# Questions tagged [geometry]

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.

31,139 questions
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### Can’t we use ‘vector product’ to find the angle between two vectors?

There are two vectors : $A = (\hat i + j + k)$ and $B = (\hat i - \hat j - \hat j)$, where $\hat i$, $\hat j$, and $\hat k$ are unit vectors along $x$, $y$, and $z$ axis respectively. We have to find ...
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### Prove than cube has a bigger volume than cuboid with the same sum of edge lengths

How to prove that a cube has a bigger volume than a cuboid with the same sum of edge lengths? Example: Cube has an edge length of 5 cm. $\ V =5 \times 5 \times 5 = 125 cm^2$ Cuboid has an edge ...
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### Characterizing points by their distance to the unit ball

Let $x,y\in\mathbb{R}^n$. Assume that, for all $z$ in the unit ball, $|x-z|=|y-z|=d_z$. From this we can deduce that $|x| = |y|$ since $0$ is in the unit ball. How can we show that $x=y$? I think it ...
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### What curve is described by $s = \langle 2t,9\sin t,9\cos t\rangle$?

What type of curve is described by the following? $$s = \langle 2t,9\sin(t),9\cos(t)\rangle$$ Attempt The $j$ and $k$ components of the curve describe a circle of radius $3$ in the $j-k$ plane and ...
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### What is the angle between two intersecting tangents to a circle?

A circle of radius $r$ with centre $C$ is located at distance $d$ from a point $P$. There are two tangents to the circle which pass through point $P$ - one on each side. They intersect the circle at ...
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### Proving two lines are parallel with intersections and midpoints

To prove : Fix points $A,C$ and set point $B$ to be the midpoint of segment $AC$. Fix point $Y$ (anywhere) and consider an arbitrary point $X$ on line $YB$. If $P$ and $Q$ are the intersection ...
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### If AH and BG are angle bisectors, how would I find IJ?

Diagram I've tried finding it, but it just doesn't seem to come out. I found $$GC=\dfrac{4}{3}$$ $$AG=\dfrac{5}{3}$$ and $$GB=\dfrac{4\sqrt{10}}{3}$$ I really don't know what to do from here, could ...
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### if triangle ABC has incenter I how is it possible to show the circumcenter of triangle BIC lies on the circumcircle of triangle ABC?

if triangle ABC has incenter I how is it possible to show the circumcenter of triangle BIC lies on the circumcircle of triangle ABC? D is the circumcenter of BIC
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### Sampling from surfaces of a 3D cube

I have a task to sample a fixed number of points from a 3D cube, so that these points can be a point cloud. But I do not know 1) how to describe the surfaces of an arbitrary 3D cubes and 2) how to ...
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### Formula to calculate change in distance to destination or origin of a straight-line path of travel

I am writing an application that consumes GPS data - and I am trying to calculate direction traveled based on a change in distance to the destination and origin. Assume that I have a straight path of ...
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### How is the similarity of two shapes formally defined?

Suppose we have an open shape $S$ of a n dimensional euclidean space with the usual topology, and another one $S'$ which is just a translated, rotated or scaled version of $S$. Clearly these two ...
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### Draw a multipolygon

I need to build a shutter like this: What is the formulas to draw each vertex? Suppose I have num which is the number of triangles (in this case ...
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### How to calculate angle from 2D projection

I have picture of interior wall. I know that angles A and B are 90deg in reality and I need to calculate angle C. A in picture is 95 deg B 123 deg C 142 deg
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### how to find circle circumference point from a point inside the circle

given the image bellow how can i find the points of a circles circumference from a point inside the circle with given X and Y ? also can how to calculate it from a point outside the cirlce ? https://...
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### why area of triangle changes when measured as components of triangles? [closed]

If we measure an area of triangle directly using a formula I got 90 square unit. But if we measure by components like 2 triangles and one rectangle and take some it counts 90.5 Why 0.5 square unit ...
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### What is the least eccentricity of an ellipse that can rest on a plane inclined at an angle $\alpha$ with the horizontal? [closed]

A perfectly rough plane is inclined at an angle $\alpha$ to the horizontal. What is the least eccentricity of an elliptic cylinder that resists rolling down the plane?
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### A collection of lines drawn between points in a regular 13-gon - how to determine where the points sit relative to each other?

So I have 4 collections of lines drawn between points each making a path. The angles are measured. The problem I am attempting to solve is to determine whether or not each of the collections of points ...
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### Parametrization for the figure '8' curve?

Is there a parametrization for the figure '8' curve, which is self-intersected?
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### How can a torus be turned to a cylinder if the circumference of the outer ring is larger?

I’m not a math professional by any means, I’m just interested in math and this topic has been on my mind for a while, and I just couldn’t find an answer. Also, on the same vein, how can you make a ...
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### Geometry proof involving triangle

Let $ABC$ be an acute angle triangle with $\angle B>\angle C$. Let $M$ be mid point of $BC$. Points $E$,$F$ are feet of altitudes from $B$ and $C$. Points $K$,$L$ are mid points of segments $ME$ ...
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### Optimal set of rectangle sizes to pack arbitrary rectangle?

I'm looking to build a set of wooden storage boxes of various standard sizes for storing small objects. I would like to choose a set of "optimal" box sizes (outside dimensions) for filling arbitrary ...
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### Using atan2 in order to rotate a polygon. [closed]

I am trying to write a function in python which takes in a polygon with Cartesian coordinates, converts them to polar ones, adds alpha then changes them back to ...
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### Generalized stereographic projection

Let $(M^n,g)$ be a closed (compact, without boundary) Riemannian manifold and let $p\in M$. Let $$\square: =c\Delta+S$$ be the conformal Laplacian of $(M,g)$. Here $c=4\frac{n-1}{n-2}$ is a ...
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### Image Analysis using cross ratios

I'm stuck trying to solve an exercise regarding an image analysis. Consider a book that measures 16 cm $\times$ 24 cm lying on a table. Let the vertices of the book be denoted by A,B,C,D and the ...
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### Ratio of Volume of sphere to Volume of cube

I was told in my class that the ratio of the area of a circle to area of a square should be greater than the ratio of the volume of a sphere to volume of a cube. But, I am not able to show this. For ...
### Generating, or counting the sides of, “square-like” polygons (with all congruent sides, and all angles either $90^\circ$ or $270^\circ$)
What are some of the polygons that have all congruent sides and all angles $90^\circ$ or $270^\circ$? Is there a pattern for generating these, or a formula for the number of sides? These don't have to ...