Questions about rectangles and its properties.

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1answer
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Determine the values of a1 and a2. Find the recurrence relation for an in terms an-1 and an-2

We want to tile a 2xn rectangular board with a 2x1 rectangular dominoes. Let an be the number of such tilings of a 2xn board. Hi everyone, I'm having trouble answering this question and not sure how ...
2
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2answers
54 views

Finding the length of the side of the equilateral triangle

Here, ABCD is a rectangle, and BC = 3 cm. An Equilateral triangle XYZ is inscribed inside the rectangle as shown in the figure where YE = 2 cm. YE is perpendicular to DC. Calculate the length of the ...
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1answer
24 views

Deskew a rectangle

I'm having a "trigonometric" issue. I have as input an image that contains a skewed rectangle. The image is like a bounding box of the rectangle. like this: ...
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1answer
22 views

Geometry - Cyclic Quadrilaterals

Three points A,B,C lie on the circumference of the circle, with center as O. If angle(ACB) = 115 deg. Need to find angle (BOC)? Please post your approach?
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1answer
25 views

Collision Detection in Finite but Limitless Space

Doing collision detection on two arbitrary rectangles is easy, given their coordinates and dimensions. In regular 2d-space, that is. But what about "finite but limitless" space, say a screen area ...
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2answers
82 views

What is the correct definition of Area?

How is the area of a rectangle: length $\times$ breadth? We know that other areas can be derived from it. Also, the area under curves uses the area of rectangles as a basis.
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0answers
17 views

Two questions about triangle that blocked at rectangle…

The area of the triangle is equal to the half area of the rectangle? The center point of the triangle is same as the center point of the rectangle? About 2 - if not, how do I calculate the center? ...
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2answers
44 views

How would I calculate the area of a rectangle on a sphere using vertical and horizontal angles?

Imagine a sphere being one's eyeball and the rectangular area being the picture of one's view. Like putting a name tag sticker on a balloon. How can I find the area of the rectangle on the sphere?
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1answer
6 views

Determining the distance across a rectangle for an arbitrary angle

I'm trying to determine the 'diameter' or distance across a given rectangle for a given angle. Ideally there should be a function f(theta) that takes a polar angle and determines the distance across ...
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1answer
18 views

How to find height, width, length of rectangular prism given SA and longest diagonal?

I've started seeing this type of question an awful lot. I made two equations (w is width, l is length and h is height) √w^2+l^2 + h^2= 64 2wl + 2lh + 2wh = 14 However, I'm not sure where to go from ...
0
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1answer
15 views

Rectangle division into shapes and connecting adjacent shapes with non-intersecting lines

Rectangle is divided into several non-convex shapes. Adjacent shape's centroids are connected with straight lines. For example (here centroids are approximate): Could it be that some of those line ...
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1answer
24 views

How can I do complex table size calculations?

For instance, I want to know: What is the most efficient way to present 256 cells in a 16:9 table, giving each cell maximum readability? In the above scenario, each cell must be sized ...
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2answers
57 views

Area of one of four regions within a rectangle

There is a figure below (a rectangle). You can see different colors depicting different regions of the figure. The labels on the top of a region defines the area of that region. Can you find the ...
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1answer
13 views

Want to make a rotating background, find the minimum size in relation to the screen.

I am making a game, and want to make a rotating background. I want to find the minimum size the background needs to be in order to not get cut off in the middle of the rotation, so I went for a 45deg ...
0
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1answer
21 views

Find the size of squares cut from a box.?

This has been taking me days to do and I really want to do it for test practice. I actually have absolutely no idea how to even start this, so if I can get a hint, advice, or something to start me ...
0
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1answer
59 views

Disprove the possibility of such a triangle.

The image is not that good, but, consider the following figure to be true without actually constructing it,how can one person find a $fault$ in it. The blue colour represents perpendicular, The ...
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0answers
40 views

Compressing an image by merging pixels [duplicate]

Let's say you have an image with dimensions (height, width) $h,w$ pixels. It is stored in a table $T[y][x]$ Unfortunately, the software you are using to generate this image can only use rectangles. ...
2
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1answer
38 views

Area of rectangle from area of square?

The definition of area usually include the area of a rectangle definition. Can one replace it with "the area of a square of side $a$ is $a^2$"? That is can one find the area of a rectangle in this ...
2
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1answer
44 views

Is there an equation to find the angle of the diagonal in a rectangle?

If we have a rectangle of length 5 and height 5 the angle of the diagonal would be 45°. We know this is true but how can we arrive at this conclusion mathematically?
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0answers
20 views

Find if the given size of the rectangle fits on the rectangle

Given a rectangle of size row = 3 and col = 2 which are occupied by other rectangles as in figure. The shaded region in green are occupied. Now what I want to find is, if a rectangle of size (p = 2 ...
0
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1answer
29 views

Calculate the width and height of a rectangle, given its diagonal and area

Here's my problem: "In a rectangle, the diagonal is 6 and area 14. The perimeter is: a) 10 b) 14 c) 16 d) 18 e) 20. So I know that $x^2 + y^2 = 36$, and that $xy = 14$, but I'm having problems ...
1
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1answer
25 views

Size of minimal covering, overlapping and disjoint

There are two ways to cover a geometric shape with primitive units: you can allow the units to overlap, or require that they be disjoint. Of course the number of units in the case of disjoint covering ...
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0answers
36 views

Find bounding box dimensions around rotated object

Consider the following rectangle with dimensions 320 by 130. After rotating the rectangle 10 degrees clockwise from the center (x: 160, y: 65), it looks like this. My question is: How do ...
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3answers
55 views

Inscribe a rectangle inside an ellipse

A rectangle is to be inscribed inside a horizontal ellipse (whose major or minor axis is parallel to x axis). Is the horizontal orientation of the rectangle (two sides parallel to x axis) the only ...
2
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2answers
72 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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2answers
55 views

internal rectangle area intersected by a circle

I need to compute the internal rectangle area intersected by a circle like (the blue area) on these 3 examples: I know every vertex (x,y) coordinate and then their distance from circle center but ...
0
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1answer
30 views

Divide-and-conquer on a rectilinear polygon

A rectilinear polygon can be characterized by its cover number - the smallest number $k$ such that the polygon can be covered by $k$ possibly overlapping squares. For example: For a square, $k=1$. ...
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3answers
47 views

Volume of a rectangular prism's walls

Sorry if this is an obvious question... I have been trying to figure this out for a little while and come up with nothing... If I have a rectangular prism, say $5\times10\times12$ meters, it has a ...
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10answers
5k views

Why is a rectangle a parallelogram, but a parallelogram is not a rectangle?

It confused me that a parallelogram is never considered a rectangle, yet a rectangle is considered a special case of a parallelogram. How is this possible?
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2answers
45 views

Percentage size of the rectangle over the inner rectangle

I need to know how much I need to zoom (in percent) the inner box to rotate the outer rectangle 12 degrees and he touched the inner rectangle with four sides on the perimeter. For example, I have ...
0
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2answers
115 views

Can a polygon have four 90 degree corners and still not be a rectangle?

On another woodworking forum, someone said that after building a case, you should measure the diagonals to ensure the case is square and that just checking if all the corners are 90 degrees won't ...
0
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2answers
45 views

Find the dimensions of the rectangle having the largest area

A rectangle is bounded by the positive $x$-axis, positive $y$-axis and the line with equation $3y= 16-2x$. Find the dimensions of the rectangle having the largest area. \begin{align} & y= ...
4
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3answers
211 views

Smallest square containing a given triangle

Given a triangle $T$, how can I calculate the smallest square that contains $T$? Using GeoGebra, I implemented a heuristic that seems to work well in practice. The problem is, I have no proof that it ...
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0answers
51 views

Simple notation questions(2) and unit tangent vector question(1)

I have a vector field $F$, and a rectangle $C$ and some $T$ as a unit tangent vector to $C$ directed anticlockwise around $C$. How is $T$ calculated? Wouldn't it just be a straight line facing ...
0
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1answer
38 views

Finding the side lengths of a rectangle given a circle passing through one of its vertices and touching two of its sides

A circle touches a rectangle $ABCD$ of side lengths $2a$ and $2b$ at $M$ and $N$ on sides $AB$ and $AD$ respectively. It also passes through the point $C$. If the perpendicular distance of the line ...
0
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1answer
33 views

Find f with A plane curve whose equation is $y - f (x) = 0$ passes through the origin.

A plane curve whose equation is $y - f (x) = 0$ passes through the origin.Consider the rectangle $R_x$ formed by the coordinate axes and lines parallel to the axis passing through the point $(x, f ...
1
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1answer
57 views

Crazy rectangles, semi-circles, and circles!

Problem is to find the ratio of the area of the circle to that of the semi-circle. Note that points $F$ and $E$ weren't given in the original diagram, and that the circle at the top-right ...
2
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1answer
41 views

What is the greek symbol that represents the ratio of the length and with in a rectangle.

I understand that there is pi, but I was provoked by a question that asked this, "I have a rectangle and if I cut a square off of it it produces the same type of rectangle. I know that the width is 1 ...
0
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1answer
18 views

Proving that a relation is acyclic

Let $S$ be the set of triples of positive numbers $(x,y,s)$. Let $R$ be a directed relation defined between triples, such that $R(b,a)$ if at least one of the following four conditions hold: ...
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2answers
548 views

Optimization of the surface area of a open rectangular box to find the cost of materials

A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of the box is twice its width. Material for the base costs ten dollars per square meter and for the ...
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2answers
124 views

Geometry Right triangles in a rectangle, find the area.

Please help, I've been struggling to figure out this problem for too long... Given the area of rectangle $ABCD = 1200 \text{ unit}^2$, find the area of right triangle $ABE$
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1answer
76 views

Points $S$ and $T$ are on side $\overline{CD}$ of rectangle $ABCD$ such $ \overline{AS}$ and $\overline{AT}$

Points $S$ and $T$ are on side $\overline{CD}$ of rectangle $ABCD$ such $\overline{AS}$ and $\overline{AT}$ trisects $\angle DAB$. If $CT = 3$ and $DS = 6$, then what is the area of $ABCD$? I have ...
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2answers
1k views

Find the area of shaded triangle inside of a rectangle.

In rectangle $ABCD$, $ P$ is the mid point of $AB$. $S$ and $T$ are the points of trisection of $DC$. If area of the rectangle is $70$ square units, with reference to the figure find area of shaded ...
0
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1answer
332 views

Working algorithm for testing two rectangles for overlapping in Earth GPS coordinates plain

Here is a seemingly simple, but actually quite tricky problem: I am trying to figure out the correct algorithm to test intersection/overlapping of two rectangles, which are plotted on the Earth's ...
0
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1answer
24 views

Filling the Unit Disk With Non-overlapping Rectangles

It intuitively seems to be true that no finite set of non-overlapping rectangles can fill the unit disk. Is this proposition really true? If so, how can one prove it?
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1answer
30 views

How to determine coordinates on two different size rectangles

Hello community I hope all is well. I was wondering if someone could shine some light on the following problem. Let's say we have 2 rectangles (A and B) which are different in size. Let's say I have ...
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0answers
18 views

Making a Circle of Rotated Rectangles

By default, the system I'm using bases rectangle position by their center. If I copy a rectangle and rotate it, the result will look like this: Because I am trying to make a circle out of these ...
2
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1answer
93 views

How do I calculate the angle to place rectangles side by side around a circumference?

I have a circle with radius $r$ and several rectangular objects. All rectangles have the same sides $a$ and $b$ (although the side $a$ may be different from side $b$). I would like to place the ...
2
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1answer
38 views

Two-color square arrangement

There are $n$ green axis-parallel squares on the plane. You may scale and translate each square arbitrarily, as long as no two of them intersect. Now you have to put paiwise-disjoint red squares on ...
3
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1answer
63 views

Colorful squares arrangement

Can you arrange a finite number of green and red squares on the plane, sides parallel to the axes, such that: Every red square intersects $M$ green squares and no red square; Every green square ...