Stack Exchange Network

Stack Exchange network consists of 175 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
0answers
2 views

How to create a 3D graph from two 2D graphs

I have an equation in the x-y plane, and another in the z-x plane. Is it at all possible to combine them into the x-y-z space? I realize that there might not be enough data to fill the gaps, but I ...
0
votes
0answers
11 views

area of triangle is proportional to scalar product of the normal vector to the chosen edge and radius-vector of third point

How can I proof that: The area of triangle is proportional to scalar product of the normal vector to the chosen edge and radius-vector of third point Thanks for helping.
0
votes
1answer
14 views

How to compute the parameters of circumscribed hypershpere?

Assume I have an $n$-dimensional simplex on the points $x_0, ..., x_n$, where each $x_i \in \mathbb{R}^n$. I would like to obtain the parameters (center and radius) of it's circumscribed $n$-...
0
votes
3answers
54 views

Find the side of the square.

The problem I am proposing to solve was posed in a math contest for students of 17-18 years old, this month. With the data in the picture, find the side of the square. I did find the solution but it ...
0
votes
0answers
19 views

Alternative way to determine whether a point is contained within an arc section of a circle?

The best way contained in answers for this question: https://stackoverflow.com/questions/6270785/how-to-determine-whether-a-point-x-y-is-contained-within-an-arc-section-of-a-c But are there some ...
0
votes
1answer
13 views

Smallest circumcircle around four non-overlapping unit semicircles

What is the radius of the smallest circle into which will fit four unit half-disks? What arrangement of the half-disks achieves this? How is it proved optimal? The best arrangement I've found fits in ...
0
votes
0answers
15 views

Projection onto a surface vs projection onto a linearization

Suppose I have a surface $S$ defined by the equation $$h(x)=0.$$ Assume that $h(x)$ is continuously differentiable as many times as we want. Let $P_S(x)$ be the function which maps $x$ onto the ...
3
votes
4answers
47 views

Congruent triangles in 3 tangent circle configuration

Two circles $\mathcal{C}_1$ and $\mathcal{C}_2$ of centers $O_1$ and $O_2$ are externally tangent at $I$ and internally tangent to a third circle $\mathcal{C}$ of center $O$ that is colinear with $O_1$...
1
vote
0answers
14 views

How to find a hyperplane with maximum number of points on one side

Given a set of points $S$ in a high dimension real space, is there an efficient way to find a hyperplane through the origin such that the number of points on one side of the hyperplane is maximum over ...
0
votes
1answer
22 views

How to convert intersection of two lines into an arc?

I am struggling with finding coordinates of a point for arc origin. I am programming a tool which converts a corner (intersection of two lines) into an arc of needed radius. SETUP PICTURE I have ...
3
votes
1answer
24 views

Parametrizing the square spiral

Related to this question concerning number spirals I have another one, more specific. While it is rather easy to arrange the natural numbers along an Archimedian spiral by $$x(n) = +\sqrt{n}\cos(2\...
1
vote
1answer
19 views

Edges of rectangle mapped to a new plane

If a rectangle plane lines 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 edges ...
0
votes
1answer
28 views

How to get the perimeter of a circle from 8r to 2 $pi$ r [duplicate]

A friend showed me a circle inside a square such that the diameter of the circle is equal to the side length of the square. The perimeter of the square is 8r. He then proceeded to take small squares ...
0
votes
3answers
38 views

Parameterizing the boundary curve of the surface defined by $x+y+z \geq 1$ and $x^2 +y^2+z^2=1$

I am unsure how to parameterize the boundary curve of the surface defined by $x+y+z \geq 1$ and $x^2 +y^2+z^2=1$, where $x,y$ and $z$ are real numbers. The boundary curve should be the circle ...
-2
votes
1answer
32 views

Proving $x_1y_1 +x_2y_2 + kx_1y_2 + kx_2y_1$ defines a scalar product in $\mathbb{R}^2$ if $|k|$ <1 [on hold]

Prove $x_1y_1 +x_2y_2 + kx_1y_2 + kx_2y_1$ defines a scalar product in $\mathbb{R}^2$ if $\left|k\right|<1$ Using definition that scalar product is a bilinear function which satisfies linearity, ...
1
vote
1answer
32 views

angle between vectors based on angles of related vectors

I have 2 sets of 2 real vectors with norm 1: $v_1, v_2$ and $\hat{v}_1, \hat{v}_2$ (so $v_1 \perp v_2$ and $\hat{v}_1 \perp \hat{v}_2$). All vectors are $n$-dimensional. We assume we know the angle $\...
1
vote
1answer
33 views

Is this shape a fair D-24?

I've been looking at polyhedra, incuding Platonic solids as well as Archimedean and Catalan solids. Catalan solids are face-transitive, which I believe implies that they are "fair dice", in the sense ...
0
votes
1answer
16 views

Proving the intersection of tangents is an excentre of a triangle and showing the circle is a tangent to a line.

I'm given an ellipse with focal points $F_1$ and $F_2$, and two points $P$ and $Q$ on the ellipse such that $F_1$ lies on $PQ$. Also, the tangents at $P$ and $Q$ intersect at a point $R$. Show that: ...
3
votes
4answers
52 views

Showing locus of points is a hyperbola

I've having trouble understanding what the question is trying to ask. And I am not sure how to start to answer the question. The diagram below shows what happens for waves on the surface of a pond. ...
0
votes
0answers
17 views

equation of nearest distance from asymptote line to its hyperbola given the foci location and hyperbola intersection with its major axis

Let there is an asymptote line $$ y = \pm \frac{b}{a}x$$ and a hyperbola $$ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$ what is the nearest distance from any point at the asymptote to hyperbola as a function ...
0
votes
0answers
8 views

Steiner tree to minimise travelling distance: Building roads to connect a network of points

Suppose we have four points in a unit square, as described in the question here. We are tasked with building a network of roads that connect all the cities. The travelling distance (T) of this network ...
-3
votes
0answers
21 views

Find the distance between this lines. [on hold]

L1:x=(y−5)/2=(z−2)/3 L2:(x−3)/4=(y−2)/3=(z−1)/2 My answer is 8/sqrt(390) but online check site it is wrong, whats the promlem?
0
votes
0answers
26 views

Geometry/Calculus Question Asking to find volume

Let $R$ be the region bounded by $y = x^2$, the $x$-axis, the lines $x = 1$ and $x = 5$. (a) Suppose $S$ is a solid whose base is $R$ and whose cross sections perpendicular to the x-axis are ...
2
votes
2answers
31 views

Differential geometry and frenet formula

Given a curve C by its arclenght (vector $r(s)$), prove that $\frac{dT(s)}{ds} \times \frac{d^2 T(s)}{ds^2} = k^2 \omega$ where k is the curvature and $\omega$ is the darboux vector. I tried using ...
2
votes
1answer
38 views

Maximizing Area of a quadrilateral inside of a square

The square ABCD has point M located on side AB and point N on side CD. Lines CM and BN intersect at point U. Lines DM and AN intersect at point V. Determine where points M and N should be placed to ...
3
votes
1answer
59 views

Pythagoras-like equality in a problem

Known Information: $△ ABC$ is rectangular and isosceles $M$, $N$ belong to hypotenuse angle measurement $\angle MAN = 45^\circ$ Requirement: to demonstrate that $$BM^2 + CN^2 = MN^2$$ Is a ...
2
votes
1answer
31 views

What value of $n$ will make a triangle contain 560 lattice points?

I recently met a rather hard problem: A lattice point is a ordered pair where both $x$ and $y$ of $(x, y)$ are both integers. A triangle is forms by of the lattice points $(1, 1)$, $(9, 1)$, and $...
2
votes
1answer
43 views

Dimensions of paper needed to roll a cone (Updated with clarifications)

I'm looking for a way to calculate the dimensions of a piece of paper needed to roll up into a cone shape. Please consider the following diagram I created (nothing is drawn to scale): In this example,...
2
votes
0answers
23 views

A rotating polygonal line with increasing side length cannot end up where it started!

Consider a polygonal line $P_0P_1...P_n$ such that $\angle P_0P_1P_2=\angle P_1P_2P_3=...=\angle P_{n-2}P_{n-1}P_{n}$, all measured clockwise. If $P_0P_1>P_1P_2>...>P_{n-1}P_{n}$, $P_0$ and $...
-3
votes
0answers
46 views

Isn't mass from purely topology in the absence of matter a contradiction? [on hold]

Consider the 3 dimensional projective space which is empty of matter minus the infinity point. We see that it has ADM mass. In other words, a perfectly fine geometry, orientable and asymptomatically ...
0
votes
1answer
23 views

Angles at centroid of a triangle

If $ABC$ is a triangle with centroid $P$, I got the impression that the angle $\angle BPA$ at the centroid should only depend on the angle $\angle BCA$ (and not on the other angles). Am I right? Is ...
0
votes
0answers
12 views

Figuring out positions of some points given other known points and angles between the known and unknown points

So the data in question is a set of points p which all have known positions in space, a set of points q which all have unknown ...
1
vote
1answer
19 views

Covering the 2-sphere with 6 hemispheres

While reading chapter 2 of Wald's General Relativity titled "Manifolds", I stumbled upon the fact that the 2-sphere $S^{2}$ cannot be mapped into $\mathbb{R}^{2}$ in a continuous 1-1 manner. Wald then ...
1
vote
2answers
23 views

inequality related to square the sum of any two sides of a triangle with respect to square of other side

Consider a,b,c are three side of a triangle. Now we need to find the relation between square the them sum of any two side of triangle with respect to third side. My approach As we know that the sum ...
10
votes
2answers
407 views

Overlapping circles covering polygon

While working in GeoGebra I noticed something odd. I had a triangle with a point inside and the point was connected to each of the vertices. For each vertice I had drawn the circle passing through the ...
1
vote
1answer
24 views

Distance between a point and low-dimensional sphere

Is there a way to analytically calculate the distance between an arbitrary point $\mathbf{x}\in\mathbb{R}^n$ and a low-dimensional sphere embedded in $\mathbb{R}^n$, say one aligned with the axis ? ...
1
vote
1answer
47 views

How would be a formal answer for an automata geometry problem?

Let an automaton $A$ sit on point $O$ $(0,0)$ and turned to the North. That automaton can execute only any combination of three different commands in each step: Move one unit forward Turn 90 degrees ...
0
votes
1answer
44 views

How many points are needed to define a circumference?

This doubt comes from a combinatorics problem in a textbook, which states: Consider two strictly parallel lines and seven dots, four of which are over one of them, and three over the other. Three ...
0
votes
1answer
18 views

Plane cutting a pyramid

Pyramid with equilateral triangle as a base, length of side of pyramid is $s=3$(not a base side). Plane goes through pyramid, and contains base edge, and is normal to a side of pyramid. If surface ...
-2
votes
0answers
19 views

How to calculate vertex, focus, axis etc. from such type of ellipse equation 3x²+8y²+12xy-18x-32y+23=0? [on hold]

Is there any way to find vertex , focus, axis, centre etc from this type of non ideal ellipse, hyperbola or parabola?
0
votes
2answers
35 views

Pair of lines problem

If the pair of straight lines $x^2+2xy+ay^2$ & $ax^2+2xy+y^2$ have exactly one line in common, then the combined equation of the two lines is given by A. $3x^2+8xy-3y^2$ B. $3x^2+10xy+3y^2$ C. ...
-1
votes
0answers
42 views

Geometry, does this shape have a name?

A Sphere with Diameter 1 perfectly inscribed in A cube with sides of 1, Removing the sphere and splitting the cube on the faces we then have 8 identical "Corners" with three sides being a tetrahedron ...
-4
votes
0answers
25 views

A problem on combinatorical geometry . [on hold]

Hey could someone help with this exercice, i have tried everything but nothing seems to suite work. Any help would br appreciated : Let ABCDEF be a convex 6 sided polygon of sides 1, prove that at ...
2
votes
1answer
75 views

Are there always two circles that together surround or intersect all points in the following scenario?

Consider $N$ points in $\mathbb{R}^2$ and $\binom{N}{2}$ circles, one for each pair of points such that it intersects both. Is it always possible to pick two of these circles that together surround or ...
5
votes
3answers
173 views

Side length of a quadrilateral incribed on a circle

I've been doing math for 10 years now, yet every so often I get stumped by a "basic" high school question. This is one of those times. Here's the question: Part a is easy; we apply the cosine rule ...
1
vote
1answer
32 views

Find the parabola given two points and $y$-max (no axis of symmetry)

Given $(0,0)$ origin, point $(3,2)$ and $y\text{-max} = 5$, find the parabola. I tried to shift point $(3,2)$ down to $(3,0)$ so that it can become symmetric to origin. Then the vertex would be $(5,\...
0
votes
1answer
57 views

Finding the lengths of $AC$ and $AD$

Triangle $ABC$ is right-angled at $A$. The angle bisector from $A$ meets $BC$ at $D$. If $CD=1$ and $BD=AD+1$, find the lengths of $AC$ and $AD$. I have tried to set up a equation with $AD$ and $AC$ ...
0
votes
2answers
48 views

What is the Geometric meaning of vector norm in Rn n>3

My question is related to the length of the vector , Sorry it may seem stupid for you as i come from engineering background not mathematics background For Vectors up to 3 dimensions (can be ...
0
votes
0answers
15 views

Chord of contact in polar coordinate

Can you please help me to derive the equation of chord of contact for a circle in polar coordinate? I have found the equation in cartesian coordinate but I cannot map that into the polar coordinate. ...
-2
votes
0answers
16 views