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. MathematicalPhysicist

    Derivation of the expansion of the potential in rectangular coordinates

    Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...
  2. M

    MHB Dimensions of a rectangular prism

    The volume of a rectangular prism can be represented by the polynomial V(x)=2x^2+9x^2+4x-15 a. The depth of the tank is (x-1) feet. The length is 13 feet. Assume the length is the greatest dimension. Which linear factor represents the 13 ft?This is probably a really easy question but I am so...
  3. Philosophaie

    I Convert from rectangular to Spherical Coordinates

    How do you convert this to Spherical Components? Spherical Convention = (radial, azimuthal, polar) ##\vec r = |\vec r| * \cos{(\theta)} * \sin{(\phi)} * \hat x +|\vec r| * \sin{(\theta)} * \sin{(\phi)} * \hat y +|\vec r| * \cos{(\phi)} * \hat z## Is this correct? ##\vec r =\sqrt{(x^2 + y^2 +...
  4. Q

    I Shear Rate in a Rectangular Channel

    Say you have a rectangular channel with a width, w (m), and a height, h (m) and an infinite length. The channel itself is fixed and none of the sides can move with respect to one another. If you know the volume flow rate, V (m3/s) of fluid through the channel, how do you calculate the shear rate...
  5. karush

    MHB S10.03.25 Write complex number in rectangular form

    $\tiny{s10.03.25}$ $\textsf{Write complex number in rectangular form}$ \begin{align*}\displaystyle z&=4\left[\cos\frac{7\pi}{4} + i\sin \frac{7\pi}{4} \right]\\ \end{align*} $\textit{ok from the unit circle: $\displaystyle\cos{\left(\frac{7\pi}{4}\right)}=\frac{\sqrt{2}}{2}$}\\$ $\textit{and...
  6. Cocoleia

    I Rectangular wave, extraction of ions from a stopping cell

    Hello. I'm not sure if this question is to project-specific, but I will try to explain as best that I can. I am working with a system such as this one, with only a few differences: http://www.sciencedirect.com/science/article/pii/S0168583X1400706X it is a cryogenic stopping cell. The part I am...
  7. U

    Rectangular to Spherical Coordinate conversion....

    Homework Statement Convert from rectangular to spherical coordinates. (-(sqrt3)/2 , 3/2 , 1) Homework Equations We know the given equations are ρ = sqrt(x^2 + y^2 + z^2) tan theta = y/x cos φ = z / ρ The Attempt at a Solution My answer was (2, -pi/3, pi/3) It should be a simple plug and go...
  8. M

    Magnetic Field Computation from Thick Rectangular Conductor

    Hello, and thanks in advance for taking a look at my question. Generally, I am trying to make a railgun force model. Since railguns depend on the magnetic field created around the rails (and the resulting Lorentz force) I need to model the magnetic field created by the current that flows...
  9. I

    Support reactions of a rigid, rectangular steel frame

    Homework Statement Solve for support reactions of a rigid, rectangular steel frame sitting on rubber pads at the four corners (See attached), when a shear force and a moment is applied at some point on the frame. All the known variables are shown in black while the unknown are in red. It is a...
  10. karush

    MHB -10.1.1 write polar to rectangular

    $\textrm{write polar to rectangular coordinates}$ $$r=5\sin{2\theta}$$ $\textit{Multiply both sides by $r$}$ $$r^2=5r[\sin{2\theta}] =5\cdot2[r\cos(\theta)r\cos(\theta)]$$ $\textit{then substitute $r^2$ with $x^2+y^2$ and $[r\cos(\theta)r\cos(\theta)$ with $xy$}\\$ $\textit{then}\\$...
  11. olgkd123

    Designing a rectangular vacuum chamber -- Help please

    Hello everyone! I want to design a rectangle vacuum chamber (12x12x72) out of 1/2 steel. I would be welding the sides together to form a seal. Would this work? any suggestions on what I could do? Thx! (I not great at this stuff so your help is much appreciated!)
  12. G

    Charge/current density inside rectangular wave guide?

    Homework Statement Given the Z component of E inside a rectangular wave guide, Find the ratio of the maximum charge density on the plane x = 0 to the maximum charge density on the plane y = 0. Additionally, Find the ratio of the maximum surface current on the x = 0 plane to the maximum surface...
  13. 6

    MHB Therefore, the volume of the rectangular prism is 84 units cubed.

    What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?
  14. D

    Magnetic flux through a rectangular loop inside a wire

    Homework Statement Homework Equations Magnetic flux = integral(B dot dA) line integral(B dot ds) = (u_o)(i_enc) (Ampere's Law) The Attempt at a Solution I can't see how Ampere's law applies because all of the magnetic field vectors along the loop will be perpendicular to that stretch of...
  15. C

    Circular polarization in rectangular waveguide

    Homework Statement In a rectangular waveguide, b = a/2, find the section, if exists, in which the magnetic field is circularly polarized (TE10 mode). Homework Equations Rectangular waveguide equations for TE10 mode (referencing Pozar book). Circular polarization (π/2 out of phase and same...
  16. M

    How to Calculate the X-Component of the Magnetic Moment in a Rectangular Loop?

    Homework Statement A rectangular loop of wire with sides H = 22 cm and W = 77 cm is located in a region containing a constant magnetic field B = 0.82 T that is aligned with the positive y-axis as shown. The loop carries current I = 334 mA. The plane of the loop is inclined at an angle θ = 30°...
  17. Q

    B Rectangular Prism out of different shapes?

    Is it possible to create a rectangular prism while using only one prism and without repeating any two shapes?
  18. Ravikant Rajan

    Derivation of discharge over rectangular weir

    How does the velocity at an elemental height h equates to √(2gh)? My application of Bernoulli's equation is not yielding the result. Please show the process. Thank you
  19. R

    Finding the Moment of Inertia for a Rectangular Sheet

    Homework Statement The horizontal side (x-axis) is length 2A and the vertical side (y-axis at x=+-A) is length B. The mass is uniform throughout the sheet so that the center of mass is at the center of the rectangle. What is the moment of inertia for. the rotation around the z-axis at the...
  20. abilolado

    A Free boundary conditions on vibrating rectangular membranes

    I've been trying to come up with wave equations to describe the motion on vibrating rectangular (more specifically, square) membranes. However, most paper I find assume fixed edges. What are the boundary conditions I need to apply to the 2D wave equations in order to have an free boundary in a...
  21. G

    Ansoft Maxwell: Rectangular Wave Circuit

    Hello, is there a way to directly use a rectangular wave as input current without using an external circuit in ansoft maxwell? The instructions from ansoft that model a toyota motor just put the sine wave function directly into the winding's current settings, can I put a rectangular wave instead...
  22. A

    Rectangular hyperbola, chord, origin

    Homework Statement Prove that the chord joining the points P(cp, c/p) and Q(cq, c/q) on the rectangular hyperbola xy = c^2 has the equation x + pqy = c(p + q) The points P, Q, R are given on the rectangular hyperbola xy = c^2 . prove that (a) if PQ and PR are equally inclined to the axes of...
  23. U

    I Understanding rectangular matrices

    So if I have a system of equations: $$x_1+x_2+x_3=1$$ and $$x_4+x_5+x_6=1$$ Then they can be put into a matrix representation \begin{equation*} \begin{bmatrix} 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1\\ \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5 \\ x_6 \\ \end{bmatrix}...
  24. S

    Moment of Inertia for connected, hinged panels

    Homework Statement [/B] There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2...
  25. M

    MHB Algebraic equation problem, rectangular flower bed

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  26. M

    MHB Width of a rectangular frame in terms of x.

    By bending a 16 cm wire a rectangular frame is made. By taking the length as x , write the width in terms of x. If the area of the frame is $11 cm^2$ show that x satisfies the equation $x^2-8x+11=0$ Solve the equation by taking the $\sqrt{5}=2.24$ Ideas on how to begin ? (Happy)
  27. N

    MHB Maximizing Volume of Rectangular Prism with 120cm x 80cm Sheet Metal

    My question is that I have to find the dimensions of a rectangular prism (cuboid), where none of the faces are square that will maximise its volume. The sheet metal I have to build it from is 120 cm by 80 cm. I don't even know where to start, I can do it if I'm given a height, width or length...
  28. Neil Chheda

    Tube End Forming - Rectangular to Circular

    Hi, I wish to manufacture a transition tube from 4"x1" rectangular section to 3" OD circular section. The height of the part is 3" and is supposed be around 2 mm (.082") thick. Currently I am planning to manufacture this in a hydraulic press using (custom made ) end forming tools. The forming...
  29. V

    Resistance Between Two Rectangular Electrodes

    Hello everyone. I have what is probably a relatively simple question. I'm trying to calculate the resistance between two rectangular copper plates submerged in water. I found this thread that briefly discusses it...
  30. Quadrat

    Induced emf in various rectangular loops

    Homework Statement [/B] Three conducting loops, all with the same resistance ##R## move towards a uniform and constant magnetic field, all with the same velocity ##v##. Their relative sizes can be identified by the grid. As the loops move into the magnetic field an induced current begins to...
  31. S

    Current induced in moving rectangular wire

    Homework Statement As shown in the figure below, a current I passes through a straight conducting wire located within this page. Rectangular circuit ABCD on the page is moving away from the straight conducting wire with speed v, while side AB remains parallel with current I. The length of side...
  32. Dotini

    B What is the source of the mysterious red rectangle in space?

    How charming! (Photo: ESA/Hubble and NASA) http://www.usatoday.com/story/tech/sciencefair/2016/04/08/star-red-rectangle-nasa-hubble/82796522/
  33. karush

    MHB Equal graphs polar and rectangular

    I couldn't get equal graphs one plot 4 leafs the other 2
  34. L

    Magnetic field in rectangular coil (not solenoid) Amperes law

    Homework Statement I have a rectangular coil with length L and the cross-section's sides has length a and b (b>a). A wire is tightly wrapped around N times. Calculate the magnetic field inside the coil. Homework Equations The problem I have is that in class we were taught how to calculate...
  35. stoky

    I Airflow rate through a rectangular section

    I need to mount several rectangular orifices or sections on a wall with those two factors: - 20 Pascals differential pressure (negative pressure inside) - Inlet air speed 1100 feet per minute (5.58 meters per minute) I've got the section of each window, and the air caudal to renovate. I would...
  36. DrPapper

    Potential of a Rectangular Pipe by Laplace's Equation

    Homework Statement Homework Equations Is my part a correct and am I on the right track for part b? If not please give me some suggestions to get me closer to the right track. Also, how would I even begin c.? We have literally done no examples like this in class. The Attempt at a Solution...
  37. B

    Diagonal of a thin rectangular foil, inertial principal axis

    I'd like to know if the diagonal of a rectangular thin foil is an inertial principal axis.I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a symmetry axis, so it shouldn't be a principal axis. Is it correct? So, if I consider that...
  38. Destroxia

    Spherical equation to Rectangular

    Homework Statement An equation is given in spherical coordinates ## \rho sin(\phi) = 8cos(\theta) ## Express the equation in rectangular coordinates a) ## (x-4)^2 + y^2 = 16 ## b) ## x^2 + y^2 + z^2 = 16 ## c) ## x^2 + (y-4)^2 = 16 ## Homework Equations ## x = \rho sin \phi cos \theta, y...
  39. Chip

    Penetrating the Rectangular Potential Barrier, E < V0

    The following code compares my result to the known correct result. Can anyone find where my error is? If you run the octave code you will see that my answer has positive concavity whereas the correct one has negative concavity...I've checked this so many times and can't find my error. I wanted...
  40. Chip

    Penetrating the Rectangular Potential Barrier, E < V0

    Homework Statement Rectangular barrier of width a and height V0 with an E < V0. What is the transmission ratio, T? Homework Equations T = C*C/A*A What am I missing in my attempted solution (variable name = TChip), which is different from the known solution (variable name = TSoln)? The Attempt...
  41. X

    Curved to Rectangular Distribution

    Hi Guys :) I have become interested in producing true random numbers of uniform distribution, and have come across this Numberphile video in my travels: The narration hints at the topic of converting numeric sequences of a curved distribution, inherently more likely to be closer to a mean...
  42. Julian102

    What is the relative area of a rectangular field?

    Homework Statement If the area of a rectangular field has length of 110 m and 80 m.If a spaceship is traveling with 0.9c velocity along the diagonal of the field.Then what is the area of the field seen by the astronaut in the spaceship? Homework Equations L=L(initial) Root over (1- (v/c)^2)...
  43. T

    Coordinate transformation from spherical to rectangular

    Iam having trouble understanding how one arrives at the transformation matrix for spherical to rectangular coordinates. I understand till getting the (x,y,z) from (r,th ie., z = rcos@ y = rsin@sin# x = rsin@cos# Note: @ - theta (vertical angle) # - phi (horizontal angle) Please show me how...
  44. I

    Android Calculator App: Convert Rectangular-Polar

    I need an android calculator app that will convert between rectangular and polar. I need these keys: ->R and ->P
  45. karush

    MHB Convert Rectangular to Polar: Solving for $\theta$

    Covert to polar $$y=3 x$$ I got... But it didn't plot on desmos... Can't show polar graph here? $$r\sin\left({\theta}\right)=3r\cos\left({\theta}\right)$$
  46. I

    MATLAB Matlab polar to rectangular coordinates

    Prepare a function m-file containing a function that converts polar coordinates in two-dimensional space to rectangular (Cartesian) coordinates. Include a suitable H1 line and some additional comment lines. The input will be 2 vectors, and the output will be 2 vectors. The length of each vector...
  47. qq545282501

    Turn spherical coordinates into rectangular coordinates

    Homework Statement Find the volume of the solid region that lies inside the cone φ= pi/6 and inside the sphere ρ=4. Use rectangular coordinates. Homework Equations x=ρ sinφ cos θ y=ρsinφ sin θ z=ρ cos φ ρ^2=x^2+y^2+z^2 x= r cos θ y= r sin θ r^2=x^2+y^2The Attempt at a Solution at first...
  48. W

    "Crow Flies Distance" On a Rectangular Grid -- Definition?

    Hi all, I am looking for a precise definition of " Crow Flies Distance" on a rectangular grid. I have not found a precise definition yet, but from what I have read, I think it would be the standard Euclidean distance ## d((x_1,y_1),(x_2,y_2)) = \sqrt {( (x_1-x_2)^2+(y_1-y_2)^2}) ## Is this...
  49. X

    Polar vector to rectangular equation

    Homework Statement The problem I'm stuck on is to come up with an equation which will model the path of the projectile in an xy-plane. We are given: r(t)={ [(v0cos(θ))t], [h+(v0sin(θ))t-(½)gt2] } v0=100 ft/s θ=60° h=4 ft so basically, r(t)={[100cos(60)t], [4+100sin(60)t-16t2]} Homework...
  50. M

    Air flow through small rectangular opening

    Hello, I have to calculate the air flow through a small rectangular opening with following data: - temperature at one side: 1200°C - temperature at other side: 20°C - pressure at hotter side is 3 mm WC lower than the colder side - the length of the opening is 240 mm - the width of the opening is...
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