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. I

    Dissapating corner moments in a rectangular underground tank

    This is a conceptual question based on a project I and a few other engineers finished at work. We are replacing the roof of a concrete tank that is part of a larger pump station for a river. Unfortunately, the roof is very integral in this structure, which means that once it's removed, the walls...
  2. D

    Trouble finding the resultant using rectangular components

    Hello, I am having trouble finding the direction of the resultant of this statics homework problem. The picture uploaded is exactly how it is shown in my book. The problem states: Homework Statement For the forces shown, S = 3.81 kip, T = 4.73 kip, and U = 3.65 kip. Determine the resultant...
  3. A

    Net force on rectangular circuit

    Homework Statement Homework Equations Right hand rules The Attempt at a Solution Am i correct for a? I drew my interpretations of the magnetic field around each section. For b) am i correct to think the internal net force in the rectangular wire is 0, and the only force acting on it is that...
  4. Q

    Problem with rectangular and triangular weir

    Homework Statement A rectangular weir (Cd = 0.623) thin crest without lateral contraction of 1 meter in length and a triangular weir (theta = 90 °) are located on the same channel. If the apex of the triangular weir (Cd = 0.593) is 0.15 meters below the crest of the rectangular weir and...
  5. B

    R^2=9cos(3Ө) Convert to rectangular cordinates

    Homework Statement Homework EquationsThe Attempt at a Solution -In order for me to figure out this problem I had to reverse the equality to isolate the Ө on the left side making the new equation 9cos(3Ө)=r^2. The first thing I’m going to do is change cos(3Ө) in terms of cos and sin. That will...
  6. karush

    MHB Find Solution for Polar to Rectangular Equation

    Polar to rectangular $$r=1-2 \sin\left({\theta}\right)$$ $${x}^{2}+{y}^{2}=\sqrt{{x}^{2}+{y}^{2 }}+2y$$ Is this an answer just hard to get $y=$
  7. K

    A rectangular conducting frame in a magnetic field

    Homework Statement A frame is made of two firm wires of length ##h## and a rod of length ##l## and mass ##m##. This frame can rotate around horizontal axis in uniform magnetic field ##B##. In a short amount of time ##τ## a current ##I## passes through the frame. What is the maximum angle that...
  8. K

    Moments of inertia of a rectangular plate

    Homework Statement Show that the moment of inertia of a rectangular plate round it's diagonal, line B-B is equal to the one round a line parallel to one of the edges and passing through the center, line C-C Homework Equations Moment of inertia: ##I=mr^2## The Attempt at a Solution For the...
  9. endiewibowo

    How to calculate mutual inductance of a rectangular loop

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  10. karush

    MHB How to Convert Polar to Rectangular Coordinates in Calculus?

    $r=3-\cos\left({\theta}\right)$ ${r}^{2}=3r-r\cos\left({\theta}\right)$ ${x}^{2}+{y}^{2}=3r+x$ How you deal with 3r ?
  11. Jason Chen

    Shape of vortex electric field line in a rectangular metal

    We know that,the shape of electric field line in a cylinder under varying magnetic field is circle,and I wonder,what's the situation if it is a piece of metal with rectangular cross section? I think it might be something like superellipses.Can somebody tell me is it true or how to treat this...
  12. karush

    MHB How to Convert Polar Coordinates to Rectangular Coordinates?

    $2\sin\left({\theta}\right)-3\cos\left({\theta}\right)$ Convert to rectangular coordinates I'm clueless?
  13. Zachreham

    Electric Potential Inside an Infinite Rectangular Trough

    1. The problem statement, all variables a nd given/known data A rectangular trough extends infinitely along the z direction, and has a cross section as shown in the figure. All the faces are grounded, except for the top one, which is held at a potential V(x) = V_0 sin(7pix/b). Find the...
  14. S

    How to determine rectangular and polar radii of gyration?

    Homework Statement [/B] Determine the rectangular and polar radii of gyration of the shaded area about the axes shown. Homework Equations dIx = y2dA Ix = ∫y2dA dA = ydx A = ∫(dA The Attempt at a Solution dIx = y2dA =(x6/16) *(x3/4) dx =(x9/64)dx Ix =(integrating from 1 to 2) ∫dIx =...
  15. V

    Magnet strength between 2 magnets

    Hi all, I have two identical magnet which measures 0.6T when I put my gauss meter on the top surface. I configured the magnets as below: I would like to know what should I expect if I measure the strength(Tesla)at the red round dot position? Would it be 1.2 tesla? Please advise. Thank you...
  16. beer

    Refesher Part Duex - Rectangular -> Cylindrical -> Spherical

    I'm at it again today. Helping the same friend (plus another) study for their final calculus exams; it's a good refresher for me as well. (I'm a senior industrial engineering major so I'm "done" with calculus, and it isn't used much in our upper level classes nor professionally to the best of...
  17. B

    Formula to find volume of a rectangular solid

    Hi all, I need help finding a formula to find the volume of a solid that has a fixed width and depth but 4 different heights. To see what I mean, please take a look at a sketch I drew below. Thanks.
  18. K

    2D-Diamond and 2D-Center Rectangular Lattice Comparison

    Hi All, Using (Mirror + Translation in 2D). I see that Diamond and Center Rectangular Lattice in 2D has the same Symmetry i.e: 1)Horizontal Mirror Plane 2)Vertical Mirror Plane 3)2-Fold Rotation Axis. and Diamond has Smaller Area. Then why we say Center Rectangular has higher Symmetry and we...
  19. C

    Lateral compression of rectangular tube

    Hi guys, Bit of a noob engineer here so looking for some guidance. I'm designing a fixture which will be constructed from stainless steel rectangular tube as shown in the diagram. If I apply a 10,000kg weight over a 100mx100mm area how do I go about calculating the stress and ultimately safe...
  20. D

    Microwave rectangular cavity resonator ?

    Homework Statement I am putting the picture of the equation given to me in book , I feel it to be wrong please tell me that is the equation written in book correct or not ! Homework EquationsThe Attempt at a Solution
  21. B

    Simplest way to align rectangular boxes

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  22. baby_1

    Find TM waves mode in a rectangular waveguide

    Homework Statement Homework Equations [/B] The Attempt at a Solution [/B] Hello As you see my solution I found TM(5 , 2.5) that is incorrect because n should be integer not float number.In Addition when I check book solution I found TM mode is TM(2,1) what is my mistake?
  23. P

    Double integral in Rectangular coordinates for anything circular

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  24. DivergentSpectrum

    Construct a regular grid in a rectangular box in 3 dimensional space

    Im trying to construct a regular grid in a rectangular box in 3 dimensional space heres what i have to work with: x has a range between xmin and xmax y has a range beween ymin and ymax z has a range between zmin and zmax the total number of points is limited to a specific number n i want the...
  25. M

    Biot-Savart and a Rectangular Loop

    Homework Statement Consider the figure on the right. Wire 1 is oriented along the y-axis and carries a current I1. A rectangular loop located to the right of the wire in the xy-plane carries a current I2. Find the magnetic force exerted by wire 1 on the top wire of length b in the loop...
  26. P

    Magnetic interaction of wire and rectangular loop

    Hi. In this video: he ignores the magnetic field from current 2(I2). Could anyone give me a good explanation why?
  27. G

    Rectangular Potential Barrier Boundary Conditions with E=V

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  28. M

    Help in split step Fourier method with initial rectangular pulse

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  29. R

    Calculating EMF Induced by Moving Rectangular Loop

    Homework Statement A rectangular loop of wire, of sides 5 and 3 cm moves away from a a long straight wire at 4ms-1 carrying a current of 2 amps. What is the EMF induced in the moving loop, when the near side of the loop is 3cm away from the wire? Homework Equations B = μ0I/2πr EMF = -dΦ/dt...
  30. J

    Why does the galaxy LEDA 074886 appear rectangular?

    LEDA 074886, also known as PGC 74886, is a dwarf galaxy with a rare rectangular shape, located at a distance of about 70,000,000 light-years ( 21,000,000 pc) ...
  31. T

    Induced current and torque in a rectangular metal loop

    Homework Statement (a) The metallic rectangular loop of length b and width a (ABCD) is mounted in an assembly, which allows it to be rotated about an axis bisecting AD and BC. The plane of the loop makes an angle θ to the horizontal and a uniform magnetic field B is applied vertically...
  32. phosgene

    Maximise the volume of a rectangular prism with 2 constraints

    Homework Statement Maximise the volume of a rectangular prism with the following constraints: the surface area must equal 2m^2 and the total edge length must be 12m. Homework Equations Using Lagrange multipliers, we construct the function we want to optimise with h(x,y,z, λ_{1}...
  33. skujesco2014

    Scattering Within Rectangular Waveguide With A Step Obstacle

    Dear PF: I'm currently working in a problem that has had me stranded for several weeks now. The problem reads as follows: (See attachment) Consider a beam of quantum particles (that is, the particles are small enough to exhibit non-negligible quantum effects) that propagates through a...
  34. S

    MHB Convert to a equation in RECTANGULAR coordinates

    What am I doing wrong? Convert r = 2sin\theta to an equation in rectangular coordinates.. x^2 +y^2 = r^2 x^2 + y^2 = 2y x^2 + y^2 - 2y = 0 x^2 + y^2 - 2y - 1 = 1 x^2 + (y-1)^2 = 1 Coordinates are (0,1) yes?
  35. T

    Rectangular Plate with Varying Density Across the Width

    So the question is A rectangular plate has length l, width w and thickness t. Its density is constant across the width, but varies with distance from one end as ρ=ρo [1 + (x/l)^2] Find the plate’s mass and the coordinates of it’s centre of mass. I Have had a bash at this question, thinking...
  36. J

    Show rectangular box of given volume has minimum surface area when

    Homework Statement show rectangular box of given volume has minimum surface area when the box is a cube [gotta show it with partial derivatives to minimize] Homework Equations surface area = 2(wl+hl+hw) volume = whl The Attempt at a Solution so this is the one I would be minimizing...
  37. P

    Analytical approach to rectangular membrane vibration

    Homework Statement I'm following a procedure in a particular paper as part of my Masters project. The paper is called 'Theoretical investigation of the sound attenuation of membrane-type acoustic metamaterials - Y Zhang, J Wen, Y Xiao, X Wen and J Wang (2012)' and can be seen...
  38. C

    Double Integral of Pythagoras over rectangular region

    Take any given point on the perimeter of a (A x B) rectange and then draw a line from that point to another point on one of the three remaining sides of the rectangle. What is the average length of the line? Well, the answer to that question involves integrals like this: \int_0^A \int_0^B...
  39. J

    Moment of inertia of rectangular tube with welded flat bar

    hello, I am trying to find the new moment of inertia total for a rectangular stainless steel 4"x2"x.25"thk with a 3"x.75" flat bar welded on top of the short side of the rectangular tube. The short side (.75") of the flat bar will be welded to the center of the rectangular tube to the 2"...
  40. S

    Fourier Transform - Rectangular Function Help

    1. Hi! I am new at this forum, and english is not my native language, so, I hope I can make myself clear. A teacher send us a list of activities, but he did not give us the theory about it (the theoretical class). So, I have read a few things on the internet and I have solved some exercises. I...
  41. D

    MHB Help Me Solve $\text{Im}(z^3)$ in Rectangular Form

    I don't how to proceed further Let $z=x+jy$ find in rectangular form: 1. $\text{Im}(z^3)$ this is where I can get to, $\text{Im}(x^3+3x^2jy+3xj^2y^2+j^3y^3)=\text{Im}(x^3+3x^2jy-3xy^2-jy^3)$ please help me.
  42. B

    Induced voltage in rectangular loop

    Homework Statement There's a magnetic field B in +\hat{z}. A rectangular loop is lying in the xy-plane. Three sides are static, the 4th one is moving with velocity v along the direction of +\hat{y}, making the rectangular larger and larger. The length of this moving side of the rectangle is L...
  43. M

    Equation to a rectangular Prism

    Hello, I am trying to understand the concept of solid geometry(spheres, cubes, polyhedra etc) as a function of their co-ordinates. for example, the general ellipsoid, is a quadratic surface which is given in Cartesian coordinates by: (x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1 a,b,c being the semi axis...
  44. D

    Rectangular loop near wire emf

    Homework Statement http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide10.pdf pg: 10-17 Homework Equations The Attempt at a Solution I do not understand conceptually, why we chose the rectangular surface to take the flux over. Can anyone explain this...
  45. S

    Off-axis magnetic field between two current-carrying rectangular loops

    Homework Statement Not exactly a homework problem, but the actual working resembles it. Basically it is a standard calculation for the magnetic field between a set of Helmholtz coils, except with a rectangular loop instead of circular ie: two identical rectangular magnetic loops (dimensions...
  46. M

    Why not Rectangular Mesh for Arbitrary Shape Domain?

    Hi all, It is well know that, rectangular or quadrilateral element gives better result over triangular meshes in finite element method. I know, Rectangular meshes has more discretization error, but my question is that, if i refine mesh up to 4 to 6 pixel width of screen, where i am wrong?
  47. T

    Rectangular Plate SHM Time Period

    Homework Statement A rectangular plate of sides ‘a’ and ‘b’ is suspended from a ceiling by two parallel strings of length L each. The separation between the strings is ‘d’. The plate is displaced slightly in its plane keeping the strings tight. Find the time period of SHM. Homework Equations...
  48. S

    MHB Give all the polar coordinates corresponding the rectangular point

    Give all the polar coordinates corresponding the rectangular point (-1, \sqrt{3}) Am i setting this up right? so would I use (r, \theta) so x = rcos(\theta) y = rsin(\theta) r^2 = x^2 + y^2 so: (-1)^2 = (-1*\frac{2\pi}{3})^2 + (-1*\frac{11\pi}{6}) ?
  49. gfd43tg

    Engineering RC circuit with rectangular pulse

    Homework Statement Consider the circuit below. If the source υs represents a 12-V, 100-ms-long rectangular pulse that starts at t = 0 and the element values are R1 = 6 kΩ, R2 = 2 kΩ, R3 = 4 kΩ, and C = 15 μF, determine the voltage response υ(t) for t ≥ 0. Homework Equations The...
  50. F

    What is the Force on a Rectangular Loop in a Magnetic Field?

    Homework Statement Let d = 0.048m, L = 0.15m, r = 0.10m in the following diagram. Assume that the current I1 = 80.0A and I2 = 40.0A. Find the net force on the rectangle of wire and the direction it points, and state the direction of the emf if the current I1 is increasing in the direction of...
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