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Four unequal lengths, each less than the sum of the other three, are the sides of each of three non-congruent cyclic quadrilaterals, [13] which by Brahmagupta's formula all have the same area. Specifically, for sides a, b, c, and d, side a could be opposite any of side b, side c, or side d.
Quadrilateral – 4 sides Cyclic quadrilateral; Kite. Rectangle; Rhomboid; Rhombus; Square (regular quadrilateral) Tangential quadrilateral; Trapezoid. Isosceles trapezoid; Trapezus; Pentagon – 5 sides; Hexagon – 6 sides Lemoine hexagon; Heptagon – 7 sides; Octagon – 8 sides; Nonagon – 9 sides; Decagon – 10 sides; Hendecagon – 11 ...
Diagram of flower parts. In botany, floral morphology is the study of the diversity of forms and structures presented by the flower, which, by definition, is a branch of limited growth that bears the modified leaves responsible for reproduction and protection of the gametes, called floral pieces.
Lost organs can be represented by a star ( ), lost perianth parts or bracts/bracteoles can be shown with dashed stroke. It is possible to show the direction of monosymmetry by a large arrow. Resupination may be illustrated by a curved arrow. Floral parts can be accompanied by numbers to show their sequence of initialization.
Each circle is labeled by an integer i, its position in the sequence; it has radius ρ i and curvature ρ −i. When the four radii of the circles in Descartes' theorem are assumed to be in a geometric progression with ratio , the curvatures are also in the same progression (in reverse). Plugging this ratio into the theorem gives the equation
The vertices of every triangle fall on a circle called the circumcircle. (Because of this, some authors define "concyclic" only in the context of four or more points on a circle.) [2] Several other sets of points defined from a triangle are also concyclic, with different circles; see Nine-point circle [3] and Lester's theorem.
A p4g pattern can be looked upon as a checkerboard pattern of copies of a square tile with 4-fold rotational symmetry, and its mirror image. Alternatively it can be looked upon (by shifting half a tile) as a checkerboard pattern of copies of a horizontally and vertically symmetric tile and its 90° rotated version.
The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.