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Solid geometry
 
 
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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, solid geometry was the traditional name for the geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
 of three-dimensional Euclidean space
Euclidean space

Around 300 Before Christ, the Ancient Greece mathematician Euclid undertook a study of relationships among distances and angles, first in a plane and then in space....
 — for practical purposes the kind of space
Space

Space is the boundless, three-dimensional extent in which Physical body and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physics usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime....
 we live in. It was developed following the development of plane geometry
Plane geometry

In mathematics, plane geometry may mean:*geometry of a plane ,*geometry of the Euclidean plane,or sometimes a plane is any flat surface that extends without end in all directions....
. Stereometry deals with the measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
s of volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
s of various solid figure
Shape

The shape of an object located in some space is the part of that space occupied by the object, as determined by its external boundary ? abstracting from other properties such as colour, content, and material composition, as well as from the object's other spatial properties ....
s: cylinder
Cylinder (geometry)

A cylinder is one of the most curvilinear basic geometric shapes: the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder....
, circular cone
Cone (geometry)

A cone is a dimension geometric shape that tapers smoothly from a flat, round base to a point called the apex or vertex. More precisely, it is the solid figure bounded by a plane base and the surface formed by the locus of all straight line segments joining the apex to the perimeter of the base....
, truncated cone, sphere
Sphere

A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface....
, prism
Prism (geometry)

In geometry, an n-sided prism is a polyhedron made of an n-sided polygon base, a Translation copy, and n faces joining corresponding sides....
s, blade
Blade

A blade is the flat part of a tool, weapon, or machine that normally has a cutting edge and/or pointed end typically made of a flaking stone, such as flint, or metal, most recently steel....
s, wine casks.

The Pythagorean
Pythagorean

Pythagorean means of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras. See:...
s had dealt with the sphere and regular solids, but the pyramid
Pyramid

A pyramid is a building where the outer surfaces are triangular and converge at a point. The base of pyramids are usually quadrilateral or trilateral , meaning that a pyramid usually has four or five faces....
, prism, cone and cylinder were not studied until the Platonist
Platonism

Platonism is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In a narrower sense the term might indicate the doctrine of Platonic realism....
s.






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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, solid geometry was the traditional name for the geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
 of three-dimensional Euclidean space
Euclidean space

Around 300 Before Christ, the Ancient Greece mathematician Euclid undertook a study of relationships among distances and angles, first in a plane and then in space....
 — for practical purposes the kind of space
Space

Space is the boundless, three-dimensional extent in which Physical body and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physics usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime....
 we live in. It was developed following the development of plane geometry
Plane geometry

In mathematics, plane geometry may mean:*geometry of a plane ,*geometry of the Euclidean plane,or sometimes a plane is any flat surface that extends without end in all directions....
. Stereometry deals with the measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
s of volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
s of various solid figure
Shape

The shape of an object located in some space is the part of that space occupied by the object, as determined by its external boundary ? abstracting from other properties such as colour, content, and material composition, as well as from the object's other spatial properties ....
s: cylinder
Cylinder (geometry)

A cylinder is one of the most curvilinear basic geometric shapes: the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder....
, circular cone
Cone (geometry)

A cone is a dimension geometric shape that tapers smoothly from a flat, round base to a point called the apex or vertex. More precisely, it is the solid figure bounded by a plane base and the surface formed by the locus of all straight line segments joining the apex to the perimeter of the base....
, truncated cone, sphere
Sphere

A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface....
, prism
Prism (geometry)

In geometry, an n-sided prism is a polyhedron made of an n-sided polygon base, a Translation copy, and n faces joining corresponding sides....
s, blade
Blade

A blade is the flat part of a tool, weapon, or machine that normally has a cutting edge and/or pointed end typically made of a flaking stone, such as flint, or metal, most recently steel....
s, wine casks.

The Pythagorean
Pythagorean

Pythagorean means of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras. See:...
s had dealt with the sphere and regular solids, but the pyramid
Pyramid

A pyramid is a building where the outer surfaces are triangular and converge at a point. The base of pyramids are usually quadrilateral or trilateral , meaning that a pyramid usually has four or five faces....
, prism, cone and cylinder were not studied until the Platonist
Platonism

Platonism is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In a narrower sense the term might indicate the doctrine of Platonic realism....
s. Eudoxus
Eudoxus of Cnidus

Eudoxus of Cnidus was a Ancient Greece astronomer, mathematician, scholar and student of Plato. Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy....
 established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height, and was probably the discoverer of a proof that the volume of a sphere is proportional to the cube of its radius
RADIUS

Remote Authentication Dial In User Service is a networking protocol that provides centralized access, authorization and accounting management for people or computers to connect and use a network service....
.

See also: Archimedes
Archimedes

Archimedes of Syracuse was a Greek mathematics, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity....
, Demiurge
Demiurge

Demiurge in philosophical and religious language is a term for a creator deity, responsible for the Creation myth of the physical universe.In the sense of a divine creative principle as expressed in ergon or energy, the word was first introduced by Plato in Timaeus , 41a ....
, Johannes Kepler
Johannes Kepler

Johannes Kepler was a Germans mathematician, astronomer and astrologer, and key figure in the 17th century Scientific revolution. He is best known for his eponymous Kepler's laws of planetary motion, codified by later astronomers based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astrononomy....
, planimetry
Planimetry

Planimetry is a representation in one plane of space like: group of building or machine or an objects. regard various scientific and technical matter and it is equivalent to the concept of plan in the technical design for a group og objects ....
, Plato
Plato

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
, Timaeus (dialogue)
Timaeus (dialogue)

Timaeus is a theoretical treatise of Plato in the form of a Socratic dialogue, written circa 360 Before Christ. The work puts forward speculation on the nature of the physical world....


...paraphrased and taken in part from the 1911 Encyclopędia Britannica

Basic topics of solid geometry


Basic topics are:

Other topics


More advanced are the study of

  • projective geometry
    Projective geometry

    In mathematics projective geometry is the study of geometric properties which are invariant under projective transformations. The field of projective geometry is itself divided into many subfields, two examples of which are projective algebraic geometry and projective differential geometry ....
     of three dimensions leading to
  • proof of Desargues' theorem
    Desargues' theorem

    In projective geometry, Desargues' theorem, named in honor of G?rard Desargues, states:To understand this, denote the three vertices of one triangle by a, b, and c, and those of the other by A, B, and C....
     by using an extra dimension
  • further polyhedra
  • descriptive geometry
    Descriptive geometry

    Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures....
    .


Analytic geometry
Analytic geometry

Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra; the modern development of analytic geometry is thus suggestively called algebraic geometry....
 and vector techniques have a major impact by allowing the systematic use of linear equations
System of linear equations

In mathematics, a system of linear equations is a collection of linear equations involving the same set of variables. For example,is a system of three equations in the three variables ....
 and matrix
Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entrywise operations such as matrix addition a key notion is matrix multiplication....
 algebra; this becomes more important for higher dimensions. A major reason to study this subject is the application to computer graphics
Computer graphics

Computer graphics are graphics created by computers and, more generally, the representation and manipulation of pictorial data by a computer....
, meaning that algorithm
Algorithm

In mathematics, computing, linguistics and related subjects, an algorithm is a sequence of finite instructions, often used for calculation and data processing....
s become important.