What is Rectangle: Definition and 244 Discussions

In Euclidean plane geometry, a rectangle is 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 occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD.
The word rectangle comes from 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 the plane by rectangles or tiling a rectangle by polygons.

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  1. Tommaso_Russo

    Rectangle inscribed in another rectangle: solutions for all cases.

    Ciao to everybody, I've encountered frequently, in forums and news groups, questions about a rectangle inscribed in another rectangle, but nowhere a general discussion on ways to solve related problems (i.e., given three of the five quantities involved - 2 sides of outer rectangle, 2 sides...
  2. M

    Cutting a rectangle with straight lines

    Hi to everyone. I'm developing a puzzle game which involves some concepts of geometry. Suppose you have a rectangle formed by points A, B, C and D. Now, I add points X1 (lies on line AB), X2 (inside the rectangle) and X3 (lies on line AC). I'd like the output to be the two rectangles...
  3. QuarkCharmer

    Rate/Relations Calc I Area of Rectangle

    Homework Statement Stewart Calculus 6E, 3.8 #4 4.) The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3cm/s. When the length is 20cm and the width is 10cm, how fast is the area of the rectangle increasing? Homework Equations A = LW The...
  4. B

    Prove that area under curve by rectangle is less than integration

    hi all, I am suppose to compare the area of curve y=x2 with rectangles beneath that curve to show that, 1/2 + 1/3 + ...+ 1/n < log(n+1) i believe this some sort of harmonic series. Is there a way around this problem? Regards
  5. A

    Lagriangian Mechanics, Rectangle (2D)

    Hi All, I'm relatively new to physics and robotics, and have been getting my head around the subject. I'm currently reading the book Introduction to Robotics by John Craig. Trying to write a simple simulation to test out some ideas to prove lagrangian dynamics...one such demo is a long...
  6. F

    Why are they using a rectangle for Guass's Law?

    Homework Statement http://www.electron.rmutphysics.com/physics/charud/scibook/Physics-for-Scientists-and-Engineers-Serway-Beichne%206edr-4/32%20-%20Inductance.pdf Please flip to page 11/30 you will see a coaxial cable. Read to the end where they begin integrating using Guass's Law...
  7. V

    Find the magnetic field at the center of a rectangle

    Homework Statement find |B| at the center of a rectangular loop of wire of sides a and b carrying current I Homework Equations B = uI/2piR The Attempt at a Solution - current flowing counterclockwise - original art work :D I did the proof for biot savart law as a...
  8. B

    Find the minimum premeter for a rectangle?

    Homework Statement A rectangular field to contain a given area is fenced off, along a stright river. if no fencing is required along the river, show that the lest amount of fencing will be required when the length of the field is twice its width. Homework Equations N/A The Attempt...
  9. B

    Find max area of rectangle inside a right triangle.

    Homework Statement Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12cm. the two sides of the rectangle lie along the legs. Homework Equations N/a The Attempt at a Solution
  10. E

    How to Insure a Rectangle Lies Inside a Polyhedron?

    Hi, How to insure that a rectangle \mathbf{R}=\{\mathbf{x}\in R^n:\mathbf{l}\leq\mathbf{x}\leq\mathbf{u}\} lies inside a polyhedron \mathbf{P}=\{\mathbf{x}\in R^n: \mathbf{A}\mathbf{x}\leq\mathbf{b}\} Thanks
  11. R

    Calc: area of rectangle under curve

    Homework Statement Let A(x) be the area of the rectangle inscribed under the curve y = e^-2x^2 with vertices at (-x, 0) and (x, 0), x >= 0 a.) find A(1) b.) what is the greatest value of A(x)? justify your answer c.) what is the average value of A(x) on the interval 0 <= x <= 2 The...
  12. R

    Calculating size of rectangle cross section

    Homework Statement A cmedium carbon steel rod has a rectangular cross section and must cope with a tension of 29 430 Newtons . The thickness of the rod is 15 mm calculate the siz of the cross section? Homework Equations A=P/Ok [b]3. The Attempt at a Solution [/b O = UTS = 750...
  13. M

    How to calc sides of rectangle inside a rotated rectangle

    I'm hoping for some help as it has been 20 years since I last used trigonometry and Google has come up empty. I'm programming simple image editing software and for a crop function I need a formula to calculate the sides of the largest possible rectangle inside a rotated rectangle, given the...
  14. T

    Rectangle inscribed in an ellipse.

    Find the area of the largest rectangle that can be inscribed (with sides parallel to the axes in the ellipse). x^2/a^2 +y^2/b^2 = 1 I came across the above problem and am not sure how to proceed with it. I drew the ellipse with the inscribed rectangle and tried repositioning the ellipse so...
  15. B

    Rectangle question and closure of the interior?

    The question says: Show that if Q = [a1,b1]x...x[an,bn] is a rectangle, the Q equals the closure of Int Q. The definition of closure that I have is Cl(A) = int(A) U bd(A). So I'd like to show that Cl(int(Q)) = int(int(Q)) U bd(int(Q)). But this just seems to be obvious to me which just makes...
  16. K

    Approximating Area of Region Bounded by y=sin(x) and x=0 to π

    Homework Statement http://www.webassign.net/mapleplots/d/e/f859372171ea15352ef17952ba81cb.gifv Use the rectangles in each graph to approximate the area of the region bounded by y = sin(x), y = 0, x = 0, and x = π. (Round your answer to three decimal places.) Homework Equations...
  17. B

    Volume of a rectangle by cross-sections

    Homework Statement There is no specific problem, I'm just confused after reading the chapter. Consider a pyramid 3 m high with a square base that is 3 m on a side. The cross section of the pyramid perpendicular to the altidude x m down from the vertex is a square x m on a side. Now I...
  18. I

    Rectangle inscribed in Triangle

    Let PQRS be a rectangle inscribed in a triangle ABC(i.e P is in AC, Q in BC and R,S are in AB). Find the locus of points that are intersection of diagonals of the rectangle. (i.e find the locus of intersection of RQ and PS)
  19. T

    Find area of a rectangle if length is given

    if the length of a rectangle = x, show that the area of the rectangle is given by A = 8x - x[2]
  20. F

    Area Moment of Inerita simple rectangle composite I'm lost

    Homework Statement Determine the moments of the inertia of the Z-section about its centroidal x0 and y0 axes. I didn't draw them in, but the x0 axis is 80[mm] up from the bottom and the y0 axis is 90[mm] from the left most point. So it is in the middle of the piece. The Attempt at a...
  21. T

    Second Moment of Area for rotating rectangle

    Hi all, first post here but I've long browsed these forums for answers in the past. I couldn't find an answer to my question through searching but I appologise in advance if it has been asked before. Homework Statement I want to find an expression which relates second moment of area to...
  22. E

    Electric Potential of charges on a rectangle

    Homework Statement Consider charges placed at the corners of a rectangle. This rectangle is a horizontal rectangle and is .43 m long and .25 m wide. At the upper right corner there is a charge of 7.0 µC. At the bottom right there is a charge of -14 µC. At the bottom left there is a charge of...
  23. S

    Rectangle inscribed in ellipse

    Homework Statement Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed in the ellipse x^2 + 4y^2 = 4 Homework Equations The Attempt at a Solution I simplified the equation of the ellipse into the ellipse formula: x^2/4 + y^2 = 1...
  24. U

    Electric Potentials (4 charges on corners of a rectangle)

    Homework Statement A rectangle has sides of length 5cm (right and left) and 15cm (top and bottom). Top left corner has charge (q1) = -5uC Top right corner has charge A = ? Bottom left corner has charge B = ? Bottom right corner has charge (q2) = 2uC a) What are the electric...
  25. H

    What is the maximum perimeter for a rectangle inside an ellipse?

    Homework Statement A rectangle is placed symmetrically inside an ellipse (i.e. with all four corners touching the ellipse) which is defined by: x^{2} + 4y^{2} = 1 Find the length of the longest perimeter possible for such a rectangle. Homework Equations Within the problem...
  26. M

    Finding the Number of Lines from A to B in a 4x7 Rectangle

    Homework Statement The number of lines from A to B if you must travel along the lines going up and right is... (there is a rectangle with that has 4 cubes going down vertically and 7 horizontally (4x7) and a is at the bottom left, be is at the top right)
  27. Z

    Torque on an open-ended rectangle

    I was at work and we build a "fence" on a trailor to keep the load in place, and we got into a disagreement about how much stress would be on each corner if we hit a bump and the boards moved up unequally. Now, there's a lot more physics in that scenario than the one I am describing but I think...
  28. L

    Optimization - area of rectangle

    Homework Statement If the perimeter of a rectangle is fixed in length, show that the area of the rectangle is greatest when it is square Homework Equations The Attempt at a Solution if the perimeter is fixed in length, then 2x + 2y = c then no idea to continue from there
  29. Hootenanny

    Solve Unperturbed Field on Rectangle w/ Small Disk

    Homework Statement The overall question is to construct an asymptotic approximation for a harmonic field on a rectangle with a small disk. However, I'm having difficulty finding the unperturbed field. Perhaps I've been staring at it for too long, but I can't seem to find a solution. The...
  30. B

    Can a Bounded Function on a Rectangle be Integrable over Q?

    Homework Statement Let Q=I\times I (I=[0,1]) be a rectangle in R^2. Find a real function f:Q\to R such that the iterated integrals \int_{x\in I} \int_{y\in I} f(x,y) \; and \int_{y\in I} \int_{x\in I} f(x,y) exists, but f is not integrable over Q. Edit: f is bounded Homework...
  31. M

    Radius of gyration (rectangle)

    I'm trying to figure out the radius of gyration of the frame about O. Homework Statement A rectangular frame is put together with massless rods having identical 1.8 lb weights placed at the corners as shown in the figure. The frame is pivoted about an axis passing through O, the center of...
  32. T

    Help Rectangle to Cylindrical coordinate question

    Homework Statement evaluate : \int\int\int_{E} e^z DV where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5 I just need help setting this up. I know that theta is between 0 and 2pi Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5)...
  33. T

    Rectangle to Cylindrical coordinate question

    Homework Statement can you explain this conversion, I am not sure. Rectangle coord : \int^{2}_{-2}\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}\int^{2}_{sqrt(x^2 + y^2 )} F(x) dzdydx = cylindrical coord : \int^{2\pi}_{0}\int^{2}_{0}\int^{2i}_{r} r*dzdrd\theta I see that x^2 + y^2...
  34. C

    Average Value of f(x,y)=sin(x+y) Over a Rectangle

    Homework Statement Find the average value of f(x,y)=sin(x+y) over the rectangle 0 ≤ x ≤ pi, 0 ≤ y ≤ pi. Homework Equations I need to know if this is the right answer please. The Attempt at a Solution I got 1/pi as a answer.
  35. S

    Related rate expanding rectangle

    Homework Statement The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3cm/s when the length is 20 cm and the width is 10cm, how fast is the area of the rectangle increasing? Homework Equations V=LW The Attempt at a Solution dL/dt=8...
  36. P

    Comp Sci Maximizing Rectangle Surface Area with Fortran Squares

    Homework Statement Hi, I have to do a project in Fortran based on solving a system. My professor mentioned one idea to me, I am trying to see if this idea is even feasible and some potential ways to progress through it before I submit a project proposal to do it. The problem is based on...
  37. Hepth

    Point in a rectangle given angles only

    Homework Statement Imagine you're given a rectangle, with lengths LX and LY. Now we place a point somewhere inside this rectangle, we don't know where it is. What we DO know, is the angle between lines from the corners to that point. (such that if it was at the center, and the point a square...
  38. L

    Statics Problem, Simple 2d rectangle with forces acting on it.

    Homework Statement A rectangular plate is acted upon by the force and couple shown. This system is to be replaced with a single equivalent force. a) for a(alpha)=40 degrees, specify the magnitude and the line of action of the equivalent force. b)Specify the value of a(alpha) if the line of...
  39. Saladsamurai

    Finding the Vertex Coordinates of a Rectangle In Cartesian Space

    I am hoping to find the coordiantes of all 4 vertices when the rectangle is in any orientaion knowing the length l, the width b, the coordinate of its center mark (xcen,ycen), and the coordinate of vertex A as shown below: This is NOT HOMEWORK so although I think it is possible to do, I am...
  40. K

    Finding Optimal Cell Size for Uniform Rectangle Packing

    Hi I'm writing a newspaper page management application and am having trouble trying to directly calculate a "best fit" column/row breakdown for displaying pages into arbitrary rectangles. The arbitrary rectangle in question is the content area of a window and can be resized at will by the...
  41. X

    Rectangle tipping point on ramp

    A uniform 10 cm x 20 cm box is placed on a ramp that rises at angle theta above the horizontal. Assuming that there is enough friction to prevent this box from sliding, what is the largest that theta can be without tipping it over? do i use torque = r*F*sin*(theta), if so how do i use it?
  42. G

    Finding the dimensions of a rotated rectangle inside another rectangle.

    Homework Statement If I have a rectangle rotated at a known angle with respect to a rectangle of known dimensions that inscribes it, how can I find the dimensions of the inscribed/inner rectangle...
  43. L

    Solving for perimeter and dimensions of a rectangle

    I understand calculus, I just don't understand how it is applied to solve these sorts of problems. Homework Statement What is the smallest perimeter for a rectangle with an area of 16, and what are its dimensions?Homework Equations A=L*W P=2W+2L The Attempt at a Solution I managed to get the...
  44. Q

    Global Extrema/Area of a Rectangle

    Homework Statement Find the dimensions of of the rectangle with perimeter 200 meters that has the largest area. Homework Equations The Attempt at a Solution This is in the section on Global Maxima/Minima so I know it has to be something with graphing a formula and finding the...
  45. L

    Laplace's equation on a rectangle (mixed bndy)

    Homework Statement I'm having issues with a deceptively simple Laplace problem. If anybody could point me in the right direction it would be fantastic. It's just Laplace's equation on the square [0.1]x[0,1] (or any rectangle you like) with a mixed boundary. Homework Equations...
  46. Y

    Calculus BC: Rectangle inside an ellipse

    Homework Statement What is thea are of the largest rectangle that can be inscribed in the ellipse 4x^2 +9y^2 = 36 A) 6 rad 2 B) 12 C)24 D) 24 rad 2 E) 36 Homework Equations Must be done using optimization and first derivitive The Attempt at a Solution I know I have to use A=...
  47. P

    Calculate the 2d height of the rectangle

    I have a rectangle i am rotating in 3d on multiple axis. i am trying to calculate the 2d height of the rectangle and I am quite lost. For example, if i rotate the rectangle on the x-axis so the top of the rectangle comes forward and the bottom moves back. i can calculate the height of this...
  48. A

    Overlapped area between a triangle and a rectangle

    Hi all: My question is how to calculate the overlapped area of a triangle and rectangle. It sounds a simple question but is there any way to do it efficiently? And is it possible there is a uniformed equation to solve such a problem? As there are many cases the triangle can overlap with...
  49. S

    Finding the Width of a Rectangle at a Changing Rate: A Related Rates Problem

    Homework Statement A rectangle has a constant area of 200m2 and its length L is increasing at the rate of 4 meters per second. Find the width W at the instant the width is decreasing at the rate of 0.5 meters per second. Homework Equations A=200 dA/dt =0 (since the area is constant)...
  50. M

    Double Integral Limits for a Sideways Rectangle

    Homework Statement I have to solve the integral of (ytan^-1(x) - 3) inside the area of the rectangle with vertices (1,0), (0,1), (2,3), (3,2). How do I set up these limits? Homework Equations This is a tilted rectangle so I can't use just values for the limits? The Attempt at a...
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