Difference Between 2D and 3D

Edited by Diffzy | Updated on: September 03, 2023

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Introduction

In geometry, 2D and 3D shapes are thoroughly explained to help you understand the various kinds of objects you encounter in daily life. The patterns and characteristics of these shapes are unique. The shapes can vary depending on a wide range of factors, including angle, sides, length, height, width, area, volume, etc. We have been taught these 2D and 3D shapes since primary school. In this article, let's explore the various kinds of two-dimensional shapes.

2D vs. 3D

These are both kinds of geometry. Geometry is the look at various shapes. It is broadly categorized into two main types: solid geometry and plane geometry (2D shapes) (3D shapes). We'll talk about the distinction between 2D and 3D shapes in this article. But first, inform us a bit more about every one of these. Because it deals with all the flat figures that are simple to draw on paper, plane geometry is also referred to as two-dimensional geometry. These figures encompass however aren't constrained to curves, lines, quadrilaterals, polygons, etc. In contrast, solid geometry, which deals with three-dimensional or solid shapes, is also referred to as three-dimensional geometry. Cones, cylinders, spheres, and other shapes are a few examples of these figures. The abbreviation for two-dimensional is 2D. It shows that the 2D shapes exist at the x-y aircraft and feature dimensions. Therefore, using the X-axes and the Y-axes, which are flat on any surface, we can draw a 2D object. Three-dimensional is referred to by the abbreviation 3D. It means that the 3-dimensional shapes occupy an extent and feature a complete of 3 dimensions (at the side of the area, just like the 2D shapes). We encounter many 3D objects every day, including bottles, books, balls, and Rubik's cubes. The Z, Y, and Z axes can be used to represent a 2D object because they also take up volume.

What is a 2D?

A Euclidean plane is indeed a Euclidean space of dimension two, called E2 in mathematics. It is a geometric space in which each point's position is determined by two real numbers. It is an affine space which incorporates the concept of parallel lines in particular. It also contains metrical qualities caused by distance, allowing it to define circles and measure angles. A Cartesian aircraft is an Euclidean aircraft with a particular Cartesian coordinate system. Because every Euclidean plane is isomorphic to it, the set 2 of pairs of real numbers (the real coordinate plane) equipped with the dot product is often referred to as the Euclidean plane.

History

Euclid's Elements Books I–IV–VI dealt with two-dimensional geometry, introducing concepts such as shape resemblance, the Pythagorean theorem regarding the equality of angles and areas, parallelism, the average of the angles in a triangle, and the three circumstances in which triangles are "equal , among many Later, the plane was described in a so-called Cartesian coordinate system, which is a coordinate system that uniquely specifies each point in a plane by a pair of numerical coordinates, which are the Signed distances from the factor to 2 constant perpendicular directed lines, measured withinside the equal unit of each reference line is called a coordinate axis or virtually an axis of the system, and the point where they intersect is known as the origin, which is usually the ordered pair (0, 0).

The coordinates can also be defined as the signed distances from the origin of the point's perpendicular projections onto the two axes. Subsequently, the plane was regarded as a field in which any two points could be multiplied and, except 0, split. This was referred to as the complicated plane. Because it is utilized in Argand diagrams, the complex plane is also known as the Argand plane. Although they were first reported by Danish-Norwegian land surveyor and mathematician Caspar Wessel, they are called after Jean-Robert Argand (1768-1822). (1745–1818) Argand diagrams are widely used to illustrate the positions of a function's poles and zeroes in the complex plane.

Different types of shapes

A circle, a triangle, a square, a rectangle, a pentagon, a quadrilateral, a hexagon, an octagon, and so on are examples of basic 2D shapes. Apart from the circle, all of the shapes are considered polygons with sides. A regular polygon has all of its sides and angles equal. An ellipse, like a circle, is a non-polygonal form. The circle and ellipse both have curved shapes, whereas polygons have a closed structure with sides. Let us now go over certain forms one by one.

Circle

A circle in mathematics is a closed two-dimensional figure in which all its points lie in the plane and are equidistant from the center. The radius of a circle is the distance between its geographic center and its outermost line. In everyday life, circles can be found in the form of wheels, pizzas, orbits, and so on.

Triangle

A triangle is a three-sided polygon with three edges and three vertices. The total of a triangle's three angles equals 180°. The best illustration of a triangular shape is a pyramid. You may also learn about triangle properties here.

Square

A square is a four-sided polygon (2-D form) with four equal-length sides and all angles equal to 90°. It's classified as a two-dimensional regular quadrilateral. The diagonals of the square also intersect at 90°. A square shape is a wall or a table with all of its sides equal.

Rectangle

A rectangle is a two-dimensional shape having four sides that are equal and parallel to one another. A rectangle's angles are all equal to 90°. A rectangle is something that has length and breadth, such as a brick or a TV.

Pentagon

A pentagon is a regular or irregular five-sided polygon (2D form). Each inner angle of a regular pentagon measures 108°, while each outer angle measures 72°. There are five diagonals in it. The Pentagon, which houses the headquarters of the United States Department of Defense, is an excellent example of the Pentagon shape.

Octagon

An octagon is an eight-sided polygon that can be regular or irregular in shape. It is a two-dimensional shape with eight angles. The total of an octagon's inner angles is 1080°. By the roadway, you can observe an octagonal-shaped stop sign board.

What is 3D?

A three-dimensional space (3D space, 3-space, or, more rarely, tri-dimensional space) is a mathematical space in which the position of a point is determined by three values (coordinates). The three-dimensional Euclidean space, the Euclidean n-space of dimension n=3, is most typically used to model physical space. 3-manifolds are more general three-dimensional spaces.

A tuple of n numbers can be thought of as the Cartesian coordinates of a point in n-dimensional Euclidean space. The set of these n-tuples is known as and may be identified as the pair generated by an n-dimensional Euclidean space and a Cartesian coordinate system. This space is known as three-dimensional Euclidean space when n = 3. (or simply "Euclidean space" when the context is clear). When relativity theory is ignored, it functions as a model of the physical cosmos in which all known matter exists.

History

Three-dimensional geometry is covered in Books XI through XIII of Euclid's Elements. Book XI introduces the concepts of orthogonality and parallelism of lines and planes as well as the definitions of solids such as parallelepipeds, pyramids, prisms, spheres, octahedra, icosahedra, and dodecahedra. Book XII explores the concept of resemblance among solids. The creation of the five regular Platonic solids in a sphere is described in Book XIII.

The invention of the quaternions by William Rowan Hamilton in the nineteenth century ushered in advances in three-dimensional geometry. The terms scalar and vector were coined by Hamilton and were initially defined within his geometric framework for quaternions. While not explicitly addressed by Hamilton, this indirectly presented the notion of basis offered here by the quaternion elements The negative of the scalar and vector parts of the product of two vector quaternions is represented by the dot product and cross product.

It wasn't until Josiah Willard Gibbs identified these two products as distinct in their own right that the modern sign for the dot and cross products was introduced in his classroom teaching notes, which were also found in Edwin Bidwell Wilson's 1901 textbook Vector Analysis, which was based on Gibbs' lectures. The work of Hermann Grassmann and Giuseppe Peano, the latter of whom introduced the present definition of vector spaces as an algebraic structure, also contributed to improvements in the abstract formalism of vector spaces during the nineteenth century.

Different types of shapes

A net is a flattened three-dimensional solid that serves as a two-dimensional skeleton outline. It can be folded and bonded to form a three-dimensional structure, making it useful for creating 3D shapes. Exploring nets for different solids and calculating their surface area and volume can be helpful.

Types of 3D shapes

Any polygon, including a square or triangle, can be used to form a pyramid. It has at least three triangular faces that come together at the apex.

3D Shape Varieties

3D shapes consist of both curved solids and straight-sided polygons, also referred to as polyhedrons. Polyhedrons are built on 2D structures with straight sides, also known as polyhedra. Let's dive into the details of these two types of 3D shapes.

Polyhedrons

Polyhedrons are three-dimensional forms. As previously stated, polyhedra are straight-sided solids with the following properties: Straight edges are required for polyhedrons. The faces are the flat sides that they should have. It must have corners, known as vertices.

Polyhedrons, like polygons in two dimensions, are classified into regular and irregular polyhedrons, as well as convex and concave polyhedrons.

The following are some of the most common polyhedra:

With six square faces and twelve edges that link its eight vertices together tightly, a cube is distinct from three-dimensional objects.

A similar relationship between the surface area (six), the number of edges (twelve), and the number of corners/vertices (eight) can be observed in the cuboid as well. This specific solid also has a polygon base featuring straight lines connecting its flat faces via both endpoints at one solitary vertex.

Parallelogram-shaped sides adorn the prism, whose terminal ends are identical polygons- another example of uniformity within this category of geometrical figures. Regular polyhedrons denoted by names such as tetrahedra or octahedra form a final section that attracts attention when discussing specifically shaped three-dimensional structures. Platonic solids are a class of regular polyhedrons, which are geometric forms with uniform faces and edges.

The most frequent type of polyhedron is the cube, which has six faces, eight vertices, and twelve edges.

Curved Solids

Curved solids are 3D shapes that have curved surfaces. Curved solids include the following: Sphere: A circular form with all points on the surface equidistant from the centre. It features a single vertex and a circular base. Cylinder: It features parallel circular bases that are joined by a curving surface.

Faces, Edges, and Vertices

Face edges and vertices are three critical 3D shape measurements that define their attributes. Faces are curves or flat surfaces on 3D shapes. Edges: An edge is a line segment that connects two faces. Vertices: A vertex is a location where two edges come together.

Cuboid

A rectangular prism is another name for a cuboid. The cuboid's faces are rectangular. All of the angles are 90 degrees.

Cube

The definition of a cube is a three-dimensional square with six equal sides. The cube's faces are all the same size.

Cone

A cone is a solid object with a single vertex and a circular base. It is a geometrical shape with a smooth taper from a circular, flat base to a point known as the apex.

Cylinder

A cylinder is a solid geometrical shape with two parallel circular bases that are joined by a curved surface.

Pyramid

A pyramid, commonly known as a polyhedron, is a geometric shape. A pyramid can be any polygon, such as a square or triangle. It features three or more triangle faces that meet at a point known as the apex.

Difference Between 2D and 3D in Points

• 2D shapes have two dimensions in total. 3D shapes have three dimensions in total.
• 2D exists in the x and y axes, whereas 3D exists in the x, y, and y axes.
• 2D shapes only occupy the area. Because 3D shapes have depth and height, they take up both area and volume.
• The 2D shapes provide a straightforward picture of anything. The architectural view of any object is provided by the 3D shapes.
• In the case of 2D shapes, every edge is quite evident. In the case of 3D shapes, some of the edges remain buried and are not visible.
• A 2D shape is fairly simple to explain since every one of its edges is visible to us. We can only describe the outside dimensions of a 3D shape because we cannot see the remainder of the edges.
• A 2D shape can be detailed without difficulty. Detailing a 3D shape is quite challenging.
• 2D forms are relatively basic and thus simple to draw. When combined, 3D shapes are considerably more complicated and might be difficult to draw.
• Two-dimensional shapes include rectangles, squares, circles, triangles, and any other polygon. Examples include Cuboids, cubes, spheres, cones, prism, cylinders, pyramids, and other 3D shapes.

Conclusion

Most of the items we see around us have three dimensions: height, width, and depth. In this post, we addressed why 2D objects have areas, and 3D objects have volumes, as well as other differences between the two.

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"Difference Between 2D and 3D." Diffzy.com, 2024. Sat. 18 May. 2024. <https://www.diffzy.com/article/difference-between-2d-and-3d>.

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