What is Rectangular: Definition and 477 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. reddvoid

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    How to identify type of wave-guide mode here, like its TE or TM TE01 , TE10, TM11, TE02, TE20 . .. I read number of half wavelengths in x direction is the m and number of half-wavelengths in y direction is n. . .but I can't figure-out how . . .can somebody please explain
  2. A

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    Homework Statement What is the magnitude of the velocity at t=4.00s? I would like to see if my approach and answer is correct. Homework Equations Position: r = {-30cos(\frac{\pi}{10}t) i + 30sin(\frac{\pi}{10}t) j - (7t) k} ft The Attempt at a Solution I took the first...
  3. O

    Double Integrals, Rectangular Region

    Homework Statement Using ∫∫kdA = k(b-a)(d-c), where f is a constant function f(x,y) = k and R = [a,b]x[c,d], show that 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32, where R = [0,1/4]x[1/4,1/2]. Homework Equations ∫∫kdA = k(b-a)(d-c) 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32 The Attempt at a Solution I tried to...
  4. C

    Magnetic Field above a Rectangular Circuit

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  5. W

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  6. H

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  7. W

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  8. D

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  9. Z

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  10. R

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  11. K

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  12. M

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  13. B

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  14. T

    Minimum Uncertainty in Electron Position: Rectangular Wave in k-space

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  15. 0

    Rectangular Fourier Transform and its Properties

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  16. S

    Double integral over a circular region using rectangular coord's

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  17. D

    MHB Finding Temperature in a Rectangular Plate: $\nabla^2u=0$

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  18. DeusAbscondus

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  19. S

    Analytical solution for thermal stresses in a rectangular plate

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  20. J

    Uniform Rectangular Magnetic Field

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  21. M

    Express the equation in rectangular coordinates

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  22. perplexabot

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  23. P

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  24. W

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  25. J

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  26. L

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  27. H

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  28. H

    Parametric Surfaces: rectangular and polar coordinates

    Homework Statement I'm not grasping how to convert a surface with known rectangular graph to a parametric surface (using some polar techniques, I assume). I would appreciate it if someone could clarify the conversion process. One of the examples is as follows: A sphere...
  29. C

    Counting electromagnetic modes in a rectangular cavity and boundary conditions

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  30. A

    Rigid body (rectangular) collision with wall

    Hello, I have a rectangular object with the following properties: Mass (m) = 1 units Moment Of Inertia (I) = 4.41 units initial velocity (v_{i}) = (5, 0) initial angular velocity (w_{i}) = 0 If the block collides with a solid rigid wall with distance vector r = (1.1, 1.4) from the...
  31. Jalo

    A.: Finding Center of Mass for a Rectangular Surface with a Hole

    Homework Statement Given a homogenous rectangular surface, sides of length a and b=4*a, with a circular hole in x=a and y=a/2, find the center of mass. Homework Equations R=1/M*Ʃmi*ri , M= total mass, r= position vector area of a circle = pi*r2 , r being the radius The...
  32. I

    Rectangular coil rotating in magnetic field

    Homework Statement A rectangular coil of 80 turns has an area of 0.01m^2. It rotates @ 3000rpm about one of its in plane axes, in a uniform magnetic field having B=1.5T. Calculate the rms voltage generated. Homework Equations 1 Tesla= 1 Weber/m^2. Change in flux of 1 Weber per second...
  33. V

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    Homework Statement I'm trying to solve the vibrations of a rectangular membrane with a rectangular hole inside. Both the inner and outer edges are fixed. I know i have to use the wave equation, but how do i write the boundary conditions in orden to incluye the hole? Any ideas? F.Y.I. I...
  34. S

    Please help elimante the parameter to find a rectangular equation.

    Homework Statement Elimnate the parameter to find a rectangular equation of the curve. x=sin t, y= csc t Homework Equations I believe trignometric identities are relevant to this problem. cscx=1/sinx The Attempt at a Solution csc x =1/ sin x thus y=1/x Is this the answer...
  35. Y

    Magnetic field direction created by rectangular circuit

    Hey guys, this is just a conceptual question so i don't think the scheme applies? I've got a circuit with a potential difference, when I use the right hand rule to determine the direction of the magnetic field created by the wire of any side of the rectangle, do I point my thumb (direction of...
  36. L

    Connect a Battery to a Solenoid - Current through a rectangular coil

    Homework Statement Connect a battery to a solenoid A cylindrical solenoid 40 cm long with a radius of 8 mm has 250 tightly-wound turns of wire uniformly distributed along its length (see the figure). Around the middle of the solenoid is a two-turn rectangular loop 3 cm by 2 cm made of...
  37. C

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    Consider a toroidal structure with a rectangular cross-section. If the toroid is defined by the surfaces r = 1cm and r = 4cm and the planes z = 0 cm and z = 2 cm, and the surface current density on the surface defined by r = 4cm is given by -60az A/m. (a) Specify the current densities on...
  38. S

    Convert this rectangular coordinate system point to spherical coordinate system

    Homework Statement The point is (0, -8, 0) r≥0 0≤θ≤2∏ 0≤\varphi≤∏ Homework Equations The Attempt at a Solution So here is what I've done so far: I know that r=8 because x and z are 0 I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation...
  39. E

    What is the force exerted by a magnetic field on a rectangular loop of wire?

    Homework Statement A rectangular loop of wire with dimensions 2.32 by 7.91 and resistance 0.557 is being pulled to the right out of a region of uniform magnetic field. The magnetic field has magnitude 3.01 and is directed into the plane of the following figure . At the instant when the...
  40. S

    Find the maximum value of a rectangular box that can be inscribed in an ellipsoid

    "Find the maximum value of a rectangular box that can be inscribed in an ellipsoid.." Homework Statement Find the maximum value of a rectangular box that can be inscribed in an ellipsoid x^2 /4 + y^2 /64 + z^2 /81 = 1 with sides parallel to the coordinate to the coordinate axes...
  41. S

    Find the most economical dimensions of a closed rectangular box [..]

    "Find the most economical dimensions of a closed rectangular box [. . .]" Homework Statement Find the most economical dimensions of a closed rectangular box of volume 8 cubic units if the cost of the material per square unit for (i) the top and bottom is 5, (ii) the front and back is 2 and...
  42. B

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    Homework Statement A rectangular loop with dimensions 4.2 cm by 9.5 carries current I. The current in the loop produces a magnetic field at the center of the loop that has magnitude 5.60×10−5 T and direction away from you as you view the plane of the loop.Homework Equations...
  43. M

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    Homework Statement A rectangular coil of 90 turns has dimensions of 22 x 65 cm and is located in a uniform 1 T magnetic field. In 1.7 s, the plane of the coil is rotated from a position where it makes an angle of 19° with the magnetic field to a position where it makes an angle of 64°...
  44. S

    Navier-Stokes equations for unique flow through a rectangular diverging pipe

    I am currently trying to provide a mathematical model that describes the flow through a diverging square pipe. I am trying to simplyfy the navier stokes equations by usings assumptions but am unsure if my current progress is correct. The problem is as follows: Fluid enters a section of a...
  45. D

    Integral calculus: plane areas in rectangular coordinates

    Homework Statement Find the area between y= 1/(x2+1) and the x-axis, from x=0 to x=1 The Attempt at a Solution so when x=0, y=1 and when x=1, y=1/2 next i plot the points, so the intersection of the given equation is (0,1) and (1,1/2) Yh= Y-higher= 1/(x2+1) Yl= Y-lower= 0 the...
  46. C

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    Homework Statement A rectangular container partly filled with water up to height , after being slightly disturbed , the urface of water begins to slosh . Assume that the water surface remains practically flast during sloshing , find the time period of the sloshing mode. take width to be...
  47. S

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  48. TheFerruccio

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  49. H

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    I'm worried about the process of solving this problem, can anyone help me? We are to make a rectangular box, including the top, that has a volume of 144 cubic inches and for which the base is twice as wide as it is deep. The bottom, which must be strong, is made of a material that is three...
  50. J

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