Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [geometry]

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

0
votes
3answers
12 views

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 ...
0
votes
1answer
33 views

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 ...
1
vote
1answer
32 views

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 ...
1
vote
1answer
37 views

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 ...
0
votes
2answers
32 views

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 ...
2
votes
0answers
29 views
+100

What is actually the geometry or analysis behind the fact that $Mob(\hat{\Bbb C})$ is simple?

Let, $Mob(\hat{\Bbb C})$ be the group of all Mobius transformations from the extended complex plane to itself i.e. from $\hat{\Bbb C} \to \hat{\Bbb C}$ . I have been able to prove that (i) $Mob(\hat{...
2
votes
2answers
52 views

Is there a right triangle with angles $A$, $B$, $C$ such that $A^2+B^2=C^2$?

A right angle triangle with vertices $A,B,C$ ($C$ is the right angle), and the sides opposite to the vertices are $a,b,c$, respectively. We know that this triangle (and any right angle triangle) has ...
5
votes
1answer
81 views

Find out a general expression for the coordinates of a point in a square based on certain distances and an angle

my problem appears to be a very simple one, but I just can't seem to figure it out, maybe I am just overlooking something… The problem is defined as the following (refer to the figure for better ...
0
votes
2answers
72 views

Determining the coefficients of $y = a x^2 + b x + c$ so that the graph contains three given points

Determine coefficients of the equation for a second order polynomial in the format: $y = a x^2 + b x + c$ Here are the $x$-$y$ coordinates of three points: $(0.8143,0.3500)$ $(0.2435,0.1966)$ $(0....
1
vote
2answers
34 views

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 ...
0
votes
4answers
36 views

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 ...
0
votes
2answers
47 views

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
1
vote
1answer
28 views

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 ...
0
votes
1answer
21 views

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 ...
1
vote
1answer
37 views

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 ...
1
vote
2answers
49 views

Intuition for orientation of tri-vectors in geometric algebra

I am learning geometric algebra from the MacDonald textbook and it states that the outer product is associative. Letting $\bf{u}$, $\bf{v}$, and $\bf{w}$ be vectors $$\bf{u} \wedge \bf{v} \wedge \bf{...
2
votes
1answer
41 views

Sums of unit vectors contained in a half-space

Consider $n$ unit vectors $\{v_1,...,v_n\}$ with $v_i\in \mathbb{R}^3$. Now define $\text{H}(w):=\{w'\in\mathbb{R}^3 \ | \ (w',w)>0\}, \ w\in\mathbb{R}^3$ (where $(\cdot,\cdot)$ is the standard ...
5
votes
0answers
100 views

Is this (1.11716..) a known/named constant?

While looking at the Wikipedia entry for the Supergolden ratio aka Narayana's cow constant (cf. https://en.wikipedia.org/wiki/Supergolden_ratio), I noticed the following construction involving that ...
2
votes
0answers
35 views

Ricci Tensor in an Einstein Manifold

I must prove that an hypersurface $M$ on $\mathbb{R}^{n+1}$ that is Einstein and compact can be only the $n-$dimensional sphere when $n>2$ The Einstein condition we permits to say that scalar ...
0
votes
1answer
22 views

Calculate center coordinates of circles surrounding a larger circle

I want to draw, say, 8 smaller circles that are adjacent to the big circle the edge of a big circle, similar to this picture. I know the center coordinates of the bigger circle $(A, B)$, its radius $(...
0
votes
1answer
31 views

Get direction vector of a line from a point and its rotation.

The title pretty much says what I need. Some details about my problem: I have a cylinder. I have a point outside this cylinder. I want to find the direction from said point to the line that passes ...
1
vote
2answers
27 views

Find a ratio of triangle's height segment

Given a right angle triangle ABC (C = 90) and a median AM. CD is the height of the triangle ...
0
votes
1answer
23 views

Wedge and common notation for “a line between two points”

I'm using a somewhat old presentation from 2011 that covers twistor geometry. It uses the notation "$L = Z_1 \wedge Z_2$" to suggest that the line $L$ is the "join of the twistors $Z_1$ and $Z_2$, ...
0
votes
1answer
23 views

What is the value of $a+2b$ if $\dfrac{OP}{EF}$ = $\dfrac{a}b$ 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=?
0
votes
1answer
15 views

Number of faces of dimension p of simplex

How can I prove that the number of faces of dimension p of an an n-dimensions simplex is represented by the binomial coefficient below? ${n+1}\choose{p+1}$
0
votes
1answer
38 views

Rewrite general form of ellipse to standard form (what happened in step 3?)

From my math book (Rewriting general form to standard from) General form: $$8y+4y^{2}-18x+9x^{2}=23$$ $$-18x+9x^2 +8y+4y^2 =23$$ What happened from step 2 to 3? $$9(x-1)^2 -9+4(y+1)^2 -4=23$$ $$ ...
2
votes
2answers
63 views

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 ...
0
votes
1answer
19 views

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
0
votes
2answers
40 views

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://...
0
votes
3answers
1k views

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 ...
0
votes
0answers
31 views

Averaging a function over solid angle

I am trying to average $r$ over the solid angle $\Omega$ in 3D. To start this I have expressed $r$ in terms of the angle $a$ and sides $x$ and $d$ in 2D with the help of the law of cosines: $r = x*cos(...
0
votes
0answers
33 views

triangle: distance between segment midpoint and opposite vertex

Assuming I have 3 vertices A, B, C forming a triangle as shown in the picture and the locations (e.g. in 2D) of A and B as well as the distances AC and BC (and obviously AB) are known (but not the ...
0
votes
0answers
15 views

Smallest enclosing disk - runtime

SED given by three points and six positions for a possible fourth point. Which position provides for the longest runtime of the (non-randomized) SED algorithm and which one for the shortest? Now I ...
0
votes
0answers
28 views

Transformation of line with fractional linear transformation

Let $T(z) = i\frac{z+1}{z-1}$, for $z\in\mathbb{C}$. How do I complete the following statement: $L\in\mathbb{C}$ is a line such that $T(L\cup\{\infty\})=L'\cup\{\infty\}$ where $L'$ is a line if ...
-1
votes
2answers
39 views

Another Stubborn Inequality

ReBonjour. Let $x$ and $y$ be two real numbers. Show that $ \frac{ |x+y|}{1+|x+y|}\leq\frac{|x|}{1+|x|}+\frac {|y|}{1+|y|}$ Thanks a lot.
0
votes
0answers
36 views

Ricci Tensor and Einstein Manifolds

What can we say about an hypersurface Einstein manifolds on $\mathbb{R}^{n+1}$ when $n\geq 3$ ? The manifolds is Einstein so Ricci tensor is a multiply of the metric $g$ on manifold: $Ric=\lambda g$ ...
0
votes
2answers
33 views

Hexagon inside square - side lengths not adding up properly - what am I not seeing?

I am trying to find the side length of a regular hexagon inscribed within a 12"X12" square. I am not trying to find the maximum side length - I've already seen the formula for that elsewhere - I am ...
-1
votes
1answer
25 views

The area of $ABCD$ is $84$. The diagonals meet at $P$, and $|AP|=5$, $|BP|=3$, $|CP|=7$, $|DP|=2$. Find the areas of the four sub-triangles. [closed]

The area of quadrilateral $ABCD$ is $84$. The diagonals intersect at point $P$. If $$|AP|= 5,\quad|BP|= 3,\quad|CP|= 7,\quad|DP|= 2, $$ calculate the area of the four triangles in quadrilateral $...
-1
votes
1answer
54 views

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?
2
votes
1answer
36 views

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 ...
0
votes
3answers
67 views

Parametrization for the figure '8' curve?

Is there a parametrization for the figure '8' curve, which is self-intersected?
2
votes
1answer
37 views

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 ...
1
vote
1answer
84 views

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 $ME$ ...
4
votes
2answers
35 views

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 ...
0
votes
1answer
34 views

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 ...
0
votes
0answers
47 views

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 ...
0
votes
2answers
40 views

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 ...
0
votes
0answers
30 views

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 ...
2
votes
4answers
67 views

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 ...
1
vote
1answer
20 views

Finding non-imaginary lines of intersection of cones that share a vertex

I found online at http://www.grad.hr/geomteh3d/prodori/prodor_stst_eng.html that "The case of total degeneration into 4 lines appears when two cones have the same vertex.In that case, the two cones ...