Questions tagged [rectangles]
Questions about rectangles and their properties.
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How do you prove that a specific shape in a regular octagon is a rectangle?
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, ...
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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 ...
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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 ...
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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;
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
...
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$\int_Q c=c\cdot v(Q)=c\sum_R v(R)$. 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 $\...
- 1,138
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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, ...
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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 ...
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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{...
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