician Felix Klein. He described it in 1882, and named it Kleinsche Flache. Like the Mobius strip, it only has one surface. Mathematicians call this a non-orientable surface. ...

## Line

A line is the path of one point moving. A line has length but no width. A line is a type of geometric figure. A line is made up of an endless number of points.

## Mobius strip

The Mobius strip or Mobius band is a looped surface with only one side and only one edge. It can be made using a strip of paper by gluing the two ends together with a half-twist. The twisting is possible in two directions; so there are two differ ...

## Neusis construction

The neusis is a geometric construction method that was used by ancient Greek mathematicians. At that time, people did not have good rules to measure distances. They did not know algebra. So, they studied geometry by moving fixed length sticks aro ...

## Non-Euclidean geometry

Non-Euclidean geometry is a type of geometry. Non-Euclidean geometry only uses some of the "postulates" that Euclidean geometry is based on. In normal geometry, parallel lines can never meet. In non-Euclidean geometry they can meet, either infini ...

## Parallel (geometry)

Parallel is a term in geometry and in everyday life that refers to a property of lines or planes. Parallel lines or planes are next to each other, but never touch each other. This means they never intersect at any point. If two lines ℓ 1 {\displa ...

## Parallel postulate

In geometry the parallel postulate is one of the axioms of Euclidean geometry. Sometimes it is also called Euclids fifth postulate, because it is the fifth postulate in Euclids Elements. The postulate says that: If you cut a line segment with two ...

## Perimeter

In geometry, perimeter is the distance around a flat object. For example, all four sides of a square rhombus have the same length, so a rhombus with side length 2 inches would have a perimeter of 8 inches. For a polygon, the perimeter is simply t ...

## Pi

The number π is a mathematical constant that is the ratio of a circles circumference to its diameter. This produces a number, and that number is always the same. However, the number is rather strange. The number starts as 3.141592653589793. and c ...

## Plane (mathematics)

Plane can also refer to airplane. A plane is a perfectly flat surface extending in all directions. It can be thought of as the ceiling of a room, only extended into all directions infinitely. A plane has two dimensions: length and width. All plan ...

## Poincare conjecture

The Poincare Conjecture is a question about spheres in mathematics. It is named after Henri Poincare, the French mathematician and physicist who formulated it in 1904. The sphere has the property that any loop on it can be contracted to a point i ...

## Point (geometry)

A point is a precise position in space. Imagine touching a piece of paper with a sharp pencil or pen, without making any sideways movement. We know where the point is, but it has no size to speak of. In geometry, a point has no size, but has a po ...

## Position

Far means that something is a long away from you. Near means it is close to you. Things can also be near and far other persons and other things.

## Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagorass theorem is a statement about the sides of a right triangle. One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right ...

In geometry, the radius of a circle or sphere, written as r {\displaystyle r}, is the shortest connection between the center and the boundary. It is either the distance from the center to the perimeter, or the distance from the center to the surf ...

## Shape of the universe

The shape of the Universe cannot be discussed with everyday terms, because all the terms need to be those of Einsteinian relativity. The geometry of the universe is therefore not the ordinary Euclidean geometry of our everyday lives. According to ...

## Side

In geometry, a side is a line that is part of a flat figure made from straight lines. It is also a face in a solid three-dimensional object. The number of sides in a polygon is often written as n {\displaystyle n}, while the number of faces in a ...

## Similarity (geometry)

Similarity is an idea in geometry. It means that two polygons, line segments, or other figures can become the same via resizing. Similar objects do not need to have the same size. Two shapes are similar if their angles have the same measure and t ...

## Solid geometry

Solid geometry is the geometry of three-dimensional Euclidean space. It includes the measurements of volumes of various solid figures. These include pyramids, cylinders, cones, spheres, and prisms. It is Euclidean geometry, but not plane geometry ...

## Sphere packing

In geometry, Sphere packing refers to a number of problems that try to arrange spheres in space. Very often, the spheres all have the same size, and the space used is usually three-dimensional Euclidean space. The problem is part of packing probl ...

## Spherical geometry

Spherical geometry is the use of geometry on a sphere. It was started for cartography, as well as for making maps of stars. It is different from Euclidean geometry, and Non-Euclidean geometry. Points are defined in the same way as they are in Euc ...

## Squaring the circle

Squaring the circle is a problem of geometry. The problem is to construct a square that has the same area as the unit circle, only by using a compass and straightedge construction method. Some people also call this problem the quadrature of the c ...

## Surface area to volume ratio

The surface area to volume ratio of an object is the relationship between two measurements. It is the ratio of Surface area to volume. It shows the comparison between the size of the outside of an object and the amount inside. Small or thin objec ...

## Symmetry

Reflectional Symmetry is a property of certain geometrical objects that appears the same when mirrored or reflected along an axis. This axis has to cross the shape through the middle of that object dividing into equal halves. In rotational symmet ...

## Tangent (geometry)

In geometry, a tangent is a straight line that touches a curve at one point. At the place where they touch, the line and the curve both have the same slope. For this reason, a tangent line is a good approximation of the curve near that point. The ...

## Tensor

A tensor is a mathematical object. Tensors provide a mathematical framework for solving physics problems in areas such as elasticity, fluid mechanics and general relativity. The word tensor comes from the Latin word tendere meaning "to stretch". ...

## Theorema egregium

Gausss Theorema Egregium is a major result of differential geometry proved by Carl Friedrich Gauss. The theorem is about the curvature of surfaces. The theorem states that curvature can be determined by measuring angles, distances and their rates ...

## Triangle center

In geometry, a triangle center is a point that can be called the middle of a triangle. There are many ways of measuring the center of a triangle, and each has a different name. On an equilateral triangle, every triangle center is the same, but on ...