"In geometry, a three-dimensional space (3-D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point."
This topic covers the properties and characteristics of three-dimensional figures such as spheres, cylinders, cones, and pyramids, and how to find their volumes and surface areas.
Points, Lines, and Planes: Understanding the basics of geometry, including how to identify and define points, lines, and planes.
Angles and Congruence: Learning about angles and how to measure and compare them, as well as the concept of congruence and how it applies to three-dimensional figures.
Triangles: Exploring the properties of triangles, including types of triangles, angles, and side lengths.
Polygons: Studying the properties of polygons, including their angles, sides, and area.
Circles: Understanding the properties of circles, including their radius, diameter, circumference, and area.
Three-Dimensional Figures: Learning about the properties of solid shapes such as cubes, prisms, pyramids, spheres, and cones, including their volume and surface area.
Transformational Geometry: Studying how three-dimensional figures can be transformed through translation, reflection, and rotation.
Geometric Relationships: Understanding the various relationships that can exist between different three-dimensional figures, including similarity, congruence, and parallelism.
Trigonometry: Learning about trigonometric functions such as sine, cosine, and tangent and their use in solving problems involving three-dimensional figures.
Coordinate Geometry: Understanding the use of Cartesian coordinates to represent points and shapes in three-dimensional space.
Cube: A cube is a six-faced 3D figure where each face is a perfect square. All six faces are equal in size, shape, and angle.
Pyramid: A pyramid is a 3D shape where the base is a polygon and each face (except the base) is a triangle that meets at a common point called the apex.
Cylinder: A cylinder is a 3D shape with two circular bases that are parallel to each other. The sides of the cylinder are curved.
Cone: A cone has a circular base and a curved surface that tapers towards a point called the apex.
Sphere: A sphere is a perfectly round 3D figure where every point on the surface is equidistant from the center.
Prism: A prism is a 3D shape where the two ends are identical polygon shapes and the other sides are parallelograms.
Torus: A torus is a 3D shape that resembles a doughnut or a tire. It is formed by revolving a circle around an axis that is in the same plane as the circle.
Ellipsoid: An ellipsoid is a smooth 3D figure that looks like a stretched sphere, and is characterized by three principal axes radii.
Tetrahedron: A tetrahedron is a pyramid-like 3D figure that has four triangular sides.
Octahedron: An octahedron is a 3D shape that has eight triangular faces, and the total number of edges and vertices is equal.
Dodecahedron: A 3D figure with twelve flat faces in pentagon shapes.
Icosahedron: An icosahedron has 20 faces that are each an equilateral triangle.
Parallelepiped: A parallelepiped is a 3D shape with six rectangular faces that are parallel like a rectangular box.
Frustum: A frustum is a 3D shape that is formed by cutting the top off a pyramid or cone.
Antiprism: An antiprism is composed of two parallel, identical polygons connected by a series of parallelogram faces.
"Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space."
"More general three-dimensional spaces are called 3-manifolds."
"A tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space."
"The set of these n-tuples is commonly denoted R^n."
"When n = 3, this space is called the three-dimensional Euclidean space (or simply 'Euclidean space' when the context is clear)."
"It serves as a model of the physical universe (when relativity theory is not considered), in which all known matter exists."
"It is only one example of a large variety of spaces in three dimensions called 3-manifolds."
"When the three values refer to measurements in different directions (coordinates), any three directions can be chosen."
"Provided that vectors in these directions do not all lie in the same 2-space (plane)."
"These three values can be labeled by any combination of three chosen from the terms width/breadth, height/depth, and length."
"While this space remains the most compelling and useful way to model the world as it is experienced..."
"...three values (coordinates) are required to determine the position of a point."
"In geometry, a three-dimensional space... is a mathematical space..."
"More general three-dimensional spaces are called 3-manifolds."
"...and can be identified to the pair formed by an n-dimensional Euclidean space and a Cartesian coordinate system."
"The Euclidean n-space of dimension n=3..."
"It serves as a model of the physical universe (when relativity theory is not considered), in which all known matter exists."
"...any combination of three chosen from the terms width/breadth, height/depth, and length."
"The set of these n-tuples is commonly denoted R^n."