Rectangle Definition and 244 Threads

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. TheMathNoob

    Find a line in the rectangle from 0.0 to some point

    Homework Statement There is a rectangle in the x-y plane with dimensions H=1, L=2. Find a line or diagonal in the rectangle in which for every point in the shaded area below that line x>y. Homework EquationsThe Attempt at a Solution The line has to intersect a point in y=1 in which x>y. This...
  2. I

    Inhomogeneous Dirichlet problem in a rectangle

    Homework Statement Solve the problem \begin{cases} u_{xx} + u_{yy} = y, \; \; 0 < x < 2, \; \; 0 < y < 1\\ u(x,0)=0, \; \; u(x,1)=0\\ u(0,y)=y-y^3, \; \; y(2,y)=0. \end{cases} Homework Equations N/A The Attempt at a Solution I start by trying to find a steady-state solution ##u_0(y)## (or I...
  3. S

    Need design for a rectangle "like" spray bottle

    to keep it simple, I will explain what I basically need. Imagine a rectangular Plastic brick. With 10 small holes on the bottom that would release fluid. There is a cap on the top of the rectangle box that the fluid will be poured into. And a press style button on the side of the rectangle to...
  4. S

    What is the optimal shape of a membrane on a rectangle under pressure?

    Homework Statement This is not a homework or anything similar, but it is a problem I am trying to solve and I don't know how to start. I do know, that the most stable structure in 3D is a sphere - that is the reason why the drops are in a spherical shape. But now imagine a rectangle and...
  5. Albert1

    MHB Find $\vec{AC}.\vec{AB}$ in Rectangle $ABCD$

    Rectangle $ABCD$ given :$\angle CAB=30^o$ ,and $\vec{AC}.\vec{AD}=\mid\vec{AC}\,\, \mid$ please find the value of :$\vec{AC}.\vec{AB}$
  6. D

    Optimizing the area of a rectangle inside a racetrack

    Homework Statement Maximize the area (in feet) of the rectangular field inside of a mile long racetrack. Homework Equations Circumference of a circle = 2πr P= 2x + 2y The Attempt at a Solution Area of the semicircles = πr^2 Area of the rectangle = 2rh A(r) = πr^2 +2rh P= 2πr + 2h + 4r...
  7. J

    MHB Area of a region in Rectangle: very tough question

    I have been stuck on this problem for 8 hours. Can anyone please help me? it would be great if full solution is provided, but even a general overview would help. PQRS is a rectangle with PQ=20 and QR=5. Point X lies on the line PQ and Y on RS such that angle PYQ is 90 degrees. Angle SXR is also...
  8. K

    Optimization Problem: Minimizing rectangle dimensions

    Hi guys, I'm a high school senior currently in calculus and vectors. We're in our application unit right now, and I'm having quite a bit of trouble with problems that give the desired volume/area, and then ask you for the minimum dimensions required for said volume. One notable problem that I am...
  9. Y

    Finding area of the affine translation of a rectangle

    Homework Statement Given a rectangle R=[1,3] x [2,4], and the affin translation F : R^2 -> R^2 defined by F(x,y) = (1,3) + A*(x,y), where A is the 2x2 matrix (2 , 7 ; 3 , 1), what is the area of the affin transelation of the rectangle R? Homework EquationsThe Attempt at a Solution When I...
  10. S

    MHB Find Area of A Rectangle With Shortcut

    hi all... how do you find area of a rectangle, if its perimeter of a rectangle is = 72 cm? i mean how to easy find it without hard work. do you have a formula or just tricks similar like.. http://calculus-geometry.hubpages.com/hub/How-to-Find-the-Area-Perimeter-and-Diagonal-of-a-Rectangle...
  11. R

    Determine angle made by a ball inside a rectangle

    From the picture i.e attached. Can there be a formula, where the ball will strike after certain number of hit, say on side b, what will be the angle the ball will make after n successive hit. I think it is just not possible, one can only measure the next angle the ball will make, provided one...
  12. G

    Vector Calculus: Mesh Size and Size of Largest Rectangle

    Homework Statement I need to find a sequence of partitions , let's call it S of R=[0,1]x[0,1] such that as the number of partitions k→∞ , then limit of the area of the largest subinterval of the rectangle in the partition, denoted a(S) tends to 0, but the mesh size m(S) is a non-zero value...
  13. AdityaDev

    Permutations and combinations - is square a rectangle?

    I was going through a p and c problem where I had to find the number of non congruent RECTANGLES. Answer includes number of squares as well. SHOULD SQUARE BE TAKEN AS A RECTANGLE?
  14. P

    Find the dimensions of the rectangle of greatest area

    Homework Statement Find the dimensions of the rectangle of greatest and least area that can be inscribed in the ellipse x^2/16 + y^2/9 = 1 with sides parallel to the coordinate axes. The Attempt at a Solution f(x,y) = (2x)(2y) = 4xy ∇f = <4y,4x> ∇g = <x/8,2y/9> ∇f = λ∇g 4y = λx/8 4x = λ2y/9...
  15. pairofstrings

    How 'x' (multiplication) found its way into formula of area of rectangle?

    Hi, I know that area of rectangle is length x breadth. I tried to find proof of area of rectangle but I found that the proof was solved by taking formula of area of square into consideration. But what I don't understand is why area of rectangle should be length times breadth, or side times side...
  16. C

    PDE for temperature distribution in rectangle

    Homework Statement A rectangular chip of dimensions a by b is insulated on all sides and at t=o temperature u=0. The chip produces heat at a constant rate h. Find an expression for u(x,y,t) Homework Equations δu/δt = h + D(δ2u/δx2 + δ2u/δy2) x∈(0,a), y∈(0,b) The Attempt at a Solution I'm...
  17. chwala

    Finding the length and width of rectangle

    Mod note: Thread originally posted in a technical math section, so is missing the homework template. I am trying to solve this problem it states as follows "A piece of wire 24 cm long has the shape of a rectangle. (a) Given that the width is W cm, show that the area, A cm^2 of the rectangle is...
  18. J

    Design the Most Stable Base for a Rectangle

    Hey guys, Im in the middle of a project and need help with the base for it. I have to develop a base for a rectangle 3 feet high by 2 feet wide by 6 inches deep. The front of the rectangle is 1 pound heavier than the back and will stand 2 feet off the ground. The base must be able to make the...
  19. P

    Find the potential difference in a rectangle

    Homework Statement [/B] Figure 20-3, referred to below, is 0.800m wide and 0.400m tall with "A" in the top left corner, "+4 microC" charge in the top right corner, "+2 microC" charge in the bottom left corner, and "B" in the bottom right corner. Two point charges of magnitude +4.00 μC and...
  20. M

    MHB The rectangle has an empty interior

    Hey! :o Show that the measure of a rectangle is zero if and only if it has an empty interior. When a rectangle has an empty interior, does this mean that the length of the sides of the rectangle are equal to zero?? (Wondering)
  21. N

    A rectangle with Charges on Each Corner - Find Missing Charge?

    Homework Statement A charge is to be placed at the empty corner of a rectangle to make the net force at corner A point along the vertical direction. What charge (magnitude and algebraic sign) must be placed at the empty corner if the three charges have the same charge of +8.45 μC?Homework...
  22. U

    Hydrostatic force on submerged rectangle

    Homework Statement (Referring to attached diagram) Find the hydrostatic force F2 on the rectangular part and the point of action of this force on rectangular area. The triangular part is submerged in oil of specific gravity 0.8, while the rectangular part is submerged in water. The whole...
  23. Dethrone

    MHB What is the rate of change for the area of the rectangle?

    Since it's the summer, I might as well take advantage of all the math helpers on the site :cool: (yay!) I'm pretty rusted when it comes to related rates, so it'd be great if someone checked my work :D Problem: A rectangle has two sides along the positive coordinate axes and its upper right...
  24. stateofdogma

    Moment of inertia of rectangle without dd int

    Homework Statement I found the moment of inertia of a rectangle, with the axis perpendicular and going through the center using double integration. But I also used what i thought to be an equivalent method, but it didn't work.Homework Equations dI=r^2dm \int dI The Attempt at a Solution I was...
  25. J

    Greens theorem boundary of a rectangle

    Homework Statement ##\mathscr{C}: x=1,x=3,y=2,y=3## ##\int_\mathscr{C} (xy^2-y^3)dx+(-5x^2+y^3)dy## Homework Equations The Attempt at a Solution ##\frac{\partial Q}{\partial x} = -10x^2 \,\,; \frac{\partial P}{\partial y} = 2xy-3y^2## ##\int\int_\mathscr{C} \frac{\partial...
  26. P

    Solving Laplace's equation for a rectangle

    Hello, Homework Statement I am trying to solve Laplace's equation for the setup shown in the attachment, where f(x)=9sin(2πx)+3x and g(x)=10sin(πy)+3y. I have managed to solve it for the setup without the rectangle (PEC), and am now trying to solve ∇2\phi=0 for that inner rectangle in order...
  27. Dethrone

    Finding electric field of charges in a rectangle

    Homework Statement Find the electric field of a charge at a corner if there are 4 equal charges at the corner of a rectangle with sides 40 cm and 20 cm. The charges are 2.5 x 10^3 C. Homework Equations E = (kq)/r^2 The Attempt at a Solution I labelled the top left charge q1, the...
  28. MarkFL

    MHB Andrew's question at Yahoo Answers regarding maximizing the area of a rectangle

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  29. B

    How Does Decreasing Wire Current Affect a Nearby Metal Rectangle?

    Homework Statement A metal rectangle is close to a long straight current carrying wire, with 2 sides parallel to the wire. If the current in the wire is decreasing, the rectangle is Homework Equations Lenz's Law: the direction of any magnetic induction effect is such to oppose the cause...
  30. K

    MHB Express rectangle area as function of x

    Hey so another expressing functions question: A rectangle has on corner on the graph of y=36-x^2, another at the origin, a 3rd on the positive y-axis, and the fourth on the positive x-axis. Express the area A of the rectangle as a function of x. What is the domain of A? For what value of x is...
  31. MarkFL

    MHB Maximizing Area of Inscribed Rectangle - Yahoo Answers

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  32. M

    Help with Calculating Force on Rectangle of Wire

    Homework Statement I really need help with part c of the question... Consider a long straight wire and a rectangle of wire as shown (see figure). Here the rectangle is a distance d = 4.9 cm from the straight wire at its nearest approach, with length L = 19.0 cm and width r = 7.0 cm (so...
  33. L

    MHB Minimizing the area of an ellipse confined to a rectangle

    Calculate the length of the axes of the ellipse's area minimum that can be confined to a rectangle of sides: 2p and 2q answer Sqrt 2p Sqrt 2q I have just solved it
  34. rsyed5

    MHB How can the lower rectangle method for area approximation be improved?

    Hi, Can someone suggest a way to improve the lower rectangle method for area approximation...? I know one way is to increase the number of rectangles so if I put 100 instead of 5 rectangles i will get a better approximation. Another way it could be improved...?
  35. K

    Where Should You Tether a Dog for Maximum Play Area?

    I am really not sure where to even start with this question, at which point, (A,B,C) would the dog have a maximum area to play if tethered by a 20ft leash?
  36. B

    Rate of forward motion from rolling rectangle vs degrees turned

    Homework Statement I'm looking for a formula that relates the distance traveled by a 'rolling' rectangle compared to a given amount of degrees it has turned. And while I have you, another problem I have with the rolling rectangle is that its center point would move up and then down with...
  37. G

    Optimization - rectangle inscribed in a right triangle

    Homework Statement A rectangle is to be inscribed in a right triangle having sides 3 cm, 4 cm and 5 cm, as shown on the diagram. Find the dimensions of the rectangle with greatest possible area. Homework Equations 1. x^{2}+y^{2}=w^{2} in terms of w=\sqrt{x^{2}+y^{2}} 2...
  38. caffeinemachine

    MHB Can 101 Discs of Radius 1/2 Cover a Rectangle That 25 Discs of Radius 1 Can?

    Hello MHB. I am having trouble with the following quesion. Let $R=\{(x,y)\in\mathbb R^2:A\leq x\leq B, C\leq y\leq D\}$ be a rectangle in $\mathbb R^2$ which can be covered (overlapping allowed) with $25$ discs of radius $1$ each. Then $R$ can be covered with $101$ rectangles of radius $1/2$...
  39. MarkFL

    MHB Khegan McLane's Math Problem: Rectangle Inscribed Between Parabola & X-Axis

    Here is the question: I have posted a link there to this thread so the OP can see my work.
  40. M

    Derivation for Moment of Inertia of Rectangle rotated through center

    Homework Statement I need to know how to derive the equation for the moment of inertia of a rectangle rotated about an axis through its center. The rectangle has sides a and b. I know the equation to be (1/12)M(a2+b2), but I am having trouble deriving it. I have searched all over the...
  41. N

    MIN/MAX area of a rectangle inscribed in a rectangle

    http://bp3.blogger.com/_4Z2DKqKRYUc/Rnz_BgODzFI/AAAAAAAAAIw/uj_cVfPI8D4/s1600-h/Img_6-23-07_Blog.jpg Could someone help me to understand how can I figure it out, how can I create a formula for finding min/max area of a rectangle inscribed in a rectangle, defined by given width and height. Also...
  42. P

    Moment of Inertia of a Rectangle

    I have been trying to do the moment of inertia of a rectangle and I have it figured out when we have the center of the rectangle as the center of the rotation. The equation is ∫∫ρ(x^2+y^2)dy dx where the first integral is from -b/2 to b/2 (if b is the height) and the second integral is -a/2 to...
  43. M

    Unknown X in Rectangle - Mystery Image

    https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn2/1381281_4851671189048_115466648_n.jpg
  44. N

    Determining dimensions of a rectangle

    Homework Statement A box has a length that is 13cm longer than its width, and the volume of the box is 60cm^3. Determine the dimensions of the box. Homework Equations V = lwh l = 13cm > w h = ? The Attempt at a Solution Since V = lwh, 60cm^3 = lwh and, l = 13cm > w w...
  45. MarkFL

    MHB Unknown's question at Yahoo Answers regarding the perimeter of a rectangle

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  46. B

    Flux through a square and rectangle

    Homework Statement Flux: a. Calculate the flux of the vector v1 = (1, 3 5) through a 2×2 square in the x-z plane (i.e., y = 0). b. Calculate the flux of the vector v2=(z, y, -x) through this rectangle:0≤ x ≤3, 0≤ y ≤ 2, z = 0.. The Attempt at a Solution I guess flux is suppose to be...
  47. E

    Finding diagonal of inscribed rectangle

    Homework Statement A quadrant contains an inscribed rectangle ABCD. Given the distance marked: CD=3m , what is length of AD? Homework Equations Area of circle = pi*r^2 Pythagorean 's theorem : a^2=b^2+c^2 The Attempt at a Solution We can draw diagonal from C to B similar to...
  48. karush

    MHB How Do You Express Vectors in a Rectangle Using Midpoint Coordinates?

    ABCD is a rectangle and O is the midpoint of [AB]. Express each of the following vectors in terms of \overrightarrow{OC} and \overrightarrow{OD} (a) \overrightarrow{CD} ok I am fairly new to vectors and know this is a simple problem but still need some input on (a) I thot this would be...
  49. D

    What is the effect of multiple forces on a 2D rigid rectangle?

    Say I have a rectangle of width w and height h centred at (0, 0) on a 2D coordinate plane. The rectangle is free to move on a frictionless medium. It is not attached at any point. Case 1: A single force F = (Fx)i + (Fx)j acts at a point (x, y) How does the rectangle move? I looked it up on...
  50. H

    Argument principle for a rectangle

    Homework Statement . I want to prove that there is one solution for e^z-z in every shifted copy of the fundamental strip by applying the argument principle to the boundary of a rectangle −M≤Rez≤M , 2kπi≤Imz≤2(k+1)πi for large M and integer k . I need help in using the...
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