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A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural ...
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
Figurate numbers were a concern of the Pythagorean worldview. It was well understood that some numbers could have many figurations, e.g. 36 is a both a square and a triangle and also various rectangles. The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem.
The rhombus has a square as a special case, and is a special case of a kite and parallelogram. In plane Euclidean geometry, a rhombus (pl.: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means
The formulas and properties given below are valid in the convex case. The word cyclic is from the Ancient Greek κύκλος (kuklos), which means "circle" or "wheel". All triangles have a circumcircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be cyclic is a non-square rhombus.
The above formula is known as the shoelace formula or the surveyor's formula. If we locate the vertices in the complex plane and denote them in counterclockwise sequence as a = x A + y A i , b = x B + y B i , and c = x C + y C i , and denote their complex conjugates as a ¯ {\displaystyle {\bar {a}}} , b ¯ {\displaystyle {\bar {b}}} , and c ...
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes . For a broader scope, see list of shapes .
This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.