Geometry

Lines & Angles

According to the Curve Wikipedia article, lines are required to be straight and so-called curved lines should actually be referred to simply as curves [1].

A horizontal line goes side-to-side or forwards-and-backwards, while a vertical line goes up-and-down. A diagonal line can either refer to a slanted line or a line that goes between two nonadjacent corners of a shape or object [2].

Lines intersect if they come together.

When lines intersect, they create one or more angles depending on the length of the lines and the number of lines that are intersecting.

Angles are typically measured in degrees (°). An entire circle is 360°. A right angle is 90°, which is equivalent to a quarter of a circle. A right angle can be symbolized with either a small square or a dot (this is demonstrated in the Right angle Wikipedia article) [3].

Two lines are perpendicular if they form a right angle (this is the case for a horizontal line and a vertical line). Two lines are parallel if they are positioned so that they'd never intersect if continued indefinitely (this is the case for two vertical lines).

Dimensions, Faces, & Bases

A 0 dimensional (0D) object is a point, a 1D object is a line, a 2D object is a flat shape, and a 3D object is non-flat shape.

The different 2D shapes that are on the surface of a 3D shape are called faces.

The term base can be used to refer to the bottom face of an object [4]. The bottom face of an object is typically only considered a base if it can, on its own, keep the object in a steady and stable position. This is why it can be said, for example, that a poor argument is "baseless" and "falls flat on its face".

Polytopes

A polytope is a shape with all flat sides [5]. Some examples of different polytopes are discussed below:

polygon - a 2D polytope [5]
- quadrilateral - a polygon with 4 sides [5]
  - parallelogram - a quadrilateral with two pairs of parallel sides [6]
    - rectangle - a parallelogram with all right angles [6]
    - rhombus (plural: rhombi or rhombuses [7]) - a parallelogram in which all sides are of equal length [6]
    - square - a parallelogram with all right angles and having all sides of equal length [6]
polyhedron (plural: polyhedra or polyhedrons) - a 3D polytope [8]
- hexahedron (plural: hexahedra) - a polyhedron with 6 faces [9]
  - parallelepiped - a hexahedron with faces that are parallelograms [9]
    - cuboid - a parallelepiped with faces that are rectangles [9]
    - rhombohedron - a parallelepiped with faces that are rhombi [9]
    - cube - a parallelepiped with faces that are squares [9]

Shape & Object Measurements

The diagonal length of a polytope refers to the length of its longest diagonal or diagonals.

The diameter of a circle refers to its longest length across [10].

An equilateral polygon has all of its sides as the same length, an equiangular polygon has all of its angles as the same number of degrees, and a regular polygon is both equilateral and equiangular [11].

Two objects are similar if they have the same shape and congruent if they have the same shape and size [12].

The term form factor can refer to an object's standardized shape and size [13]. Some examples of objects with a form factor are mentioned in the Form factor Wikipedia article.

Length can refer to the longer measurement of a rectangle, the longest measurement, or the longer base measurement. Width can refer to the shorter measurement of a rectangle, the side-to-side measurement, or the shorter base measurement. Depth can refer to front-to-back or vertical measurement [14] [15] [16] [17] [18 pages 11+60].

Landscape vs. Portrait Orientation

An item that is in landscape orientation is wider-than-taller, whereas an item in portrait orientation is taller-than-wider [19].

Display Pixels & Resolution

Modern-day displays show a picture by creating a grid of congruent rectangular cells. The cells in this grid are known as pixels. When the word resolution is applied to these displays, it's referring to the dimensions, rows, or columns of pixels [20].

Dimension Measurements

Dimension measurements measure the sides of a shape or item. As is mentioned in the Writing article, this website will use an x to separate numbers in dimension measurements, with the x serving as a substitute for the word "by" [21]. Some important examples of dimension measurement are discussed below:

Paper and photo print sizes typically give the smaller dimension followed by the bigger dimension [22] [23].
Images and video typically use width followed by height [20].
Display resolution will typically fit in one of the three categories:
- Like images and videos, display resolution with a definitive orientation typically uses width followed by height [20].
- Flexible-orientation displays typically use the larger number followed by the smaller number for resolution.
- Flexible orientation displays on devices measured in portrait orientation sometimes have the smaller number first for resolution [24] but other times have the larger number first [25].
Boxes and other containers are typically measured as length-by-width-by-height/depth, with length being the longer base measurement and width being the shorter base measurement [17].
The GS1 organization, which is responsible for barcodes, also specifies a variety of other supply chain standards [26]. One such standard is the GDSN Package Measurement Rules Standard, which specifies two ways of positioning and measuring items:
- For "consumer (end-user) trade items" [18 page 9], GS1 specifies to locate the "default front" [18 page 9] of an item and to then assign width, height, and depth based on this front [18 page 11]. Locating the front seems to be largely based on surface area and product markings [18 page 9]. When it comes to orienting the front, the ideal seems to be to do so via product markings; however, if this option isn't available, GS1 specifies giving the item a portrait rather than landscape orientation [18 page 10].
- For a "non-consumer trade item" [18 page 59], GS1 specifies to locate the "natural base" and to then assign depth/length, width, and height based on this base. In this context, the depth/length is the longer side of the base and the width is the shorter side of the base. For items that don't have a specific height, the height is assigned to the shortest length [18 page 60].

As is demonstrated by these and other examples [14] [15] [16], there's not a universal consensus regarding how to measure shapes, objects, and items. Therefore, in order to measure shapes, objects, and items, the following system will be used for dimension measurements:

Paper and photo print sizes will give the smaller dimension followed by the larger dimension.
Images and videos will take the width followed by the height.
Display resolution will use the larger dimension followed by the smaller dimension unless the display is only meant to be used in portrait orientation.
For 3D items that have specific side-to-side, height, and front-to-back measurements, the dimensions given will be side-to-side, then height, and finally front-to-back. This will be indicated by placing a W for width after the 1st number, an H for height after the 2nd number, and a D for depth after the 3rd number.
For 3D items that lack a specific side-to-side measurement or front but have a specific depth, the dimensions given will be longer non-depth measurement, then shorter non-depth measurement, and finally the depth measurement. This will be indicated by only placing a D for depth after the 3rd number.
For 3D items measured without specific side-to-side, height, and front-to-back measurements, the dimensions given will simply be largest to smallest. This will be indicated by not using any letters for any of three dimensions.

Axes

3D space is typically measured with three axes: x, y, and z [27]. This is shown in the image below [28]:

These axes can also apply to the measurements of objects. For example, HDD, SSD, and SSHD manufacturers will sometimes describe the height of these devices as the z-height to indicate that the height of these devices is the shortest dimension [29] [30] [31] [32] [33] [34].