वर्गाकार

वर्ग आयत की एक विशेष दशा है, क्योंकि इसमें चार समकोण हैं। वैसे ही यह सम चर्तुर्भुज (रोम्बस), एवं समानांतर चतुर्भुज की भी विशेष दशा है।

 

t भुजा वाले वर्ग का परिमाप (पेरिमीटर) :

${\displaystyle P=4t.}$ 

एवं क्षेत्रफल है:

${\displaystyle A=t^{2}.}$ 

मूल में केन्द्रित वर्ग जिसकी भुजा लम्बाई 2 है, की भुजाओं के निर्देशांक हैं (±1, ±1), जबकि उसके आंतरिक क्षेत्र में सभी बिंदु (x₀, x₁) सम्मिलित हैं, &ऋणात्मक;1 < x_i < 1.

वर्ग का प्रत्येक कोण समकोण है, यानि 90 अंश पर है।

• It has all equal sides and the angles add up to 360 degrees. Wyoming is also a square because it has that nickname(see State nicknames).
• If a circle is circumscribed around a square, the area of the circle is ${\displaystyle \pi /2}$  (about 1.57) times the area of the square.
• If a circle is inscribed in the square, the area of the circle is ${\displaystyle \pi /4}$  (about 0.79) times the area of the square.
• A square has a larger area than any other quadrilateral with the same perimeter ([1]).
• A square tiling is one of three regular tilings of the plane (the others are the equilateral triangle and the regular hexagon).
• The square is in two families of polytopes in two dimensions: hypercube and the cross polytope. The Schläfli symbol for the square is {4}.
• The square is a highly symmetric object. There are four lines of reflectional symmetry and it has rotational symmetry through 90°, 180° and 270°. Its symmetry group is the dihedral group ${\displaystyle D_{4}}$ .

In non-euclidean geometry, squares are more generally polygons with 4 equal sides and equal angles.

In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle.

In hyperbolic geometry, squares with right angles do not exist. Rather, squares in hyperbolic geometry have angles of less than right angles. Larger squares have smaller angles.

Examples:

Six squares can tile the sphere with 3 squares around each vertex and 120 degree internal angles. This is called a spherical cube. The Schläfli symbol is {4,3}.

Squares can tile the Euclidean plane with 4 around each vertex, with each square having an internal angle of 90 degrees. The Schläfli symbol is {4,4}.

Squares can tile the hyperbolic plane with 5 around each vertex, with each square having 72 degree internal angles. The Schläfli symbol is {4,5}.

• घन
• पायथागोरस सिद्धांत

• वर्ग आंकलन
• Animated course (Construction, Circumference, Area)
• एरिक डब्ल्यू वेइसटीन, मैथवर्ल्ड पर Square
• Definition and properties of a square With interactive applet
• Animated applet illustrating the area of a square