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27-459: In 1723, the Château Vaudreuil was built for Philippe de Rigaud, Marquis de Vaudreuil - its formal gardens occupying the space that is now the square. The Chateau burned down in 1803 and it was suggested by The Hon. Jean-Baptiste Durocher and The Hon. Joseph Périnault that the space be transformed into a public square, known as New Market Place. In 1809, Montreal's oldest public monument

54-520: 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 term " oblong " is used to refer to a non- square rectangle. A rectangle with vertices ABCD would be denoted as [REDACTED]   ABCD . The word rectangle comes from

81-462: A drink or dining in the open air. And on the other side of the place, the famous restaurant Saint-Amable (the oldest restaurant in town) welcomes Montreal celebrities and locals in a crooner jazz atmosphere. Near Place Jacques-Cartier on rue de la Commune, an original piece of the wall of the old fortified city can still be seen in the basement restaurant of the Auberge du Vieux-Port. At the upper end of

108-431: A pentagon. The unique ratio of side lengths is a b = 0.815023701... {\displaystyle \displaystyle {\frac {a}{b}}=0.815023701...} . A crossed quadrilateral (self-intersecting) consists of two opposite sides of a non-self-intersecting quadrilateral along with the two diagonals. Similarly, a crossed rectangle is a crossed quadrilateral which consists of two opposite sides of

135-406: A rectangle along with the two diagonals. It has the same vertex arrangement as the rectangle. It appears as two identical triangles with a common vertex, but the geometric intersection is not considered a vertex. A crossed quadrilateral is sometimes likened to a bow tie or butterfly , sometimes called an "angular eight". A three-dimensional rectangular wire frame that is twisted can take

162-434: A rectangle is a rhombus , as shown in the table below. A rectangle is a rectilinear polygon : its sides meet at right angles. A rectangle in the plane can be defined by five independent degrees of freedom consisting, for example, of three for position (comprising two of translation and one of rotation ), one for shape ( aspect ratio ), and one for overall size (area). Two rectangles, neither of which will fit inside

189-435: A rectangle. A parallelogram with equal diagonals is a rectangle. The Japanese theorem for cyclic quadrilaterals states that the incentres of the four triangles determined by the vertices of a cyclic quadrilateral taken three at a time form a rectangle. The British flag theorem states that with vertices denoted A , B , C , and D , for any point P on the same plane of a rectangle: For every convex body C in

216-414: A unique rectangle with sides a {\displaystyle a} and b {\displaystyle b} , where a {\displaystyle a} is less than b {\displaystyle b} , with two ways of being folded along a line through its center such that the area of overlap is minimized and each area yields a different shape – a triangle and

243-432: Is a convex quadrilateral which has at least one pair of parallel opposite sides. A convex quadrilateral is De Villiers defines a rectangle more generally as any quadrilateral with axes of symmetry through each pair of opposite sides. This definition includes both right-angled rectangles and crossed rectangles. Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another which

270-477: Is the perpendicular bisector of those sides, but, in the case of the crossed rectangle, the first axis is not an axis of symmetry for either side that it bisects. Quadrilaterals with two axes of symmetry, each through a pair of opposite sides, belong to the larger class of quadrilaterals with at least one axis of symmetry through a pair of opposite sides. These quadrilaterals comprise isosceles trapezia and crossed isosceles trapezia (crossed quadrilaterals with

297-406: Is used in many periodic tessellation patterns, in brickwork , for example, these tilings: A rectangle tiled by squares, rectangles, or triangles is said to be a "squared", "rectangled", or "triangulated" (or "triangled") rectangle respectively. The tiled rectangle is perfect if the tiles are similar and finite in number and no two tiles are the same size. If two such tiles are the same size,

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324-865: The Château Saint-Louis in Quebec City remained the official residence of the Governors General of New France , the Château Vaudreuil was to remain as their official home in Montreal up until the British Conquest in 1763. In 1767, it was purchased by the Marquis de Lotbinière . He sold it in 1773, when it became the Collège Saint-Raphaël . It was destroyed by a fire in 1803. Completed in 1726, it

351-742: The Latin rectangulus , which is a combination of rectus (as an adjective, right, proper) and angulus ( angle ). A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram , and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical , elliptic , and hyperbolic , have so-called rectangles with opposite sides equal in length and equal angles that are not right angles. Rectangles are involved in many tiling problems, such as tiling

378-569: The Place stands Nelson's Column , built in memory of Admiral Horatio Nelson . The statue was removed in 1997 to preserve it from the weather, and was subsequently replaced with a copy. Ch%C3%A2teau Vaudreuil Château Vaudreuil was a stately residence and college in Montreal , Quebec, Canada. It was constructed between 1723 and 1726 for Philippe de Rigaud, Marquis de Vaudreuil , as his private residence by Gaspard-Joseph Chaussegros de Léry . Though

405-421: The fire in 1803, a group of merchants, led by The Hon. Jean-Baptiste Durocher and The Hon. Joseph Périnault , purchased the land. On the condition that it would be used for public markets , they gave the government a small, oblong , strip of land (that had made up part of the formal gardens ), which was first named New Market Place and from 1847 became known as Place Jacques-Cartier . This canny deal made by

432-561: The merchants had the effect of increasing the value of the adjacent properties built around the 'square', which remained in private hands. In 1809, Nelson's Column was built by the citizens of Montreal in what had been part of the Château's formal gardens . [REDACTED] Media related to Château de Vaudreuil at Wikimedia Commons 45°30′28″N 73°33′10″W  /  45.50769°N 73.55264°W  / 45.50769; -73.55264 Rectangle In Euclidean plane geometry ,

459-418: The other, are said to be incomparable . If a rectangle has length ℓ {\displaystyle \ell } and width w {\displaystyle w} , then: The isoperimetric theorem for rectangles states that among all rectangles of a given perimeter , the square has the largest area . The midpoints of the sides of any quadrilateral with perpendicular diagonals form

486-464: The outside and exceed 180°. A rectangle and a crossed rectangle are quadrilaterals with the following properties in common: [REDACTED] In spherical geometry , a spherical rectangle is a figure whose four edges are great circle arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length. The surface of a sphere in Euclidean solid geometry is a non-Euclidean surface in

513-510: The plane by rectangles or tiling a rectangle by polygons . A convex quadrilateral is a rectangle if and only if it is any one of the following: A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular . A parallelogram is a special case of a trapezium (known as a trapezoid in North America) in which both pairs of opposite sides are parallel and equal in length . A trapezium

540-439: The plane, we can inscribe a rectangle r in C such that a homothetic copy R of r is circumscribed about C and the positive homothety ratio is at most 2 and 0.5  × Area ( R ) ≤ Area ( C ) ≤ 2  × Area ( r ) {\displaystyle 0.5{\text{ × Area}}(R)\leq {\text{Area}}(C)\leq 2{\text{ × Area}}(r)} . There exists

567-417: The same vertex arrangement as isosceles trapezia). A rectangle is cyclic : all corners lie on a single circle . It is equiangular : all its corner angles are equal (each of 90 degrees ). It is isogonal or vertex-transitive : all corners lie within the same symmetry orbit . It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°). The dual polygon of

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594-511: The sense of elliptic geometry. Spherical geometry is the simplest form of elliptic geometry. In elliptic geometry , an elliptic rectangle is a figure in the elliptic plane whose four edges are elliptic arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length. In hyperbolic geometry , a hyperbolic rectangle is a figure in the hyperbolic plane whose four edges are hyperbolic arcs which meet at equal angles less than 90°. Opposite arcs are equal in length. The rectangle

621-403: The shape of a bow tie. The interior of a crossed rectangle can have a polygon density of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise. A crossed rectangle may be considered equiangular if right and left turns are allowed. As with any crossed quadrilateral , the sum of its interior angles is 720°, allowing for internal angles to appear on

648-468: The street is lined with lighted trees. At any time of year, one can find restaurants on both sides of the street and many more on the surrounding streets of Vieux Port, notably on Rue Saint-Paul . It is a car-free zone in the summer. During the summer season, Jardin Nelson offers a garden restaurant on Place Jacques-Cartier. Other restaurants similarly offer classical Parisian -style "terraces" for taking

675-464: The tiling is imperfect . In a perfect (or imperfect) triangled rectangle the triangles must be right triangles . A database of all known perfect rectangles, perfect squares and related shapes can be found at squaring.net . The lowest number of squares need for a perfect tiling of a rectangle is 9 and the lowest number needed for a perfect tilling a square is 21, found in 1978 by computer search. A rectangle has commensurable sides if and only if it

702-594: Was built in the classical style of the French Hôtel Particulier by King Louis XV 's chief engineer in New France , Gaspard-Joseph Chaussegros de Léry . The central building was flanked by two wings with two sets of semi-circular stairs leading up to a terrace and the main entrance. It stood beyond the end of Rue Saint-Paul , which was kept clear of buildings on that side to afford it a clear view, while formal gardens led up to Notre-Dame Street . Following

729-465: Was raised there, Nelson's Column . In 1847, the square was renamed in honour of Jacques Cartier , the explorer who claimed Canada for France in 1535. The broad, divided street slopes steeply downhill from Montreal City Hall and rue Notre-Dame to the waterfront and rue de la Commune . During the high tourist season, the street hosts many street artists and kiosks . During the Christmas season,

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