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.
Homework Statement
Given that:
Write an equivalent integral in spherical coordinates.
Homework Equations
(Triple integral in spherical coordinates.)
(Conversions from rectangular to spherical coordinates.)(What spherical coordinates entail)
The Attempt at a Solution
The region...
Is the Fresnel-Kirchhoff formula (FKF) valid also for gaussian beams? I a book starting from the gaussian intensity:
U_0(x,y)=\sqrt{\frac{2}{\pi\omega_0^2}}\exp\left(-\frac{t^2+s^2}{\omega_0^2}\right)
it said that using the FKF in free space the gaussian beam spreads (in far-field assumption)...
Homework Statement
Determine the dimensions of a rectangular box, open at the top, having volume
4 m3, and requiring the least amount of material for its construction. Use the
second partials test. (Hint: Take advantage of the symmetry of the problem.)
Homework Equations
The...
Homework Statement
r(u,v)=u i +v j +(1/2)v k
Homework Equations
The Attempt at a Solution
x=u : y=v : z=(1/2)v
because x=u and y=v, x & y are the parameters
so r(x,y)=x+y+(1/2)y=x+(3/2)y
but the answer says it is y-2z=0. What am I not seeing correctly?
Homework Statement
If an electron is in an infinite rectangular prism well, with sides of length a, b, and c where c is the shortest and (b^2)*c=a^3, for what value of the d=b/c is the first excited state of the electron minimized? This isn't the complete problem but it's the part that's...
Homework Statement
change from rectangle to spherical coordinate :
z^2 = x^2 + y^2
I know that :
z = pcos(phi)
x = psin(phi)cos(theta)
y = psin(phi)sin(theta)
there fore
z^2 = x^2 + y^2 in spherical coordinate is
p^2cos(phi)^2 = (psin(phi)cos(theta))^2 +...
A horizontal hollow rectangular mild steel tube 30mm x 50mm with 4mm wall thickness and 350mm long, which is part of a frame has 2 lengths of studding 300mm long , 180mm apart and equidistant from the ends, welded to the 50mm face of the tube.
A total perpendicular load of 400Kgs is...
Dear all,
I am trying to solve a simple model with Comsol to find the pressure drop in a rectangular channel W=5mm, h=0.6mm, L=10mm. When i try to set the inlet velocity to 0.5m/s the solver shows the error message "Maximum number of Newton iterations reached". The solver works fine if i set...
Homework Statement
Homework Equations
n/a
The Attempt at a Solution
I set up the intgral at
integral from 0 to 5 of integral from 0 to 5y of 8e^(y^2)dxdy
I solved it as an iterated integral so I solved the first part, then ended up with integral from 0 to 5 of 40ye^(y^2)...
Homework Statement
A uniform rectangular plate of width d, height h, and weight W is supported with its top and bottom edges horizontal. At the lower left corner there is a inge, and the upper right corner there is a cable. For what angle \theta with the vertical will the tension in the cable...
Homework Statement
The figure shows a metallic block, with its faces parallel to coordinate axes. The block is in a uniform magnetic field of magnitude 0.020 T. One edge length of the block is 25 cm; the block is not drawn to scale. The block is moved at 2.8 m/s parallel to each axis, in turn...
The Basis of this question is that:
* Rockets launched at an angle follow the path of a rectangular hyperbola when thrust greater than their mass is produced.
* That rockets fall in the path of a parabola when thrust is no longer produced, this only applies when the rocket has both x and y...
Hi guys
I am currently using Comsol to model a single rectangular channel, a typical one found in a fuel cell (with symmetry boundary). Dimension of the inlet and outlet area is of the order 10e-3 and the length of the pipe is 0.1 m.
I am having difficulty getting the expected result. The...
Homework Statement
Draw a picture to illustrate the two-dimensional drumhead in the x-y plane. Label the coordinates of the sides of the drumhead. Use this picture to illustrate the "modes" of vibration.Homework Equations
\frac{\partial^{2}Z}{\partial x^{2}} + \frac{\partial^{2}Z}{\partial...
Homework Statement
The hyperbola y = 1/x in the first quadrant can be given the parametric definition (x, y) = (t, 1/t), t>0.
Find the corresponding parametric form of its evolute, and sketch both curves in the region 0<x<10, 0<y<10
Homework Equations
Curvature formula...
Homework Statement
Hello,
the problem ask you to pass this integral
\displaystyle\int_{-2}^{2}\int_{-\sqrt[ ]{4-x^2}}^{\sqrt[ ]{4-x^2}}\int_{x^2+y^2}^{4} x {dz}{dy}{dx}
to sphere coordinates, but I don't really know how
Homework Equations
Well, I know the basics formulas...
A rectangular block has dimensions 2.9cm x 3.5cm x 10.0cm. The mass of the block is 615.0 g. What are the volume and density of the block?
how do you do it?
Homework Statement
A rectangular loop of wire lies in the same plane as a straight wire, as shown http://i30.tinypic.com/347fupw.jpg". There is a current of 2.5 Amperes in both wires. Determine the magnitude and direction of the net force on the loop.
Homework Equations
Not sure. I am...
Homework Statement
Suppose you have an a x b rectangular array of distinct integers (think of it as a matrix if you would like). Now suppose we first move across the columns and take a permutation of the entries in each column. Informally, we can imagine the integers in the array as cards, and...
Hi,
I have got a simple problem which makes me struggle.
I have a rectangular thin conductive sheet (2D) of width w, height h
and conductivity suspended in air.
I would like to calculate with COMSOL/Femlab the electrical resistance between one of the corners of the conductive sheet and any...
So I know x=(r)cos(theta)
and y=(r)sin(theta)
As well as r^2 = x^2 + y^2
And (theta)=tan^-1 y/x or sin^-1 y/r or cos^-1 x/r
If I want to convert the polar coordinates (7.6 , 285(degrees)) to rectangular coordinates, to the nearest hundredth, what would I do?
And also...
Homework Statement
Hey i know that we can change it by using
r^2=X^2+y^2
and
tan(theta)=y/x;
but finding some problems in converting the area surrounded by
X=0; Y=0; x+y=1; x+y=2 to polar coordinates .
yr of course you can convert X=0 to theta=pi/2 and Y=0 to theta=0;
But i...
Hi, I have the fields for a rectangular waveguide in terms of cartesian components, that is, Ex, Ey, Hx, Hy. I need to convert these to polar components in terms of r and theta.
I've done this the other way around, converted a circular waveguide field which was written in terms of r and theta...
Homework Statement
For an air-filled waveguide rectangular wave guide with the top and bottom made of PEC and
the left wall made of PMC and the right wall of PEC. The dimensions are a=5cm b=3m. Find the dominant mode propagating in this wave guide
(a is length and b is the height)
Homework...
Homework Statement
F(w) is the Fourier transform of f(t). Write down the equation for F(w) in terms of f(t).
A rectangular pulse has height H and total length t0 in time. Show that as a function of w, the amplitude density is propertional to sinc(wt0/2).
Homework Equations
F(w) =...
hello again folks, this is the last problem that I haven't gotten in this week's homework. see attached image.
Homework Statement
Two rectangular pieces of glass (see attached image, I painstakingly made it with a very fussy/crash-ey program) are laid on top of one another on a plane surface...
I am told in the problem that i am to minimize the amount of cardboard needed to make a rectangular box with no top have a volume of 256 in^3? I am to give dimensions of box and amount of cardboard needed.
Can anyone help
Homework Statement
The rectangular and polar coordinates of a point are (x,y) and (r, Theta ) and theta equals 67 degrees
Homework Equations
??
The Attempt at a Solution
I know nothing about this does anyone know an equation or anything PLEASEE thanks.
Homework Statement
can anyone please send me the link to calculate the moment of inertia of cuboid,rectangular and triangular lamina ??(along with figure)
Homework Equations
The Attempt at a Solution
Hello everyone; here is the problem that I’m currently working on:
===============================================
a- Find the principal moments of inertia of a flat rectangular plate (mass = 30g, a = 80 mm, b = 60 mm) that rotates about a diagonal with velocity ω = 15 rad/s.
b- What are...
Hello, I just have a question about dot products of different coordinate systems.
I was wondering if anyone can explain why unit vector z(rect.) DOT unit vector r(spherical) is equal to cos(theta). As well, I was hoping if anyone could explain z DOT (Theta) = -sin(theta)?
THe following exercise deal with the steady state distribution of the temperature in either 2-dimensional plates or 3-dimensional regions.
Problem: A 10X20 rectangular plate with boundary conditions . at the lower side where there is poor insulation the normal derivative of the temperature is...
1. Find the resultant of two forces of 40 lbs. and 50 lbs. acting at an angle of 60○ between them.
2. Three forces of 30 gms, 50 gms, and 60 gms respectively act at an angle of 120○ from each other. Find the resultant by rectangular-resolution (a) by making the 30-gm force lie on the x-axis...
I'm given a complex function in the exponential form:
2.5j e^(-j40*pi)
Transforming this into the standard Cartesian form is pretty straight forward, but the extra j multiplying the 2.5 is kind of throwing me off. I don't know if I did it right, but this is what I did:
2.5j...
Homework Statement
A particle moves with position as a function of time in seconds given by the vector ~r = (5t^3, 3t − 6t^4)m.
What are the rectangular coordinates of the particle’s position at t = 2.5 s?
What are the rectangular coordinates of the particle’s velocity at t = 2.5 s...
Homework Statement
Convert into rectangular coordinates:
r = \frac {1}{1-cos(theta)}
Homework Equations
The Attempt at a Solution
r = \frac {1}{1-cos(theta)}
r –r(cos) = 1
(why can't I get a minus sign to display correctly? - I'm trying to show r -...
Homework Statement
Convert into rectangular coordinates:
r = tan(theta)
Homework Equations
The Attempt at a Solution
r = \frac {sin}{cos}
I used
r = \sqrt{x^2+y^2}
and
cos = \frac {x}{r}
x = (r)(cos)
sin = \frac {y}{r}
y = (r)(sin)...
Homework Statement
How much force is required to tip an object?
Given- It is a rectangular prism 1m tall, .5 m wide, 2m long.
The center of gravity is .75m from the ground vertically and otherwise centered.
The force can be applied wherever it is easiest to solve the problem.
Homework...
COMSOL Rectangular mesh (VERY URGENT)
I am trying to modify the mesh of a COMSOL simulation. I need to make my mesh rectangular instead of triangular that COMSOL defined already.
Thanks.
Engin
Homework Statement
A WxH rectangular loop of wire, with resistance R, lies on a table a distance s from a separate long straight wire carrying a current I.
If the loop is pulled to the right, parallel to the wire, with the speed v, then what is the magnitude of the current induced on the...
1. I can't seem to find a formula to figure out the area of an upright rectangular glass rod. Can someone point me in the right direction?
2.
The Attempt at a Solution
Homework Statement
change from polar to rectangular coordinates
Homework Equations
\cos{theta}+r^2\sin{theta}=\tan{theta}
The Attempt at a Solution
I got
x^2 + y^2 + x + y = \frac{y}{x}\sqrt{x^2+y^2}
does that look right?
Homework Statement
r^2= 2cos^2 θ+3sin^2θ
Homework Equations
X= r cosθ
y= r sinθ
The Attempt at a Solution
√r=√2cos^2 θ+3sin^2θ
r = 2 cos θ+ 3 sin θ
r = 2x + 2 y.
I doubt that i even got close to the correct answer so I like to ask anyone who knows how to deal with this...
Homework Statement
Hi,
I need to calculate the voltage drop in an n by m grid. There are resistors 4 resistors connected to a square; R1 for horizontals and R2 for verticals. There's a voltage applied at point B and point A is grounded.
I need to create a MATLAB function that will solve for...
1. A rectangular tank 2.0 m by 2.0 m by 3.5 m high contains gasoline, with a density of 0.68E3 kg/m3, to a depth of 2.5 m. What is the gauge pressure anywhere 1.2 m below the surface of the gasoline?
2. P=Ps + Pl Pl=density (g) (h)
3. I'm sure this is an easy problem, but I...
Homework Statement
Find the dimensions of the rectangular box of largest volume that can be inscribed in a sphere of radius 1.
Homework Equations
v=w*l*h, Set the partials equal to 0, then solve a system, etc.
The Attempt at a Solution
I'm really just unsure of the constraints that...