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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 article says that root rectangles are part of the broader group of dynamic rectangles. It also says that dynamic rectangles have irrational (in the mathematical sense) proportions. But a lot of root rectangles have rational proportions. Hambidge himself illustrates a root-4 rectangle, which is rational. So is root-1, a square.
Sierpiński Carpet - Infinite perimeter and zero area Mandelbrot set at islands The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
The stem of a plant, especially a woody one; also used to mean a rootstock, or particularly a basal stem structure or storage organ from which new growth arises. Compare lignotuber. caudiciform Stem-like or caudex-like; sometimes used to mean "pachycaul", meaning "thick-stemmed". caudicle diminutive of caudex.
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 ...
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A root of a polynomial is sometimes said to be degenerate if it is a multiple root, since generically the n roots of an n th degree polynomial are all distinct. [1] This usage carries over to eigenproblems: a degenerate eigenvalue is a multiple root of the characteristic polynomial.