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Golden rectangle. a b = a+b a = φ. 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 ...
A dynamic rectangle is a right-angled, four-sided figure (a rectangle) with dynamic symmetry which, in this case, means that aspect ratio (width divided by height) is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge 's books. These dynamic rectangles begin with a square ...
The diagonals of a square are (about 1.414) times the length of a side of the square. This value, known as the square root of 2 or Pythagoras' constant, [1] was the first number proven to be irrational. A square can also be defined as a parallelogram with equal diagonals that bisect the angles.
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.
Ulam spiral of size 201×201. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible. For comparison, a spiral with random odd numbers colored black (at the same density of primes in a 200x200 spiral). The Ulam spiral or prime spiral is a graphical depiction of the ...
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of can be found using difference of two squares: (since ) Therefore, the linear factors are and . Since the two factors found by this method are complex conjugates, we can use this in ...
Pattern Blocks. Pattern Blocks are a set of mathematical manipulatives developed in the 1960s. The six shapes are both a play resource and a tool for learning in mathematics, which serve to develop spatial reasoning skills that are fundamental to the learning of mathematics. Among other things, they allow children to see how shapes can be ...