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A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base. It is named after Giovanni Gerolamo Saccheri , who used it extensively in his 1733 book Euclides ab omni naevo vindicatus ( Euclid freed of every flaw ), an attempt to prove the parallel postulate using the method reductio ad absurdum .
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. [13] Right trapezoids are used in the trapezoidal rule for estimating areas under a curve. An acute trapezoid has two adjacent acute angles on its longer base edge. An obtuse trapezoid on the other hand has one acute and one obtuse angle on each base.
Shape Area Perimeter/Circumference ... This is a list of volume formulas of basic shapes: [4]: 405–406 ... List of formulas in elementary geometry. 2 languages ...
Consequently, rectangles exist (a statement equivalent to the parallel postulate) only in Euclidean geometry. A Saccheri quadrilateral is a quadrilateral with two sides of equal length, both perpendicular to a side called the base. The other two angles of a Saccheri quadrilateral are called the summit angles and they have equal measure. The ...
where K is the area of a convex quadrilateral with perimeter L. Equality holds if and only if the quadrilateral is a square. The dual theorem states that of all quadrilaterals with a given area, the square has the shortest perimeter. The quadrilateral with given side lengths that has the maximum area is the cyclic quadrilateral. [43]
Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.