वर्गाकार
| वर्ग | |
|---|---|
 वर्ग की भुजाएं एवं विकर्ण आपस में समकोण पर मिलते हैं | |
| किनारे एवं शीर्ष | 4 |
| श्लाफ्ली चिन्ह | {4} {}x{} |
| en:Coxeter–Dynkin diagram |     |
| सममिति समूह | डाईहेडरल (D4) |
| क्षेत्रफल (with t=edge length) | t2 |
| आंतरिक कोण (अंश | 90° |
तलीय यूक्लिड ज्यामिति में वर्ग एक सम-चतुर्भुज है, जिसके चारो कोण ९० अंश के होते हैं।
वर्गीकरण
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।
मापन सूत्र
t भुजा वाले वर्ग का परिमाप (पेरिमीटर) :
एवं क्षेत्रफल है:
मानक निर्देशांक
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 < xi < 1.
गुण
वर्ग का प्रत्येक कोण समकोण है, यानि 90 अंश पर है।
अन्य तथ्य
- 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 (about 1.57) times the area of the square.
- If a circle is inscribed in the square, the area of the circle is (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 .
गैर यूक्लिड ज्यामिती
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}. |