Skip to main content

Questions tagged [rectangles]

Questions about rectangles and their properties.

Filter by
Sorted by
Tagged with
-3 votes
0 answers
56 views

How do you prove that a specific shape in a regular octagon is a rectangle? [closed]

In regular octagon ABCDEFGH, how do you prove that ADEH is a rectangle? This is assumed in many problems that find the area of an octagon. Since AD and EH are symmetrical diagonals, they are equal, ...
Anonymous's user avatar
2 votes
2 answers
79 views

How to determine the elevation at the edges of a tilted rectangle?

The rectangle is slanted in direction B to C and the elevation at point B (between the edge and the floor) is 1.2 cm. C is the only edge that touches the floor. How to determine the elevation at ...
TheLostInUnknown's user avatar
0 votes
0 answers
48 views

Elliptical Grid Mapping in Shader

I wanted to make a Elliptical Grid Mapping Shader, but it is not a perfect square and it is rotated. If i multiply the coords by sqrt(2.) and divides them after again, it is an square, but still ...
Taxy's user avatar
  • 21
2 votes
1 answer
73 views

A square divided into congruent rectangles

Can a 1*1 unit square divided into congruent rectangles with irrational side lengths? The answer might seem trivial, but there are two irrational numbers in which both their sum multiple is rational; ...
 S.Pascal's user avatar
3 votes
1 answer
65 views

Square with irrational side partitioned into rectangles

Given a square with sidelenght $\sqrt{2019}$ partitioned into finite number of rectangles one needs to show that at least one of them must have both sides irrational. It's obviously one of them must ...
Anton Shcherbina's user avatar
0 votes
1 answer
51 views

Calculating the corners of a rotated outer rectangle that encapsulates minimally an inner rectangle.

I have two rectangles that start as the same size. When I rotate one of these rectangles I want it to encapsulate the other rectangle taking up the minimum possible area. The coordinates of the ...
Jfloaty's user avatar
  • 13
4 votes
2 answers
95 views

Cutting Up a Rectangle and Piecing Together a Square of the Same Area

Original Question Given a rectangle $ABCD$ where $AD=a$ and $AB=b$, cut up the rectangle into some pieces such that piecing the pieces back together will form a square with the same area as the ...
Cheese Cake's user avatar
  • 1,249
0 votes
2 answers
74 views

Center position of an orthogonal rectangle that has a side or corner touching a circumference

I need to find how distant the center of an orthogonal rectangle is from the center of a circle, given a specific angle. The dimensions of the rectangle are proportional to the circle radius, so they ...
musicamante's user avatar
-1 votes
1 answer
57 views

Find the number of rectangles not containing the shaded square [closed]

I wish to find the number of rectangles that don't contain the shaded square: Image of the grid: I used the way of finding the total number of rectangles and subtracting the rectangles containing the ...
Đỗ Quốc Khánh's user avatar
3 votes
4 answers
451 views

Prove that triangles $VAC$ and $VBD$ have equal areas and equal perimeters....

The question Let $VABCD$ be a quadrilateral pyramid with a rectangular base. $\angle AVC =\angle BVD$ prove that triangles $VAC$ and $VBD$ have equal areas and equal perimeters. The idea Because the ...
IONELA BUCIU's user avatar
13 votes
1 answer
469 views

Covering a circle using rectangles

What is the maximum area that can be covered with $3$ rectangles inside a radius $1$ circle?(i.e. maximum area $=\pi$) The rectangles can be any length and height you want, and can rotate and reflect. ...
A Math guy's user avatar
1 vote
0 answers
28 views

$\int_Q c=c\cdot v(Q)=c\sum_R v(R)$. Is my elementary proof ok? (James R. Munkres "Analysis on Manifolds")

I am reading "Analysis on Manifolds" by James R. Munkres. We begin by defining the volume of a rectangle. Let $$Q=[a_1,b_1]\times [a_2,b_2]\times\cdots\times [a_n,b_n]$$ be a rectangle in $\...
佐武五郎's user avatar
  • 1,210
3 votes
0 answers
96 views

Recurrence relation for the number of rectangle in a $d$-dimensional cube

Inspired by this question I tried to find a recurrence relation for the number of rectangles in a $d$-dimensional hypercube $C$. Let call this number $r_d$. It is known that $r_d$ has a closed form, ...
Marco's user avatar
  • 2,675
3 votes
1 answer
82 views

Parameterization of the set of oriented rectangles

I am interested in the set of oriented rectangles, that are centered on the origin, and can be described by their width, height and angle. I am looking for a "good" parameterization that is ...
user209974's user avatar
1 vote
0 answers
89 views

Problem 3-35(b) in "Calculus on Manifolds" by Michael Spivak. Please tell me how to complete (b) using the author's hint.

Problem 3-35 (a) Let $g:\mathbb{R}^n\to\mathbb{R}^n$ be a linear transformation of one of the following types: $$\begin{cases} g(e_i)=e_i & i\neq j \\ g(e_j)=ae_j & \end{cases}$$ $$\begin{...
佐武五郎's user avatar
  • 1,210
1 vote
1 answer
256 views

Area of a right angled triangle given the dimensions of an inscribed rectangle

Is there a way to find the area of the right-angled triangle given the dimensions of the rectangle? The rectangle can fit into the same right-angled triangle in two ways, as shown below: Let $a$ = ...
Developer's user avatar
2 votes
2 answers
66 views

Maximize rabbit pen size (no calc) [duplicate]

Question: To make an enclosure for your pet rabbits, you want to fence a rectangular pen against your house. Only 3 sides will need to be fenced. You have 170 feet of fencing material, and want to ...
Capt's user avatar
  • 61
-1 votes
1 answer
60 views

Value of angles of a quadrilateral [closed]

$ABCD$ is a rectangle, $\overline{AC}$ and $\overline{BD}$ are its two diagonals, $O$ their intersection point, and $\angle COD=68^{\circ}$. What is the value of $\angle (BAO-OBC)$?
Md. Sayan Khan's user avatar
1 vote
2 answers
259 views

Prove some results in a cube...

Question Let $ABCDA'B'C'D'$ be a cube and the points $M, N, Q$ the means of the sides $A'B', A'D', DC$. We denote by $\alpha=(MNQ)$. a) If the line $D'C'$ intersects the plane $\alpha$ at the point $T$...
IONELA BUCIU's user avatar
13 votes
2 answers
302 views

Is this a new point on the nine-point-circle of a triangle?

I was trying to get a feel for how to solve another question about the largest triangle that can fit in a unit square, by constructing the smallest enclosing square of a triangle in Geogebra. While ...
KDP's user avatar
  • 1,111
1 vote
1 answer
108 views

Find all possible values of the perimeter of a rectangle with sides $x, y \in \mathbb{Z}^+$, where its area is given by $A=3x+3y+\sqrt{9x^2+9y^2}$

Find all possible values of the perimeter of a rectangle with sides positive integers $x$ and $y$ where its area is given by $A=3x+3y+\sqrt{9x^2+9y^2}$ In other words if $xy=3x+3y+\sqrt{9x^2+9y^2}$, ...
sinichgaja's user avatar
1 vote
2 answers
101 views

Longest line in a rectangle [closed]

Given a rectangle, how can one show that the euclidian distance between any two points inside the rectangle (or on its borderies) is smaller or equal than the distance of the diagonal of that ...
emelie's user avatar
  • 439
1 vote
1 answer
79 views

Geometry inequality question (picture attached) [closed]

This question is from a mock test of GRE Quant section. Unfortunately, they only provided the answer key without explanation. The question asks: Quantity $A = a + b$ Vs. Quantity $B = 200 - c$ Which ...
Ali Naveed's user avatar
-1 votes
2 answers
118 views

Help me understand the answers

THE PROBLEM Let $ABCD$ be a rectangle and $E, F$ the means of the sides $AB$, respectively $AD.$ We know that there is a point $M$ on the segment $AC$ such that $\angle EMF = 60$ and $AC^2 = 4*ME*MF$ ...
IONELA BUCIU's user avatar
3 votes
1 answer
170 views

Proving that no tile can fill both squares and equilateral triangles

Cut up a square into a finite number of identical tiles. Here is one possibility: How do I prove that the tiles could never be rearranged to form an equilateral triangle (with filled interior and no ...
bobuhito's user avatar
  • 791
0 votes
0 answers
77 views

How can I check if a rotated rect intersects a non-rotated rectangle?

I have a rotated retangle and a rectangle. Both are defined by their corners (however, for the non-rotated ones I also have access to topLeft, topRight, etc). Is there a way I can check if they ...
Fabrizio's user avatar
  • 113
3 votes
2 answers
167 views

Find an angle in a rectangle. [closed]

A few days ago, I came across a problem that has driving me insane. It seems so simple, but I just can't solve it, it's like a blind spot to me. Here's the problem: A point $N$ is taken on the side $...
data water's user avatar
3 votes
2 answers
78 views

What pair of rectangle shapes is exchanged by cutting off a square?

What pair of rectangle shapes is exchanged by cutting off a square? According to https://oeis.org/A059966 the golden rectangle has period one when cutting off a square. What pair of rectangle (shapes)...
it's a hire car baby's user avatar
0 votes
0 answers
38 views

Parallel lines passing through rectangle angles

I have a rectangle (side length L1 and L2) and two parallel lines passing through two opposite angles: (sorry the image is missing due to stackexchange policy) I know that the (perpendicular) distance ...
Antonio Azevedo's user avatar
19 votes
2 answers
477 views

You have $n$ rectangles of area $1$ (and variable height). Pack as many as possible in a semicircle of area $n$. How many leftovers will there be?

You have $n$ rectangles of area $1$ (and variable height). Pack as many of these rectangles as possible in a semicircle of area $n$. How many leftover rectangles will there be, in terms of $n$? How to ...
Dan's user avatar
  • 25.8k
-2 votes
1 answer
80 views

What is the distance between the centres of two touching rectangles?

What is the distance between the centres of the two rectangles shown in the image? This distance should be expressed in terms of the lengths of the sides of the rectangles and the angle $\alpha$ in ...
Blazing Blast's user avatar
0 votes
0 answers
23 views

How to round output rectangles of SquarifiedTreemap algorithm so they can fit a grid with every tile being 1x1

This can be trivial but nonetheless I need help... :) I have a grid, every tile of the grid is 1x1. I'm using SquarifiedTreemap algorithm to divide the grid in rooms, but the result values are in ...
suchoparek's user avatar
3 votes
2 answers
152 views

Cutting a rectangular piece from a right triangle

A piece of sheet metal has the shape of an acute right-angled triangle AB with side BC and height AA' each having 12 cm. From it, a rectangle with two vertices is cut on the base BC and the other two ...
user avatar
0 votes
1 answer
172 views

Questions about ratio and overlapping figures

As I am helping my younger brother on his math papers (bought on external sources), I came across a question that seems unsolvable. I feel that the question is not complete as they did not state the ...
Hahaha's user avatar
  • 13
0 votes
0 answers
65 views

How to determine the maximum area of a rectangle in a coordinate system with a function?

I am currently struggling with a math problem and was wondering if someone could help me out. The problem is as follows: In a coordinate system, a rectangle is drawn with one corner at the origin, one ...
cricket900's user avatar
6 votes
1 answer
144 views

Find the number of points inside a rectangle if the rectangle is divided into $210$ triangles.

A number of points is drawn inside a rectangle. The rectangle is divided into 210 triangles whose vertices coincide with the vertices of the rectangle and/or the points drawn inside the rectangle. ...
Zero's user avatar
  • 357
2 votes
1 answer
60 views

Geometry of a rectangle and a semi circle [closed]

Given a rectangle $ABCD$ where $AB=|2a|$ and $BC= |\sqrt2a|$. On the side of $AB$, as a diameter, a semi-circle is constructed externally. Let $M$ be an arbitrary point on the semi-circle, the line $...
Pratyush's user avatar
1 vote
2 answers
57 views

$S$ and $Q$ are situated in opposite regions with respect to $PR$ in $\triangle PQR$ ,What is the length of $QS$?

I am currently working on an Olympiad math problem, and I am struggling to find a solution. I would greatly appreciate your help in solving this problem. I was unable to solve the problem because I ...
Raihan Sarker's user avatar
1 vote
0 answers
79 views

Find the position of a rectangle that touches a given circle when the direction of the line joining their centres are known.

I have a rectangle, the sides of which are parallel to $x\text{-}$ and $y\text{-axis}$. The length of the sides are known, i.e., width = $W$ and height = $H$. I also have a circle of radius $R$ with ...
Nicolas's user avatar
  • 111
0 votes
1 answer
74 views

number of subrectangles

I have a square matrix generated by a cyclic shift of a vector which contains only 0's and 1's. For example, $$ \begin{matrix} 1 \; 1 \; 0 \; 1 \; 1 \\ 1 \; 1 \; 1 \; 0 \; 1 \\ 1 \; 1 \; 1 \; 1 \; 0 \\...
user43283's user avatar
  • 113
0 votes
1 answer
25 views

I couldn't understand the last part of the argument. Why is the length of a side in a 4 sided stuff proportional to angle?

Why is DE =3? I don't quite get it. What theorem did he use? https://www.youtube.com/watch?v=Dk9mfrIL7FQ I also don't understand why all four corners of a four sided object is in a circle if the sum ...
user4951's user avatar
  • 1,714
6 votes
0 answers
129 views

Squeezing a convex shape between two squares

You are given a convex shape $S$ in the plane. You are allowed to apply any affine transformation to $S$. Then, you have to pick an axes-parallel square contained in (the transformed) $S$, and an axes-...
Erel Segal-Halevi's user avatar
0 votes
1 answer
270 views

How many circles of radius R with a D distance between them, fit in rectangle of B x L

i have a rectangle of B x L meters and i want to know how many circles with R radius can fit if there is a space of D between them. All the values wil be integers always. I tried this. With this ...
Daniel Florez Cortes's user avatar
0 votes
1 answer
62 views

Are "rectangle" subsets of a flat torus exactly the products of connected sets?

I think the following statement on flat-tori is true, but I feel uncertain and am thus posting as a sanity check: First the convetions I am using: The $1$-torus is the quotient space $\mathbb{T}^1 := ...
Dasi's user avatar
  • 256
0 votes
1 answer
49 views

Hyperplane Separation Theorem for non-axis aligned rectangles?

I'm trying to understand how the Hyperplane Separation Theorem works. I found a function on MATLAB that implements it, accepting the parameters rect1 = [0 0; -1 3; 6 4; 7 1]; rect2 = [12 0; 14 1; 13 ...
MFerguson's user avatar
  • 137
0 votes
0 answers
193 views

A function to transform a rectangle into a triangle and vice versa.

I have two input variables, let's call them x and y, which are the inputs to a function. There is a condition for these two inputs: x+y must be equal to or less than 1. So, my input space would look ...
Arash Heidari's user avatar
0 votes
1 answer
209 views

Is the converse of Vertically opposite angles true?

When two straight lines intersect the vertically opposite angles are equal. But, can we say that, if the vertically opposite angles of two lines are equal then the lines are straight? The angles ...
Apoorva Shukla's user avatar
0 votes
0 answers
30 views

how many rectangles in a circle with defined measurements

example of rectangles in circle i have various size plates as follows 12m 10m 8m 6m 4m i need to be able to calculate how many rectangles i need in a quardrant(can be mirrored for other quadrants) the ...
user1121110's user avatar
0 votes
1 answer
95 views

Proof of the equation for a rectangle in the Cartesian coordinate system with distances and absolute values [closed]

Can anyone help me find an approach to deriving the equation $$ \left\lvert \frac{x}{p}+\frac{y}{q} \right\rvert + \left\lvert \frac{x}{p}-\frac{y}{q} \right\rvert = c $$ for a rectangle in the ...
RaWa's user avatar
  • 11
-2 votes
1 answer
38 views

Align end of lines of ellipse on top of rectangle border

I know the question includes source code but the problem itself is purely mathematical, so maybe this is the right place anyway I have the following code to draw circles, squares, ellipses and (wrong) ...
somsam43's user avatar

1
2 3 4 5
13