In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal ; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term "oblong" is used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD.
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. A kite may also be called a dart, particularly if it is not convex.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.
In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a "diamond", after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle, and the latter sometimes refers specifically to a rhombus with a 45° angle.
In geometry, a trapezoid in North American English, or trapezium in British English, is a quadrilateral that has at least one pair of parallel sides.
In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, , which is , where is approximately 1.618.
A touchscreen is a type of display that can detect touch input from a user. It consists of both an input device and an output device. The touch panel is typically layered on the top of the electronic visual display of a device. Touchscreens are commonly found in smartphones, tablets, laptops, and other electronic devices.
In mathematics, an invariant is a property of a mathematical object which remains unchanged after operations or transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the term is used. For example, the area of a triangle is an invariant with respect to isometries of the Euclidean plane. The phrases "invariant under" and "invariant to" a transformation are both used. More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class.
The term composition means "putting together". It can be thought of as the organization of the elements of art according to the principles of art. Composition can apply to any work of art, from music through writing and into photography, that is arranged using conscious thought.
A ternary plot, ternary graph, triangle plot, simplex plot, or Gibbs triangle is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram. In game theory, it is often called a simplex plot. Ternary plots are tools for analyzing compositional data in the three-dimensional case.
In software engineering, a class diagram in the Unified Modeling Language (UML) is a type of static structure diagram that describes the structure of a system by showing the system's classes, their attributes, operations, and the relationships among objects.
Visual design elements and principles describe fundamental ideas about the practice of visual design.
The bishop and knight checkmate in chess is the checkmate of a lone king by a king, a bishop, and a knight. With the stronger side to move and with perfect play, checkmate can be forced in at most thirty-three moves from any starting position where the defender cannot quickly win one of the pieces. The exception is the "stalemate trap". These exceptions constitute about 0.5% of the positions. Checkmates are possible with the defending king on any square at the edge of the board but can be forced only from positions with different material or if the defending king is in a corner controlled by the bishop or on a square on the edge next to a corner; however, mate adjacent to the corners not controlled by the bishop is only two moves deep, so it is not generally encountered unless the defending side plays inaccurately. Although this is classified as one of the four basic or elementary checkmates, it occurs in practice only approximately once in every 6,000 games.
Photographic composition techniques are used to set up the elements of a picture. These are the techniques which resembles the way we humans normally see a view
Drafting tools may be used for measurement and layout of drawings, or to improve the consistency and speed of creation of standard drawing elements. Tools such as pens and pencils mark the drawing medium. Other tools such as straight edges, assist the operator in drawing straight lines, or assist the operator in drawing complicated shapes repeatedly. Various scales and the protractor are used to measure the lengths of lines and angles, allowing accurate scale drawing to be carried out. The compass is used to draw arcs and circles. A drawing board was used to hold the drawing media in place; later boards included drafting machines that sped the layout of straight lines and angles. Tools such as templates and lettering guides assisted in the drawing of repetitive elements such as circles, ellipses, schematic symbols and text. Other auxiliary tools were used for special drawing purposes or for functions related to the preparation and revision of drawings. The tools used for manual technical drawing have been displaced by the advent of computer-aided drawing, drafting and design (CADD).
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s.
The diagonal method (DM) is a rule of thumb in photography, painting and drawing. Dutch photographer and lecturer Edwin Westhoff discovered the method when, after having long taught the rule of thirds in photography courses, he conducted visual experiments to investigate why this rule of thirds only loosely prescribes that points of interest should be placed more or less near the intersection of lines, rather than being rigid and demanding placement to be precisely on these intersections. Having studied many photographs, paintings and etchings, he discovered that details of interest were often placed precisely on the diagonals of a square, instead of any "strong points" that the rule of thirds or the photographic adaptation of the golden ratio suggests. A photograph is usually a rectangular shape with a ratio of 4:3 or 3:2, from which the diagonals of the photograph are placed at the bisection of each corner. Manually placing certain elements of interest on these lines results in a more pleasing photograph.
Rabatment of the rectangle is a compositional technique used as an aid for the placement of objects or the division of space within a rectangular frame, or as an aid for the study of art.
