# 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 Green's function for 2-D Laplacian within square/rectangular boundary

From the table of Green functions on Wikipedia we can get the generic 2-D Green's function for the Laplacian operator. But how would one apply boundary conditions like u = 0 along a rectangular boundary? Would we visualize a sort of rectangle-based, tilted pyramid, with logarithmically changing...
2. ### Probability of finding a particle in the right half of a rectangular potential well

Hi guys it's me again. I need help with this exercise which reads: a particle of mass m, placed in an infinite rectangular one-dimensional potential well that confines it in the segment between ##x = -\frac{a}{2} and x=\frac{a}{2}##, is at instant ##t=0## in the state: ##|\psi \rangle =...
3. ### Chosing air blowers to force air through a solar heat storage array

hi guys: i plan to make solar collector using rectangular hollow steel bar 4×8cm filled with gravel as heat storage and blow air through it and direct that air as preheated for gas combustion oven to reduce gas consumption .can i use a normal fan or it has to a blower?
4. ### A Rectangular higher order edge element (finite element method)

I have solved many finite element problems using nodal based (rectangular element) for higher order. now i am trying to solve electromagnetic problem using vector element (Nedelec or Whitney). I know only triangular edge based element with first order only and not higher order. i am searching...
5. ### Help for bending calculation rectangular steel tube

Hi all In order to make a metal preframe for a French window as an entrance door, I began to estimate the possibility of building it in rectangular steel tubes of 100 x 50 x 3 mm, laid independently of the walls that could not accept such a load because it was timber framed. The preframe will...
6. ### Stress in rectangular vessel subjected to hydrostatic pressure

Hi, it's not easy to find formulas for stress in rectangular pressure vessels. However, I've found some in a Polish book titled "Podstawy konstrukcji aparatury chemicznej" (Fundamentals of the design of chemical process equipment) by J. Pikon. The problem is that the book provides equations for...
7. ### Fourier transform of rectangular pulse

Here is the question: Here is my answer
8. ### Rectangular Box with two non zero potential faces

I believe what I have to do to solve this problem is find the potential at each end face and then use the super position principle to find the net potential. So my boundary condition v and iv will give the potential at each respective position. Im just a bit confused about my boundary V...
9. ### Boundary Conditions for an infinite rectangular pipe

Does setting up the problem symmetrically on this axis and the boundary conditions applied make sense? I don't believe I will have a problem solving for the potential inside, but i just want to make sure I have my B.C and axis correct before proceeding. EDIT: Or should this be a 2-D lapace...
10. ### Evaluating the boundary conditions for a rectangular pipe

I have attached an image of the pipe in the attachmnts. The pipe is parallel to z-axis form (-∞,∞) and sides of length a. So my boundary conditions for this problem are as follows 1.) V=0 at y=0 2.)V=0 at y=a 4.)∂v/∂x=0 @ x=0 3.)V0 @ x=a I am a little confused on the fourth boundary...
11. ### How Is Polar to Rectangular Conversion Used in Complex Number Calculations?

I'm having trouble trying to calculate how the answer below was achieved from an example i have seen, see below: 208L0 - 2.5L90 x 27.42L36.9 which is then calculated to 255.12L-12.4. I have tried converting everything to rectangular form, subtract where required and the convert back to polar...
12. ### MHB -11.7.94 Find the rectangular equation

$\tiny{11.7.94 Kamahamai HS}$ Find the rectangular equation of the curve $r=\sin\left(\theta+\dfrac{\pi}{4}\right)$ \$r=\sin \theta{\cos \dfrac{\pi}{4} +{\cos \theta{\sin \dfrac{\pi}{4}}}} =\sin \theta\left(\dfrac{\sqrt{2}}{2}\right)+\cos \theta\left(\dfrac{\sqrt{2}}{2}\right)...
13. ### Converting integration of rectangular integral to spherical.

I'm going to type out my LaTeX solution later on. But in the meantime, can anyone check my work? I know it's sloppy, disorganized, and skips far more steps than I care to count, but I'd very much appreciate it. I'm not getting the answer as given in the book. I think I failed this time because I...
14. N

### Working With A Rectangular Garden

The length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden. (a) Draw a diagram that gives a visual representation of the problem. (b) Write the equation for the perimeter y of the walkway in terms of x. For (a), see...
15. ### Please evaluate this double integral over rectangular bounds

Summary:: Could someone please evaluate this double integral over rectangular bounds? Answer only is just fine. [Mentor Note -- thread moved from the technical math forums, so no Homework template is shown] Hi, I'm trying to find the answer to the following integral over the rectangle...
16. ### Find the length XY from the rectangular diagram

i saw this question on the internet. The people responding were of the opinion that the length##xy=1##, but no working...first of all is the answer ##1## correct? i am trying to find the steps to solution, i have managed to find an angle ##57.27^0## by cosine rule, i tend to think that i need...
17. ### Can i draw a helical coil around a rectangular core in Ansys maxwell?

I am doing core loss calculations in Ansys Maxwell for a project, in which I need to draw a helical coil around a rectangular core to get a more realistic model. But I haven't really found any helpful material. I don't know if its possible, but if it is I would really appreciate your help. Thank...
18. ### Heat transfer problem for a long rectangular bar

Summary:: Determine the temperature distribution in a bar (very long– 2D) with rectangular cross section, in steady state, with imposed flux at one face, convection at the opposing face (Tinf, h), and imposed temperature (T1) at the two remaining walls. I am trying to find the analytical...
19. ### I Determine the Transformation from Cylindrical to Rectangular coordinates

In physics is usually defined that in cylindrical coordinates ##\varphi \in [0,2 \pi)##. In relation with Deckart coordinates it is usually written that \varphi=\text{arctg}(\frac{y}{x}). Problem is of course because arctg takes values from ##-\frac{\pi}{2}## to ##\frac{\pi}{2}##. What is the...
20. ### How to explain TE20 mode in a rectangular waveguide from reflection

In Feynman's lectures, he explained the ##TE_{10}## mode of waveguide by considering a line source in the middle of waveguide as below: since the adjacent sources are all out-of-phase, which means to have interference, the adjacent optical path would be about half of wavelength as below: where...
21. ### I Fourier transform of rectangular pulses

Hi, I was trying to find Fourier transform of two rectangular pulses as shown below. The inverted rectangular pulse has unit height, -1, and lasts from -π to 0. The other rectangular pulse has unit height, 1, and lasts from 0 to π. I was making use of Laplace transform and its time shifting...
22. ### Solving this exercise in mechanics -- Tipping over this rectangular object

A body is placed on a surface with friction Force is applied to the right at the upper end of the body What is the condition that will cause the body to roll over?
23. ### Torque on a rectangular coil in a uniform magnetic field

So this was a section taken out from a question which I am trying to do shown below I have drawn a sketch to help me visualise of what is going on I have used Fleming's left hand rule to help me determine what direction the force is facing on each side of the coil. For the last part in...
24. ### Engineering Magnetic field near a rectangular bus bar

An old field theory notebook has given me a formula for a long straight conductor that H = I/2πd which suggests 2.3873T at 0.2mm. Is it a reasonable approximation to use this as a basis for selecting the sensor? Any help much appreciated.

29. ### Resources for the rectangular segmentation of an image (ML)

Hi I see there are several articles about how CNN's are used to isolate and classify an object within an nxm rectangular region. While I know how to classify an image into one of p classes, I am not sure how to segment an image into rectangular regions which contain certain objects and, let's...

31. ### I Analytical Open Channel Rectangular Fluid Flow

Hi All, I'm looking for an analytical solution to the open channel rectangular fluid flow profile. The flow is bounded by three walls but the top is open to atmosphere. Assume steady state flow that is parallel and incompressible.I've already found information involving a rectangular flow...
32. ### MHB Finding the impedance in rectangular and polar form

I don't fully understand how to work out the impedance from the given equation (5j-5)x(11j-11)/(5j-5)+(11j-11). Any help would be greatly appreciated. Thanks. The answer needs to be in rectangular and polar form.
33. ### Convolution Problem -- Triangular and Rectangular pulses

Homework Statement Homework Equations y(t)=x(t)*h(t)=∫x(λ)⋅h(t-λ)⋅dλ The Attempt at a Solution [/B] Is what I have the correct interpretation or or am I wrong? Thanks
34. ### MHB Convert polar equation r= 1/1+sin(theta) to rectangular equation

The equation is: r= 1/1+sin(theta) I know the answer is supposed to be: x^2+y^2=(1-y)^2 I can't figure out the steps to get to the answer.
35. ### MHB Convert polar equation sec(theta)=2 to rectangular equation

My professor gave us a study guide with the solutions: The equation is: sec(theta)=2 I am supposed to convert it to a rectangular equation. I know the answer is going to be y^2-3(x)^2=0 I don't know how to get to the answer he gave us.
36. ### Time of Fall in triangular and rectangular frame

Homework Statement This question is actually two question. We have two hollow frames - one is rectangular and another is triangular. the rectangle is rotated and fixated such that the angles in shape are ##\alpha , \beta = 90 - \alpha## and the angle of triangle is ##\alpha##. We have two balls...
37. ### Calculation of Velocity and Shear rate in rectangular channel

Hi everyone, I would like to know the formula for calculation of velocity and shear rate in my rectangular fluid channel. Here are the important values regarding my rectangular channel. W= 2.5 mm, H=3 mm, L=35 mm. Fluid: Diluted Bacterial suspension derived from wastewater. Flow rate: 0.125...
38. ### MHB Convert r=7cos(theta) into a rectangular equation

So we're learning to plot polar equations, which easy enough. But I got a question in the homework that wasn't covered in class: Convert r=7cos(theta) into a rectangular equation. Use x and y values. I know how to convert when it's x=r*cos(theta) or y=r*sin(theta) and r and theta is given. But...
39. ### B Seat arrangements around a rectangular table

Suppose 6 people want to sit in circular table. This case is considered as cyclic permutation. How about if the 6 people want to sit around a rectangular table? 1. Let say they sit on the longer sides of the table, 3 people on each side and no one sit on shorter side of the table. Is this...
40. ### Self-inductance of a toroid with a rectangular cross section

I have found answers on how to calculate the self-inductance of toroid of rectangular cross section, however my question says that "The winding are seen as a thin homogeneous currentlayer around the core" (excuse the translation). What does that mean for N? Does it mean N=1?
41. ### Statics problem -- Rectangular plate lying on two inclined surfaces

Homework Statement https://www.img.in.th/image/VNaqVa https://www.img.in.th/image/VNa3k9 This is my home work. Homework EquationsThe Attempt at a Solution I have a problem with the force at A and B. I don't know how to use NA NB in the term of α and β to use moment calculation. I got that...
42. ### Pressure on a vertical rectangular plate submerged in water

The question goes as follows..: A car driver has an accident and drives into a lake. The car sinks to the bottom. The distance from the car door to the water surface is 10m. The car door is 0.9m wide and 1.3m tall. Assume that the car door can be approximated as a vertical rectangular plate and...
43. ### MHB Drawing a Rectangular Diagram with Tikz - Dan Seeks Guidance

I thought I'd try out the tikz thing. I am trying to draw a square with the four points A, B, C, and D labeled along with functions listed by each "arrow." I based my code on the triangle that was on the tikz example. Something is obviously wrong. Heck I'd just be happy to get the square to...
44. ### Shear rate in rectangular "channel"

Hi everyone, Non-physics student here, and slightly in over my head :D I am slightly stumped for ideas regarding the calculation of the shear rate in a rectangular type channel, which I need to effectively simulate a blood flow type condition in a channel that has to be rectangular due to the...
45. ### Polar equation to rectangular equation

Homework Statement [/B] a - a fixed non-zero real number r=e^(a*theta), where -pi/2<theta<pi/22. The attempt at a solution r^2=(e^(a*theta))^2 x^2 + y^2 = e^(2*a*theta) ln(x^2 + y^2) = 2*a*theta ln(x^2 + y^2) = 2*a*(pi+arctan(y/x)) Is this OK?
46. ### Energy Gap of 2 states in a deep rectangular potential well.

What is the energy gap between the ground state (n=0) and the first excited state (n=1) of an electron trapped in a deep rectangular potential well of width 1Å?
47. T

### Differentiate between rectangular beam and flange beam

Homework Statement How to differentiate between rectangular beam and flange beam ? In the question below , the answer provided is flange beam , I'm wondering can i design it as rectangular beam Homework EquationsThe Attempt at a Solution Since there's no clue whether the flange beam or...
48. ### Resistance of a semicircular conductor with a rectangular cross section

Homework Statement There is a conductor with the square-shaped area. the Radii are r1 , r2 with width b and resistivity ## \rho_R##. Find the resistance R between A and B 2. Homework Equations ##I = \iint_A\vec J \cdot d \vec A## ## \vec J = \kappa \vec E ## ## \vec E = \rho \vec J## ## V =...
49. ### MHB Maximizing area of rectangular portion of athletic field

An athletic field is to be built in the shape of a rectangle x m long capped by semicircular regions of radius r m at the two ends. The field is to be bounded by a 200 m racetrack. Express the area of the rectangular portion of the field as a function of x alone. What value of x gives the...
50. ### Maximum volume from a rectangular cardboard

Homework Statement Homework Equations First derivative=maxima/minima/vertical tangent/rising/falling When f'(x)>0 → the function rises The Attempt at a Solution $$V=(15-2a)(8-2a)=4a^2-46a+120$$ $$V'=8a-46,~~V'=0\rightarrow a=5.75$$ But: ##~2a<8,~~V(a=4)=0## So 5.75>4 And: ##~V''=8## so it...