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A root-phi rectangle divides into a pair of Kepler triangles (right triangles with edge lengths in geometric progression). The root-φ rectangle is a dynamic rectangle but not a root rectangle. Its diagonal equals φ times the length of the shorter side. If a root-φ rectangle is divided by a diagonal, the result is two congruent Kepler triangles.
The root 4 rectangle has a proportion 1:2, which means it's equivalent to two perfect squares put together. COMMENT: Any rectangle with sides of ratio 1:i, where i is any integer, is like putting i squares side by side. It has nothing to do with 2 being √4: every number is the square root of its square.
A rectangle with edges in ratio √2 : 1 can be created from a square piece of paper with an origami folding sequence. Considered a proportion of great harmony in Japanese aesthetics — Yamato-hi (大和比) — the ratio is retained if the √2 rectangle is folded in half, parallel to the short edges.
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or 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 (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
The key idea of the data structure is to group nearby objects and represent them with their minimum bounding rectangle in the next higher level of the tree; the "R" in R-tree is for rectangle. Since all objects lie within this bounding rectangle, a query that does not intersect the bounding rectangle also cannot intersect any of the contained ...
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
The root-5 rectangle can be constructed from a 1:2 rectangle (the root-4 rectangle), or directly from a square in a manner similar to the one for the golden rectangle shown in the illustration, but extending the arc of length / to both sides.
A regular octahedron with an inscribed sphere, illustrating the square root of 6 ratio between edge length and radius Root rectangles illustrate a construction of the square root of 6 An equilateral triangle with circumscribed rectangle and square; the side of the square is (+) /, and the diagonal of the rectangle is the square root of 7.