Questions tagged [rectangles]

Questions about rectangles and their properties.

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5
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1answer
66 views

Tiling a square with 3:1 rectangles

It is known that a square can be tiled with $n$ rectangles whose length is double their width for any $n > 4$. In particular, no two rectangles can overlap and no part of any rectangle is outside ...
-1
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0answers
22 views

Rectangle on a Plane - how to find vertices

There is a Plane with equation ax + by + cz + d = 0 where a, b, c, d are known. There is a Rectangle on the above plane for which the length l and breadth b are known. Now two points P0 (x0, y0, z0) ...
0
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1answer
57 views

Area of a rectangle inscribed in a semicircle as a function of $x$

The question given is, The figure shows a rectangle with two vertices on a semicircle of radius 2 and two vertices on the x-axis. Let $P(x, y)$ be the vertex that lies in the first quadrant. (a) ...
-1
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1answer
54 views

Given $AB = 2$ and $AC = 3$, what are $AD$, $BD$, $m∠BAD$ and $m∠ABD$? [closed]

Given $AB = 2$ and $AC = 3$, what are $AD$, $BD$, $m∠BAD$ and $m∠ABD$?
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1answer
34 views

Calculate height and width of rotated rectangle

I hope this is an easy one. I need to calculate the new height and width of a scaled rotated rectangle. I know all its corners $(A, B, C, D)$, its rotation angle ($o$) and its center ($M$). Now one ...
4
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0answers
126 views

Finding the rectangle of minimum area that can be divided into five rectangles such that the lengths of all their sides are different naturals.

Find the rectangle of minimum area that can be divided into five rectangles such that the lengths of all their sides are different natural numbers. I found a 11x11 rectangle such that when we divide ...
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0answers
11 views

The number of grid points p in a configuration of lines.

In some proof of theorem I have information Let A, B, and C denote the number of X, Y, and Z lines. By a classical results in geometry, the number of grid points p in a configuration with A, B and C, ...
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1answer
45 views

How do I calculate the new position of a given rectangle after subjecting it to rotation and scaling?

I want to calculate the new position of a modified version of a given rectangle. The given rectangle is shown in Yellow. The rectangle undergoing rotation and scaling is shown in Red. Step-1: The ...
0
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1answer
44 views

Volume of 3D shape with rectangle as base [closed]

The base is rectangular with $4 \times 9.5$ dimensions. There are three edges extending at a $90^\circ$ angle from the base with lengths $0.2, 0.5$ and $0.3$. How would you calculate the total volume?...
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1answer
40 views

Find the size of inner rectangle rotated 45 degrees within another rectangle

As picture, when rotation is 45 degrees, there are multiple combinations of w and h, but if the ratio w/h is known, how do I calculate the size of inner rectangle? Thanks. P.S. the pink one is a ...
1
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1answer
37 views

How to find the vertices of a rectangle when the slope of the direction is given?

The title might be a bit confusing but I'll do my best to explain this. So this image is given: The coordinates of vertex A are (3,2). We also know that [AD] and [BC] measure 1 unit each and [AB] &...
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1answer
37 views

find a rectangle limited to 4 lines

I want to find center of rectangle given w = width and h = height. The rectangle is limited ...
0
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1answer
60 views

How to calculate the width and heights of three rectangles for a given frame

Three rectangles all of different sizes, two aligned left and one right Considering the image above, where: rectangles A, B and C must preserve their aspect ratio ...
1
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0answers
16 views

Partioning rectangles into rectangles and valid sub-rectangle extension rules.

Given a rectangle $A$ composed of unit squares, we then fuse grid squares into sub-rectangles $B_i$ in a way that the $B_i$ partition $A$. Example: XXO YZO YWW ...
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2answers
81 views

Rotated rectangle with dimensions $c \times d$ inscribed in a rectangle with dimensions $a \times b$. How to express $d$ knowing $a,b,c$?

What we know: length of $a$, $b$, $c$ $a$ and $b$ are the sides of the large rectangle what I need to find: length of $d$ or just one angle (yellow color) I found some solution on the internet with a ...
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0answers
45 views

How can I rotate a rectangle complete 360 degree

I implemented the logic to rotate rectangle $90$ degree but the logic is not working for complete $360$. It rotates until $90$ then goes in reverse direction until $180$ then again come back on $225$ ...
0
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2answers
85 views

Check if ellipse lies inside rectangle

I have Ellipse center Cx, Cy and radius (major radius Rx and minor radius Ry) with an angle of α (or α = rotation). Rectangle cordinates are (x1,y1), (x2,y2), (x3,y3) and (x4,y4). The Ellipse can be ...
0
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1answer
33 views

Calculate rectangle inside ring parameters

Imagine we have a rectangle (with sides A, B) that fits into the ring (r1, R2). If r1, A and B are known, what is the equation for R2? (that is in my particular case) What are the interrelations ...
1
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1answer
79 views

Find the angle BEC in this quadrilateral - where have I gone wrong?

Question : I have received this question as a challenge from my teacher in Year 8 and I seem to make no progress. All I know is that $DC$ is parallel to $AB$, and that $DA$ is parallel to $AB$ ...
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0answers
45 views

Unit Outward Normal Vector of a rectangle element

I know if we have a triangle with $P_1=(x_1,y_1)$, $P_2=(x_2,y_2)$ and $P_3=(x_3,y_3)$ as its vertices and edge $e_i$ goes from vertex $P_j$ to $P_k$ and $k$ stays on the left when one travels from $...
1
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1answer
29 views

Sequence of continuous functions that convergent to the indicator function pointwisely.

Let $L=[a_1, b_1]\times \cdots \times [a_n,b_n]$ be a closed rectangle in $\mathbb{R^n}$. Prove that there exists a sequence of continuous functions $\{ f_n \}_{n=1}^{\infty}$ s.t. each $f_n$ is ...
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2answers
68 views

Why the Lebesgue outer measure of the boundary of rectangle in $\mathbb{R^n}$ is zero?

Let $A$ be a closed rectangle in $\mathbb{R^n}$ and let $m^*$ be Lebesgue outer measure. And let $\partial A$ be the boundary of $A$. Then, prove that $m^* (\partial A)=0.$ Since $A$ is a closed ...
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1answer
150 views

How to rotate a rectangle inside a rectangle with different scales

I have the following information: A computer-generated Rectangle 1 with width=530 and height=686 and an upper-left-hand origin and positive values going right and down. A computer-generated ...
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0answers
32 views

Finding the position percentage of the object in the a similar sized small rectangle

I am trying to find the position percentage of the object in the lower smaller square. So the use case is, in the first square(big square) there is an object positioned at 69.335% from the leftmost ...
4
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0answers
95 views

Square and two types of rectangles [duplicate]

A $60\times 60$ square $S$ is divided into $2\times 5$ rectangles. Prove that no matter how this is done there is a way to divide $S$ into $1\times 3$ rectangles so that each of the above $2\times 5$ ...
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0answers
30 views

Recover corner coordinates of a rectangle from normalised coordinates of the corners

Given a rectangle with unknown corners $\vec{t}, \vec{u}, \vec{v}$ and $\vec{w}$, where $\vec{t}, \vec{u}, \vec{v}, \vec{w} \in \mathbb{R}^{2}$, and $\vec{t} + \vec{u} + \vec{v} + \vec{w} \neq \mathbb{...
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0answers
43 views

Is there a simple way to know how many rectangles in some shaped grid there are if one knows the number of their corner points?

Is there a simple way to know how many rectangles in some shaped grid there are if one knows the number of their corner points? I.e. if I have some grid (possibly non-equilateral, other than ...
3
votes
1answer
163 views

Most efficient way to pack circles with different radii in a rectangle of given size

Given a rectangle of size $x$, $y$, I would like to fit the maximum circles in it. The second rule is that my circles come in 3 different radii $r_1$, $r_2$, $r_3$, and I need the maximum number of ...
0
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1answer
42 views

Calculate remaining two corners of rectangle given two points and angle

I have a rectangle given two corners at opposite ends that we'll call A and B. I need to be able to figure out the remaining corners given these two points and the angle by which the rectangle is ...
1
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1answer
57 views

Prove that a list of smaller rectangles form a cover of a rectangle as long as they satisfy two simple conditions

From the coding question Perfect Rectangles on leetcode. Given an array $\text{rectangles}$ where $\text{rectangles}[i] = [x_i, y_i, a_i, b_i]$ represents an axis-aligned rectangle. The bottom-left ...
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0answers
25 views

Area moments of parts of a rectangle divided by a line

I want to calculate the areas (and possibly their first and second moments) of a rectangle split into two parts by a line. It would be very helpful for me if there're closed form expressions for this ...
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0answers
67 views

Two dissection problems for rectangles

Let us consider two integer rectangles (that is, with sides of integer length) $S$ and $T$ of the same area. Then, obviously, $S$ can be dissected into several integer rectangles $A_1$, ..., $A_n$ (we ...
0
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5answers
130 views

Geometry : Ratio of area of a triangle to the rectangle containing it

$ABCD$ is a rectangle. $P,Q$ and $R$ are the midpoint of $BC$,$CD$ and $DA$. The point $S$ lies on the line $QR$ such that $SR:QS = 1:3$. The ratio of the triangle $APS$ and rectangle $ABCD$ is .... ? ...
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2answers
81 views

A rectangle P is divided into smaller rectangles by segments parallel to its sides. We call a point a t-point if its a vertex of two small rectangles. [closed]

A rectangle P is divided by segments parallel to its sides into smaller rectangles. We call a point a t-point if it is a vertex of exactly two such small rectangles. Prove that the number of t-points ...
1
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1answer
42 views

(Synthetic-)Geometrical theorems on the quadrature of a rectangle

I've been trying to find ways to prove the circle inversion theorem without the use of algebra, and the last part requires the equality between a square and a rectangle. I've managed to find two ...
0
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1answer
60 views

Numerically compute intersection of infinite line and rectangle

I'm trying to numerically compute where an infinite line defined by two points intersects a (finite) rectangle also defined by two points. Here's a illustration of the various ways that the line can ...
1
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1answer
69 views

Is there a specific name for parallel line segments that are the same length and aligned?

I'm trying to name an algorithm that identifies line segments with the following properties. They are parallel. They have the same length. Their endpoints are aligned along the perpendicular axis. ...
0
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1answer
30 views

Pool board question about trajectories of balls!

In this problem we are dealing with rectangular pool boards. Our boards have pointwise holes at the corners and nowhere else. A pointwise pool ball is running on the board and it never stops but falls ...
2
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0answers
104 views

Rotate and fit an rectangle into another rectangle.

I have the task of fitting a rotated rectangle into another rectangle. Inner rectangle shall touch outer rectangle on each side with one edge of inner rectangle. Rectangle in rectangle Given values $a,...
1
vote
1answer
47 views

how big can be a rectangle inscribed into a square if...

Please forgive my English. In a square with side AB, there is inscribed a rectangle, whose area is $\frac{3}{8}$ the square area, if the measure of AB is 28, how long can be $AP$, where $P$ is the ...
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0answers
21 views

How can I calculate trigonometry based on cartesian coordinates

I would like to draw a rectangle based on a center point lat and lon assuming a given length and width, let's say 4.5m and 1.5m, respectively. I guess, we need the bearing too. I've made a simulation ...
1
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1answer
124 views

Optimization : Solve $4$ unknowns using $4$ equations

Suppose we have 4 points say A($x_1,y_1,z_1$), B($x_2,y_2,z_2$),C($x_3,y_3,z_3$), D($x_4,y_4,z_4$). Where $x_1,x_2,x_3,x_4,y_1,y_2,y_3,y_4$ are known points and rest $z_1,z_2,z_3,z_4$ are unknown ...
2
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2answers
102 views

There is a rectangle in 3-dimensional space. If I am only given the $x$ and $y$ coordinates, how do I find the $z$ coordinates? [closed]

We are given the $x$ and $y$ coordinates of the four vertices of a rectangle. How do I find the $z$-coordinates? I know that this 3 dimensional rectangle must obey all the usual conditions of ...
0
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0answers
31 views

Isometric Polygons - Rectangle and a Rhombus

I need to cut a rectangle into 4 and make an isometric rhombus, I managed to do it if I cut the rectangle into 3, but not 4. as you can see ABCD is a rectangle, E is the middle point of AD, by doing ...
4
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0answers
98 views

How many points are needed to place in a $2 \times 5$ rectangle to make sure there are $2$ points with distance less (not equal) than $\sqrt2$?

At least how many points are needed to place in a $2 \times 5$ rectangle to make sure there are $2$ points with distance less (not equal) than $\sqrt{2}$? I guess the answer is $10$, but I don't have ...
0
votes
1answer
145 views

How should I find the four vertices of a rectangle if I have its center of gravity and it length and width?

basically all I want to know is in the question. I know that in a square if I have the length of it and its center of gravity I can find the vertices by this formula: If the coordinates of the center ...
2
votes
1answer
72 views

Find the height of the following rectangle

We have a rectangle ABCD, and a point P on the diagonal AC. From P we see BC at an angle $\alpha$. Knowing $\alpha$, AP and AB, find BC. Here's a probably unnecessary illustration of the problem, with ...
24
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0answers
354 views

How many "prime" rectangle tilings are there?

Given two tilings of a rectangle by other rectangles, say that they are equivalent if there is a bijection from the edges, vertices, and faces of the tilings which preserves inclusion. For instance, ...
1
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0answers
58 views

Filling Gaps with Rectangles & Triangles

I'm quite new to Stack Exchange, and I also wasn't too sure where I should post this. This came up for me when I was doing some programming for a small game-project, and the task I found myself ...
0
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1answer
69 views

Area Between Four Rectangles and a Semi Circle.

Given a halved circle with radius $R$ and four rectangles inside it such that one of the side touches the middle line of the circle. If the area of the four rectangles are maximum, what is the area ...

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