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Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite ...
The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 arctan( 1 / φ ) = arctan(2), or approximately 63.43°. A rhombus so obtained is called a golden rhombus.
A convex quadrilateral is equidiagonal if and only if its Varignon parallelogram, the parallelogram formed by the midpoints of its sides, is a rhombus. An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular. [3]
Rectangle – A parallelogram with four angles of equal size (right angles).; Rhombus – A parallelogram with four sides of equal length. Any parallelogram that is neither a rectangle nor a rhombus was traditionally called a rhomboid but this term is not used in modern mathematics.
A perfect parallelepiped is a parallelepiped with integer-length edges, face diagonals, and space diagonals. In 2009, dozens of perfect parallelepipeds were shown to exist, [3] answering an open question of Richard Guy. One example has edges 271, 106, and 103, minor face diagonals 101, 266, and 255, major face diagonals 183, 312, and 323, and ...
If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1260 ahead. Let's start with a few hints.
The rhombic dodecahedron is a polyhedron with twelve rhombuses, each of which long face-diagonal length is exactly times the short face-diagonal length [1] and the acute angle measurement is (/). Its dihedral angle between two rhombi is 120°. [2]
Poison Profits. A HuffPost / WNYC investigation into lead contamination in New York City