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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 that all of its sides are equal in length.
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
A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal quadrilaterals that are also equidiagonal quadrilaterals are called midsquare quadrilaterals. [2]
Parallelograms include rhombi (including those rectangles called squares) and rhomboids (including those rectangles called oblongs). In other words, parallelograms include all rhombi and all rhomboids, and thus also include all rectangles. Rhombus, rhomb: [1] all four sides are of equal length (equilateral). An equivalent condition is that the ...
25 Geometry and other areas of mathematics. 26 Glyphs and symbols. ... Rhombus (equilateral parallelogram) Lozenge; Rhomboid; Rectangle. square (regular quadrilateral)
All of the area formulas for general convex quadrilaterals apply to parallelograms. Further formulas are specific to parallelograms: Further formulas are specific to parallelograms: A parallelogram with base b and height h can be divided into a trapezoid and a right triangle , and rearranged into a rectangle , as shown in the figure to the left.
All kites tile the plane by repeated point reflection around the midpoints of their edges, as do more generally all quadrilaterals. [33] Kites and darts with angles 72°, 72°, 72°, 144° and 36°, 72°, 36°, 216°, respectively, form the prototiles of one version of the Penrose tiling , an aperiodic tiling of the plane discovered by ...
Around 300 BC, geometry was revolutionized by Euclid, whose Elements, widely considered the most successful and influential textbook of all time, [16] introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof.
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