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. T

    Calculate Average Emf in Rectangular Coil

    Homework Statement A rectangular coil of wire has 65.0 turns and is 30.0cm by 43.0cm . Initially the plane of the coil is perpendicular to a uniform external magnetic field. It is then rotated till its plane is at an angle of 35.0∘ with that field. The magntude of the external field is 1.90T...
  2. T

    Evaluating dA for the Rectangular Region R

    Homework Statement Evaluate dA, where R is the rectangular region described in 0 ≤ x ≤ 10ln7 and 25 ≤ y ≤ 50 Homework Equations dA = dxdy or dA = dydx The Attempt at a Solution I drew the rectangle on a Cartesian plane, but the problem is I don't know what the question is asking. I...
  3. Raerin

    MHB Converting r=4+4cos(theta) into rectangular form

    So how do I convert r=4+4cos(theta) into rectangular form? I know that r^2 = x^2+y^2 and that rcos(theta) = x. Would the start of the solution be: sqrt(x^2 + y^2) = 4+4x If yes, I don't know where to go from there.
  4. R

    Find arcsine(-2) using the rectangular representation of sin w

    Homework Statement Find \sin^{-1}(-2) by writing [tex]sin w = -2[/itex] and using the rectangular representation of \sin w Homework Equations Rectangular representation of \sin w The Attempt at a Solution I think my biggest problem here is I have literally no idea what the...
  5. S

    Tunneling from Rectangular barrier - Exponential Decay ?

    Tunneling from Rectangular barrier - Exponential Decay ?? Consider the Rectangular Potential Barrier. If one solves bound state Problem in this case, wavefunctions of Exponentially Decaying and rising kind are found for the Region in the Barrier. ψ = A eαx + B e-αx Yet Most Books and...
  6. P

    Rectangular vs Tapered vs Elliptical Wing planform

    I wonder what are the advantages and disvantages of the rectangular, tapered and elliptical wing planforms.
  7. Lebombo

    Convert the polar equation to rectangular form.

    Homework Statement r = 3sin\theta since x= rcos\theta x = 3sin\thetacos\theta and since: y = rsin\theta y = 3sin^2\theta Then I'm sort of stuck..
  8. Lebombo

    Find the corresponding rectangular coordinates for the point.

    Homework Statement Find the corresponding rectangular coordinates for the point. (-2, \frac{5\pi}{3}) x = -2cos(\frac{5\pi}{3}) x = -2cos(\frac{2\pi}{3}) x = -2* \frac{-1}{2} = 1 y = -2sin(\frac{5\pi}{3}) y = -2sin(\frac{2\pi}{3}) y = -2*\frac{\sqrt{3}}{2} =...
  9. U

    TE Waves in Rectangular Wave Guide

    Hi guys I'm having difficulty understanding why the boundary conditions lead to dX/dx = 0. Why must Bx = 0 at x = 0 and x = a?
  10. L

    Convolution of a linear and rectangular function

    Hi everyone Homework Statement I want to to calculate the convolution of the following two functions h(t)=\left\{\begin{array}{ll} t, & 0 \leq t \leq 10 \\ 0, & otherwise\end{array}\right. and the function x(t)=\left\{\begin{array}{ll} A, & 0 \leq t \leq 10 \\ 0, &...
  11. O

    Rectangular Waveguide: Boundary Conditions for Electromagnetic Waves

    Homework Statement I have a rectangular, hollow, conductor. Something like this: The length in z direction should be infinite. The propagation of electromagnetic waves in the conductor are given via the equations: Homework Equations \Delta \vec{E} = \frac{1}{c^2}...
  12. S

    Couple calculations Polar to Rectangular Form

    Homework Statement I need to find i1+i2 Homework Equations for i1=0.092<-98.86 i2=-4i1-j10/25=-4i1-0.4 i1=0.092<-98.86 x=rcosθ=0.092cos(-98.86)=-0.0142 y=rsinθ=0.092sin(-98.86)=-0.0909 i1=-0.0142-j0.0909 Therefor...
  13. karush

    MHB Convert r = 5sin(2θ) to rectangular coordinates

    convert r=5\sin{2\theta} to rectangular coordinates the ans to this is $\left(x^2+y^2\right)^{3/2}=10xy$ however... multiply both sides by $r$ to get $r^2=5\cdot r \cdot \sin{2\theta}$ then substitute $r^2$ with $x^2+y^2$ and $\sin{2\theta}$ with $2\sin\theta\cos\theta$ and divide each side...
  14. D

    MCNP planar source (rectangular)

    Hello to everybody, I need some explanation on how to use SDEF variables to define correctly a planar rectangular source. Let say this source is emitting in all direction but I am interested in a side of the source surface where a point detector is located. I used in my example VEC (VEC =001)...
  15. B

    Load Impedences - Rectangular to Polar

    Homework Statement Can you simplify rectangular expression 1/j30 + 1/10 + 1/(15-j25) The answer is .134 angle(28.07) Homework Equations The Attempt at a Solution I got = 1/j30 + 1/10 + 1/(15-j25) = -j.03+.1+.06+j.04 = .16 + j.01 = .16 angle(3.57) The...
  16. M

    Nyquist frequency for a system with rectangular pixels

    hey everyone, so i know to calculate the nyquist frequency for a system (for digital imaging in PET and SPECT in this example) given the pixel size its just f = 1/ 2 * pixel size but for pixels that are rectangular and have a larger and smaller dimension, which one should be used here...
  17. F

    Rectangular Waveguide With Dipole in it

    Hi, I know that to receive or inject a signal into a rectangular waveguide (I'll just call it a waveguide from now on with the assumption that I mean rectangular waveguide), you can get a dipole of some sort, and poke it into the waveguide. What I'm wondering about is, if I got a dipole...
  18. S

    Chemical Engineering Computation - Rectangular Matrix Formulation

    Hello all, I've got a somewhat mixed concept question from a Chemical Engineering computational methods class. I'm completely lost with this question, as I do not fully understand what it entails. The question (and data) is this: Homework Statement Data Set Given X Y 0.00 -2.17...
  19. R

    Rectangular function & Inequalities

    Note: I think I solved this while writing this topic, did not want to scrap it! if you think its wrong let me know! I am trying to manipulate the rectangular function with different arguments and came across a confusing one Trying to show: \prod (x^2) = \prod (\frac{x}{\sqrt{2}}) Recall that...
  20. J

    Spherical cylindrical and rectangular coordinates

    Homework Statement Suppose that in spherical coordinates the surface S is given by the equation rho * sin(phi)= 2 * cos(theta). Find an equation for the surface in cylindrical and rectangular coordinates. Describe the surface- what kind of surface is S? Homework Equations The...
  21. K

    TM waves in a rectangular waveguide

    Homework Statement Having trouble understanding why it is that inside a waveguide sides x=a,y=b propagating in z, subject to b.c. E parallel= 0 and Bperp=0... that for TE Bz=Bcos(pinx/a)cos(pimy/b) but for TM Ez=Esin(pinx/a)sin(pimy/a)? Homework Equations E parallel= 0 and Bperp=0 For...
  22. A

    Finding the Fourier Series of a periodic rectangular wave

    Homework Statement The problem/question is attached in the file called "homework". In the third signal (the peridic rectangular wave), I am requested (sub-question b) to find the Fourier series of the wave. Homework Equations The file called "solution" presents a detailed solution to the...
  23. H

    Possible Rectangular Potential Barrier Transmission Problem

    1. The Problem Statement An electron of effective mass m* = 0.2me and energy E = 0.1 eV hits a barrier of height 0.4 eV and width t = 5 nm. What is the probability of transmission through the barrier? Use the simplest estimate which is an exponential function. Homework Equations I think...
  24. A

    Torsion of rectangular cross section rotated at an angle?

    I want to use a rectangular cross section to act as a torsion spring that can be adjusted. The idea is that the adjustment would be made via rotating the rectangular cross section about it's center at an angle theta. I've used parallel axis theorem before, but I don't think that is applicable...
  25. O

    The moment of inertia of a rectangular plate about its diagonal

    Homework Statement Find the moment of inertia of a rectangular plate of mass m, sides 2h and 2k , rotates about its diagonal. Homework Equations I= Ʃmr^2 The Attempt at a Solution I=Ʃ m(x^2 +y^2) , let 2h parallel to x-axis, 2k parallel to y-axis. I= m(x cosθ)^2 + m (y cos ∅)^2 where...
  26. Philosophaie

    Formulating x^n Coordinate System for Non-Rectangular/Spherical Riemann Manifold

    I want to be able to formulate x^{n} coordinate system. x^{n} =(x^{1}, x^{2}, x^{3}, x^{4}) How do you do this when the Riemann Manifold is not rectangular or spherical? Also how do you differentiate with respect to "s" in that case. \frac{dx^n}{ds}
  27. L

    Complex numbers rectangular form

    Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression: Z = Z1 X Z2 / Z1 + Z2 If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form. Homework Equations Multiplication and division of complex...
  28. K

    Analytical solutions for electric field of finite rectangular sheet

    Hi, I have been trying to find analytical solutions for a finite rectangular sheet, say, in the xy plane, with dimensions a and b. Assume it is uniformly charged. An excellent (and short) description of the problem is here. The three integrals for Ex(x,y,z), Ey(x,y,z) and Ez(x,y,z) given on...
  29. A

    Confused about vectors into rectangular components

    So, i have been learning about forces, vectors and such. I know many times for convience we break vector forces into rectangular components...fx=Fcostheta, fy=Fcostheta. It is easier to do regular alegbra verus vector alegrba My question is both fx and fy are scalars, but then they can be...
  30. B

    Uniqueness of identity elements for rectangular matrices

    Let A be the set of n \times n matrices. Then the identity element of this set under matrix multiplication is the identity matrix and it is unique. The proof follows from the monoidal properties of multiplication of square matrices. But if the matrix is not square, the left and right...
  31. F

    A Beam of rectangular cross section 200mm deep and 100mm wide

    Homework Statement Please visit my flickr link for a scanned image of the problem statement. http://www.flickr.com/photos/93763273@N05/8815418518/lightbox/ Homework Equations M/I = σ/y = E/R This is the flexure or bending formula. The Attempt at a Solution a) = 8.333 kN...
  32. S

    Projection of a distance in rectangular coordinates

    My problem is that I believe I have a wrong concept somewhere, and I can't find what I'm doing wrong exactly. For this problem let's suppose what I want to do is find the rectangular coordinates of BC. I had two "possible solutions" I tried to achieve this, . First the correct one: (I...
  33. M

    Laplace's Equation: Steady-State Temperature in a Rectangular Plate

    Homework Statement A long rectangular metal plate has its two long sides and top at 0°. The base is at 100°. The plate's width is 10cm and its height is 30cm. Find the stead-state temperature distribution inside the plate. Homework Equations ∇2T = 0 T(x,y) = X(x)Y(y) X(x) = Acos(kx) +...
  34. Saitama

    Velocity of end points of rectangular frames

    Homework Statement (see attachment, ignore those marks done with the pen) Homework Equations The Attempt at a Solution I think this has to do with calculating torques and forces but I don't know about which point to calculate torque about. I know this is a very less attempt...
  35. MarkFL

    MHB Convert 7sqrt5 cis(tan−1 (2)) to Rectangular Form - Yahoo! Answers

    Here is the question: Here is a link to the question: Express in the form a + bi, where a and b are real numbers.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  36. E

    Triple Integration from Rectangular to Spherical Coordinates

    Homework Statement Convert the integral from rectangular coordinates to spherical coordinates 2 √(4-x^2) 4 ∫ ∫ ∫ x dz dy dx -2 -√(4-x^2) x^2+y^2 Homework Equations x=ρ sin∅ cosθ y=ρ sin∅ cosθ z=ρ cos∅ In case the above integrals cannot be understood: -2...
  37. Petrus

    MHB Calculate (1/2 + i√3/2)^100

    Hello MHB, calculate \left(\frac{1}{2}+i\frac{\sqrt{3}}{2} \right)^{100} in the form a+ib progress: I start to calculate argument and get it to r=1 (argument) then \cos\theta=\frac{1}{2} \ sin\theta=\frac{\sqrt{3}}{2} we se it's in first quadrant( where x and y is positive)...
  38. C

    A uniform rectangular block of length 37.0 cm is placed so that its ce

    Homework Statement A uniform rectangular block of length 37.0 cm is placed so that its centre of mass is a distance of 1.50 cm away from the edge of the table. Since its centre of mass is still over the table (i.e. not sticking out past the edge), the block is stable. An identical block is...
  39. C

    A force F is exerted on the top right corner of a rectangular plate at

    Homework Statement A force F is exerted on the top right corner of a rectangular plate at an angle 60o above the horizontal, as shown below. The magnitude of the torque of the force F about point A, the lower left corner is given by See picture please ...
  40. S

    Fair to say there are twice as many square matrices as rectangular?

    Fair to say there are "twice" as many square matrices as rectangular? Is it fair to say that there are at least twice as many square matrices as there are rectangular? I was thinking something like this... Let R be a rectangular matrix with m rows and n columns, and suppose either m < n...
  41. P

    Rectangular Waveguide centered at the origin

    Hello, If a rectangular waveguide (or square well, etc) is centered at x=a/2, y=b/2, solution (e.g. for TE mode) is: H = Ho Cos(m*pi*x/a) * Cos(n*pi*y/b) (n,m = 0,1,2,...) So for TEn=0,m=1, H = Ho Cos(pi*x/a). If it is centered at the origin, you get even and odd solutions: H = Ho...
  42. K

    How to Calculate Heat Transfer Rate in Rectangular Fin Design?

    Homework Statement A straight, rectangular fin made from 2024 aluminium has a thickness of t = 3mm and length L = 20mm. Base temperature is 100 °C and it is exposed to a fluid at 20 °C. h = 60 W/m^2-K k = 185 W/m-K (a) Determine the heat transfer rate from the fin to the fluid per unit...
  43. G

    Will a rectangular truck fit into a half circle formed tunnel when

    A truck with a width of 2,40 and height of 3,41 is driving through a tunnel that is formed like a half circle and has the radius of 3,60. Will it work? Now, this is a very pathetic question because this is junior high level geometry. I could blame the incapacity to solve this question on...
  44. S

    MHB Triangular prism on top of rectangular prism in the shape of a house......

    What formula would you use to calculate the area (excluding the base)? What formula would you use to calculate the volume? What would its longest side be?
  45. E

    Transformations of Double Integrals with Rectangular Domains in the 1st Quadrant

    Suppose we have the double integral of a function f(x,y) with domain of integration being some rectangular region in the 1st quadrant: 0≤a≤x≤b, 0≤c≤y≤d. Would the following transformation generally be acceptable? (I've quickly tried it out several times with arbitrary integrands and domains...
  46. I

    I need to find a low deflection rectangular steel tube

    What I need is a 1"x.5" rectangular tube .065" wall and 84" long steel tube that will have the least or very low deflection. I have been trying to educate myself today on the different grades of SS which would be preferable for rust resistance. If I understand things correctly 304 SS is the...
  47. S

    Thermodynamics: Heating a Rectangular Box

    Homework Statement This question is from a thermodynamics test from a previous science olympiad competition that I am using to study from for a future test. "Consider two neighboring rectangular houses built from the same materials. One of the houses has twice the length, width, and height...
  48. A

    Eliminate T to Show SHM of a Rectangular Plate

    Q:A rectangular plate of sides a and b is supended from a ceiling by two parallel strings of length L each(Fig). The Separation between the strings is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute SHM. Find the time period...
  49. M

    Calculating Weight Savings with Rectangular Section Beam

    Here is the original question, i know the first answer as 182mm A square section cantilever beam, 3 m in length, carries a concentrated load of 10 kN at its free end. If the maximum bending stress is not to exceed 30 MPa determine the minimum dimensions of the section. Ans 182mm, What...
  50. Z

    Solving for the Height of a Rectangular Hyperbola

    Homework Statement An arch is the shape of a hyperbola. IF it s 300m wide at its base and has a maximum height of 100m, how high is the arch 30m from the end ? Note: this is a rectangular hyperbola. Homework Equations (y-h)^2 - x^2 = a The Attempt at a Solution I determined the...
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