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Questions tagged [rectangles]

Questions about rectangles and their properties.

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1answer
28 views

Is packing rectangles exactly into a larger rectangle NP-complete?

I want to pack a number of rectangles into a larger rectangle, however, unlike other questions that I could find, I would like to do so exactly, without allowing any wastage. I do not really care ...
2
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3answers
66 views

If a rectangle can be split into n and into n+14 squares, then n=18. What is the meaning of this

This problem seems to be a geometrical one, but actually it is an algebraic one. If you split the rectangle into n squares and into n+k squares, then what does that means? What is this supposed to ...
6
votes
1answer
77 views

Shortest distance between two rectangles in 2D

Given the center points and dimensions of two rectangles and the angles $\theta_1$ and $\theta_2$, how to calculate the shortest distance between two rectangles ($d$)? $\theta$ is the angle that the ...
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0answers
8 views

Collision resolution of rotated rectangles

Imagine two rotated rectangles that overlap/intersect in R². How far in each axis would rectangle A (in red) have to be translated to no longer intersect rectangle B (in blue) given the center of ...
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1answer
31 views

Maximizing the size of n similar equilateral triangles from a rectangle

I have 3 rectangles of greenhouse sheeting material. They are each 12 feet long and 4 feet high. I want to use this material to clad a 3/4 icosahedron dome structure. What that means is that I will ...
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0answers
21 views

Find a point on a circle which contains a rectangle using another point, the angle between the two and the rectangle's dimensions

I'm trying to construct a mathematical formula that will calculate a point (x,y) on a circle which contains a rectangle with a width ...
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0answers
27 views

How to fill a rectangle with smaller specific rectangles that have cardinal information about their adjacent neighbours

Lets say its 6x6 grid that is represented by top left(0,0) and bottom right(1,1) in coordinate system. Next, I have set of objects with their cardinal directional information about each of their ...
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1answer
50 views

How to find sides of rectangle that is inscribed in other rectangle?

We have smaller rectangle inscribed in the bigger rectangle as shown on the picture. The bigger outer rectangle is inclined for a certain angle. We know height and width of the bigger rectangle and ...
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0answers
19 views

Scaling rectangle and keeping ratio when height and/or width exceed container

I have a 2D box with a Height of 206 and a Width of 202. Inside of this box is a Rectangle. ...
0
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1answer
23 views

Calculate resizing factor for N small rectangles inside a large rectangle to cover maximum area

I have a variable number of small rectangles which are natively 39 x 83 (width by length). I will also have an arbitrary sized, container rectangle that I need to fit all of the smaller rectangles ...
1
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1answer
34 views

Ratio between the areas of two rectangles inscribed in a triangle and the area of the triangle

Let's denote $A(X)$ the area of the polygon $X$. Let $S$,$R$ be rectangles inside a triangle $T$. Find the maximum value of: $$\frac{A(R)+A(S)}{A(T)}$$ My try The only property i know (from a ...
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1answer
41 views

Edges of rectangle mapped to a new plane

If a rectangular plane lies in quadrant I and is transformed by a polynomial function, will the edges of the rectangle always map to the edges of the transformed plane? Will all points along the ...
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0answers
29 views

Rectangle function and integration

There are given: $$\mbox{rect}(f/2a)=\left\{\begin{matrix} 1, & -a<f<a\\ 0,5 &\begin{vmatrix} f \end{vmatrix}=a \\ 0& \begin{vmatrix} f \end{vmatrix}>a \end{matrix}\right.$$ $...
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2answers
47 views

How to solve an equation with truncated unknowns?

In order to provide some context, here's the problem that took me to the question: I'm attempting to fill a rectangle of known dimensions (w: width, h: height) with squares whose side is s. I also ...
6
votes
1answer
94 views

Is there a simple perfect squaring of a 1366 by 768 rectangle?

So, a simple perfect squaring of a rectangle is a tiling of that rectangle by squares whose side lengths are all distinct integers. Additionally, not subset of the squares must form a smaller ...
1
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1answer
51 views

Error in 6th Grade Curriculum Book

This problem appeared in a 6th grade math book for the purpose of finding area, since the two sides are 25cm it is known that the opposite angles are congruent, so they must meet over the midpoint of ...
3
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1answer
63 views

Rectangles in Hyperbolic geometry

This says rectangles don't exist in hyperbolic geometry. But according to this you can model the euclidean plane in Hyperbolic geometry. Wondering why you can't model the rectangle, I thought if you ...
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0answers
59 views

Max width of rectangle inside another rectangle in diagonal

Given the hatch sizes (length $a$ and width $b$ of the external rectangle) and the length of the material (internal rectangle, $d$), what is the max width $c$ of the material that can pass from the ...
2
votes
3answers
47 views

What is the area of $PXQY$ in the rectangle $ABCD$ in the following diagram?

In $ABCD$ rectangle $AB=6$, $AD=8$, $AE=ED$, $BF=FC$, $EP=PQ=QF$. Find the area of $PXQY$. Source: Bangladesh Math Olympiad 2014 Junior Category I cant prove that which type of quadrilateral it is....
2
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4answers
97 views

What is the value of $x$ in $ABCD$ rectangle where $AE = 4, BE = 6, CE=5$ and $DE = x$?

In the diagram of rectangular $ABCD$, $AE=4, BE= 6, CE = 5$ and $DE=x$, find the value of $x$ Source: Bangladesh Math Olympiad 2015 Junior Catagory I can not relate these information with $DE$.
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1answer
60 views

Find the Area of Rectangle that has Two similar triangle

A rectangle DEBC has triangle ABC.AB and AC intersect side DE at points F and G respectively. FG = 4, The perimeter of triangle ABC is double of the perimeter of Triangle AFG. The area of Triangle ABC ...
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1answer
177 views

Find the bottom right coordinate of rectangle?

Given a rectangle with X, Y (Integers) as the top left vertex. Assuming that the rectangle is axis parallel and height and width cannot be negative what can be said about the bottom right vertex of ...
6
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1answer
45 views

Minimum number of rectangles to cover diagonal-free grid

I'm trying to figure out the minimum number of rectangles required to cover an $n \times n$ grid, minus the diagonal. What this is means is the following: Suppose we have an $n \times n$ grid, with ...
1
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1answer
75 views

Determine if a Rectangle is Inside, Overlaps, Doesn't Overlaps Another Rectangle

Using the center's x- and y-coordinates, width and length of each rectangle, determine if the second rectangle is inside, overlaps or doesn't overlap the first rectangle. I know that if I divide the ...
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1answer
24 views

Why the arccos of adjacent leg is not equal to arcsin to the oposit leg for the right triangle

Silly question. I have a right triangle with adjacent leg $A = 81.67$ and an opposite leg $B = -1225.53$. So hypotenuse $C$ will be $\sqrt{(A^2 + B^2)} = 1228.25$. $\arccos(A / C) = 1.50$ and $\...
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1answer
39 views

What is the area of the rectangle?

The diagram shows a rectangle and a line X parallel to its base. Two points A and B lie on X (A is outside and B is inside the rectangle). The sum of the areas of the two shaded triangles is 10cm. ...
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1answer
31 views

How to re-scale a rectangle to a smaller area?

I have a rectangle of X by Y, with an area Z. I need to re-scale the rectangle so that it's area is no larger than the pre-defined AREA_MAX, preserving the original aspect ratio. How would I go about ...
0
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1answer
47 views

What is the value of $a+2b$ if $\frac{OP}{EF}=\frac{a}{}b$ in $ABCD$ rectangle?

BD is diagonal in ABCD rectangle and E, F is the mid point of BC, CD respectively. Line BD intersects AE, AF at O, P respectively. If $\dfrac{OP}{EF} = \dfrac{a}b$, then a+2b=?
5
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1answer
99 views

Tiling a 7x9 rectangle with 2x2 squares and L-shaped trominos

It's possible to cover a 7x9 rectangle using 0 2x2 squares and 21 L-shaped trominos, for example: ...
3
votes
1answer
102 views

Arrange $n$ tiles in a rectangle pattern

Is there a way to find how to arrange $n$ tiles in order to form a rectangle that is closest to a square? As I result I am looking for the dimension of that rectangle if it exists. For example, here ...
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1answer
43 views

Maximized dimensions of bounding box around rotated rectangle [closed]

Given an orthogonal rectangle with sides a and b, what rotations $\theta$ result in a bounding box with maximum height c.q. ...
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0answers
18 views

Matching widths of two different functions

Say I have a rectangular function as follows $$f(x) = \begin{cases} 1 & \text{$|x|$$\leq$$x_0$} \\[2ex] 0 & \text{otherwise} \end{cases}$$ I want to match its width (which in this case is $...
3
votes
1answer
69 views

Covering a circle with rectangular labels

I've got an applied math problem. Suppose that you have a circle of diameter $1$ (we can scale units so that this is the case) and labels of width $d_1, d_2, ..., d_n$ (the labels can be as long as ...
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1answer
87 views

Coordinates of the centroid in a 3D rectangle

I have a 3D rectangle and I have to find the 3D coordinates of its centroid. I tried to take 4 vertices, one let's say the origin $o$ and the three adjacent vertices $a, b, c$. I computed the ...
2
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1answer
60 views

Four squares, all of different areas, are cut from a rectangle, leaving a smaller rectangle…

Four squares, all of different areas, are cut from a rectangle, leaving a smaller rectangle of dimensions $1\times2$. If the largest square has area 64, and the other three squares have side lengths ...
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1answer
40 views

Calculate side lenght of triangle from two rectangle on top of each other

I want to calculate the side lenght of $b$. I have two rectangles with one at 0° (screen) and I have one rectangle at 20° (turned image). With respect to the middle point. Both rectangles have a ...
1
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1answer
210 views

How many components are required for partitioning a square between two colors?

Suppose $n$ disjoint points, some red and some blue, are organized on a line. We want to partition the line to two subsets, one containing all the red points and one containing all the blue points. ...
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2answers
89 views

How to develop a method to know if my box can pass around a corner?

[EDIT2] Following the help I got in the comments + answers I found $$\begin{align} a &\leq \sqrt{H^2-b^2} \\[4pt] a &\leq \sqrt{h^2-b^2} \end{align}$$ as the answer with this process https:...
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1answer
29 views
2
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0answers
47 views

how to calculate the amount rectangles can you get out of a bigger rectangle

I am looking to make a program to calculate how many rectangles you can get out of a bigger rectangle. I want both the size of the big rectangle and the smaller ones to be adjustable. But while ...
17
votes
5answers
3k views

Radius of a circle touching a rectangle both of which are inside a square

Given this configuration : We're given that the rectangle is of the dimensions 20 cm by 10 cm, and we have to find the radius of the circle. If we somehow know the distance between the circle and ...
7
votes
1answer
104 views

Is it possible to fill 1×1 rectangle with 1×½, ½×⅓, ⅓×¼,…, 1/n×1/(n+1) rectangles?

Is it possible to fill $1\times1$ rectangle with $1 \times \frac{1}{2}$, $\frac{1}{2} \times \frac{1}{3}$, $\frac{1}{3} \times \frac{1}{4}$.., $\frac{1}{n}\times\frac{1}{n+1}$... rectangles? This ...
1
vote
1answer
37 views

Maximum Angle of Rotation of without Clipping of Rectangle

Given a rectangle $A$ of width $a_x$ and height $a_y$ and a rectangle $B$ of width $b_x$ and height $b_y$ with the same center as $A$, with $b_x>a_x$ and $b_y>a_y$, calculate the maximum ...
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2answers
66 views

About the definition that a subset $A$ of $\mathbb{R}^n$ has measure zero in $\mathbb{R}^n$ in Munkres “Analysis on Manifolds”(p.91)

I am reading James R. Munkres "Analysis on Manifolds" now. Definition. Let $A$ be a subset of $\mathbb{R}^n$. We say $A$ has measure zero in $\mathbb{R}^n$ if for very $\epsilon > 0$, ...
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2answers
103 views

Generalization of the Riemann Sums

As a complement to this formula, I have been considering a formula for a generalized Riemann Sum. However, in this case there are multiple facets to consider. We can represent three of the Riemann ...
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1answer
234 views

Similarity between Trapezoidal Sum and Riemann Sums

Is it accurate to say that a Trapezoidal Riemann Sum includes one more term than the corresponding Left, Right, or Midpoint Riemann Sum? Using the following notation for the latter three: Riemann ...
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0answers
58 views

Why is $\operatorname{rect}(\frac{1}{2}-\sqrt{w}) = \operatorname{rect}(w-\frac{1}{2})$

I have to determine the first order probability density function for $w(t, \epsilon)$, with the hypothesis that I have two statistically independent functions $x(t, \epsilon)$ and $y(t, \epsilon)$ ...
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0answers
12 views

Adjust overlaying square (x, y) when parent square's anchor is changed.

I'm working on a project that involves drawing shapes on a grid using a WebGL rendering library. Currently, I have to draw a simple rectangle and then draw another rectangle on top of that rectangle, ...
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2answers
39 views

center of gravity given four weights [closed]

I have this problem. I have four points that corresponds to four vertices of rectangle. Every vertex has a load cell that return a weight. How can I calculate the center of gravity, in a range of 0-...
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2answers
208 views

Is it always possible to cut disjoint 0.359 of two rectangles?

There are two rectangles, red and blue. Is it always possible to cut two disjoint rectangles, one containing 0.359 the area of red and one containing 0.359 the area of blue? The following figure ...