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

learn more… | top users | synonyms (1)

0
votes
2answers
5 views

Need help with alternative method to equation of a tangent at the point of a circle

so I know a simpler of looking for the equation of a tangent at the point of a circle is to differentiate, my lecturer would rather we not use calculus and has charged us with looking for an alternate ...
7
votes
4answers
25k views

Is there a way to rotate the graph of a function?

Assuming I have the graph of a function $f(x)$ is there function $f_1(f(x))$ that will give me a rotated version of the graph of that function? For example if I plot $\sin(x)$ I will get a sine wave ...
2
votes
1answer
23 views

Question regarding curl in dimensions higher than 3

According to the wikipedia page about curl curl can be defined implicily as $$(\nabla \times \textbf{F} ) \scriptsize{\bullet} \normalsize{\hat{n}} = \lim_{A \rightarrow 0} \frac{1}{|A|} \oint_C ...
3
votes
1answer
52 views

placing balls inside ball

Is it possible to put pairwise disjoint open 3d-balls with radii $\frac{1}{2},\frac{1}{3},\frac{1}{4},\dots$ inside a unit ball? not an original question, I found it somewhere in the internet ...
0
votes
0answers
9 views

Differentiation between the unit spheres and the hypersurfaces in $\mathbb C^n$

Let $\Sigma ^{n-1}$ be the complex unit sphere in $\mathbb C^n$, $$\Sigma^{n-1}=\{(z_1,...,z_n)\in \mathbb C^n; z_1\bar {z_1}+...+z_n\bar {z_n}=1\}$$ and let $S^{n-1}_{\mathbb C}$ be the hypersurface, ...
1
vote
1answer
496 views

definition of thickness of a shape (ring)

I want to know how thickness is defined. Let me start with the simplest shape due to its symmetry. This is a circle. Assume a circle with radius of 1. If we draw a circle with the same center and ...
2
votes
1answer
496 views

Internal polygon formed by drawing diagonals in a regular polygon

In an n-sided (n>4) regular polygon, label the vertices {0, 1, ..., n-1}. For each vertex i, draw a pair of diagonals: from i to (i+2) mod n and from i to (i-2) ...
1
vote
0answers
893 views

Volume of comma-like teardrop shape or a 3d paisley shape

Whats the formula for the volume of a comma-like teardrop shape or 3d paisley shape? In other words, how to revolve a curve around another curve? Take any arbitrary case you like to show just the ...
391
votes
11answers
404k views

Is this Batman equation for real?

HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
1
vote
1answer
24 views

Support of a clamped B-spline

Let a B-spline of degree $p$ be defined by its parametric equation $$ \mathbf{r}(t) = \sum_{i=0}^n N_i^p(t)\mathbf{P}_i$$ where the $n+1$ control points are denoted by $\mathbf{P}_i$. The basis ...
0
votes
0answers
41 views
+50

Quaternion to Euler with some properties

I am trying to create a map editor (for GTA SA-MP), and the source game data contains objects with quaternion rotation, whereas I need the editor to output the objects with Euler rotation (XYZ) in ...
1
vote
2answers
17 views

The number of intersection points between a trivial loop and any other loop in the torus

In a torus, let $C_1$ be a trivial loop (contractible to a point) and let $C_2$ be any simple loop (trivial or meridian or longitude). What is the intersection number of $C_1$ and $C_2$. I think that ...
10
votes
2answers
263 views

Can any higher-dimensional Spheres be rotated everywhere equally?

You can rotate a circle so that every point on it (just the perimeter, not the interior) moves "equally". That is, every point moves with the same speed and even has the same "acceleration" ...
10
votes
6answers
638 views

538.com's Puzzle of the Overflowing Martini Glass - How to compute the minor and major axis of an elliptical cross-section of a cone

FiveThirtyEight.com Riddler Puzzle / May 13 The puzzle goes like this; "It’s Friday. You’ve kicked your feet up and have drunk enough of your martini that, when the conical glass (🍸) is upright, the ...
4
votes
4answers
621 views

Why, intuitively, do different shapes with the same surface area have different volumes?

This is something that's always bothered me. I am well aware that you can easily see why this is the case with math. I mean, even in the 2-D case, take a square with side length $1$, and it has a ...
6
votes
1answer
65 views
+50

can a convex polygon have only one boundary point at locally maximum distance from its centroid?

It's easy to see that given any convex polygon P and any point c in its interior, there is at least one point m on the boundary of P at locally maximum distance from c: simply choose m to be a vertex ...
0
votes
0answers
21 views

Inverse points concurrence on the circumcircle

Let $ABC$ be a triangle, and $P,Q$ two inverse points with respect to its circumcircle. Let the circle through $A,P,Q$ meet $AB,AC$ at $A_c,A_b$ respectively. Analogously define $B_a,B_c,C_a,C_b$. ...
0
votes
0answers
40 views

Dual of a maximization problem

We have a positive, smooth, increasing concave function $f:\mathbf{R}^n\to \mathbf{R}^+$ and $k$ smooth, increasing constraint functions $f_i:\mathbf{R}^n\to\mathbf{R}$. I've recently encountered two ...
-1
votes
1answer
39 views

Maximun no. of diagonals that can be drawn so that all the parts they divide into are triangles?

In a convex n-gon (n>4) no three diagonals are concurrent (intersect at the same point). What is the maximum number of the diagonals that can be drawn into this polygon so that all the parts they ...
0
votes
1answer
36 views

Is these angles 90 degrees?

If I have the following triangle: Where $\angle B=\angle C = O$ And $AP$ bisects $\angle A$ so essentially $\angle BAP = \angle CAP = \frac12 \angle A$ We can prove that $\angle APB = \angle APC$ but ...
1
vote
0answers
8 views

Gradient and Laplacian of a submanifold

let $M^n$ be a smooth an $n$-dimensional sub-manifold of a $\mathbb{R}^{m}$. Denote by $\nabla^{M}$ and $\nabla^{\mathbb{R}^{m}}$ be the gradient of $M$ and $\mathbb{R}^{m}$ respectively. Similarly ...
0
votes
1answer
463 views

How to get perpendicular line to an edge of a polygon.

This is a pretty basic geometry question, but I couldn't find an answer clear enough for me on Google (I don't know much about math). Let's say I have a rectangle. I have the coordinates for the four ...
1
vote
1answer
42 views

Conics and conics of the form $ax^2+by^2+c=0$

The problem of finding rational points on conics is usually discussed (for example in the book of Silverman and Tate) for conics of the form $ax^2+by^2+c=0$. I assume that those conics are in ...
4
votes
3answers
82 views

The value of $(a+b)$, according to the question.

My friend gave me a question I tried my best, but I'm low on triangle concept. Points $ O, A, B, C... $ are shown in the figure where $ OA=2AB=4BC=...$ and so on. Let $A$ be the centroid of a ...
1
vote
0answers
10 views

Obtain the set of points from Voronoi diagram

Given a planar infinite two dimensional mesh graph such that each small polygon of the mesh is convex, is it correct to assume for any such mesh there exists a set of points such that the these ...
1
vote
1answer
17 views

Geometric generation principle form constructing the Hilbert Curve

I have some questions on the generation of the Hilbert's space-filling curve. Any help to clarify doubts a-e would be very appreciated. The Hilbert's space-filling curve is a function ...
0
votes
0answers
13 views

Finding centriod given circumcenter, orthocenter, and direction from the origin.

I pose this problem to figure complete a answer on a problem with I have gotten far in but I am stuck here. I don't want to delete my answer because of how far I gotten anyways here is the issue I'm ...
0
votes
1answer
31 views

Voronoi edges example

I have 4 line segments: 0 0 2 0 // 1st line segment 2 0 2 1 // 2nd line segment 2 1 0 1 0 1 0 0 and I wrote some CGAL code to print the Voronoi edges. However, ...
1
vote
2answers
32 views

Find the equation of tangent line passing $(2,3)$ and perpendicular to $3x+4y=8$.

I need to find the equation of tangent line passing $(2,3)$ and perpendicular to $3x+4y=8$. Need help in this and also show me how you got the answer. I will be very thankful.
1
vote
1answer
10 views

Finding the Centre of an Abritary Set of Points in Two Dimensions

I am currently working on a program that needs to transform one set of coordinates by shifting them to the center of the screen. The points are offset from the middle of the screen - either to the ...
1
vote
1answer
28 views

Geometry (Locus and constructions)

I want to find the equation for the locus that is at the same distance from the point $(2,3)$ to the line $x=1$. Im not sure if I am right or wrong? Is the locus just the two point at a distance=1 ...
1
vote
2answers
126 views

New Golden Ratio Construction with Two Adjacent Squares and Circle. Have you seen anything similar?

The below Golden Ratio Construction results in a ratio of PHI (1.6180...) between the blue line and red line, as found in Geogebra. This seems like a simple construction of the golden ratio, yet so ...
1
vote
1answer
22 views

Why/What is this shape possible/classified as?

From supernatural season 9 episode 23. Circle is divided to 6 parts with a hexagram(? I guess), but then each line is divided to 5 parts with kissing circles, the fact that all the circles are ...
1
vote
1answer
19 views

Given a right triangle's perimeter and difference between median and height to the hypotenuse, find it's area.

I have been trying to solve the following problem for a while: You are given a right triangle ABC (angle C is right). The perimeter ABC is 72. CK is the median, and CM is the height to the ...
1
vote
1answer
41 views

Area of triangle which hypotenuse=10 [duplicate]

A right triangle has a hypotenuse equal to 10 and an altitude to the hypotenuse equal to 6. Find the area of the triangle.
4
votes
0answers
38 views

Can a portion of a hypocycloid be a regular polygon?

Hypocycloids are curves that generally don't include straight lines. A significant exception is a hypocycloid with 2 cusps, generated by rolling one circle inside another having twice the radius of ...
7
votes
1answer
85 views

I would like to show that all reflections in a finite reflection group $W :=\langle t_1, \ldots , t_n\rangle$ are of the form $wt_iw^{-1}.$

I would like to show that all reflections in a finite reflection group $W := \langle t_1, \ldots , t_n\rangle$ are of the form $wt_iw^{-1}$ for some $i$ and some $w \in W$ Clearly all such elements ...
0
votes
1answer
383 views

Minkowski difference of two convex polygons

I just want to make sure that the following algorithm is correct for computing the Minkowski difference of two shapes $A,B$: $\text{Minkowski}(A,B) = \text{ CH } \{x: x = a - b \text{ for } a \in ...
1
vote
2answers
39 views

Geometry construction

I appreciate any help. I want to find the angle $ADC$. I have drawn the circle in Geogebra, and the angle $ADC=120^\circ.$ But how can I give an argument that is always will be $120^\circ$ if angle ...
3
votes
0answers
22 views

Surface of the intersection of $n$ balls

Suppose there are $n$ balls (possibly, of different sizes) in $\mathbb R^3$ such that their intersection $\mathfrak C$ is non-empty and has a positive volume (i.e. is not a single point). Apparently, ...
9
votes
1answer
51 views

How do you calculate the smallest cycle possible for a given tile shape?

If you connect together a bunch of regular hexagons, they neatly fit together (as everyone knows), each tile having six neighbors. Making a graph of the connectivity of these tiles, you can see that ...
52
votes
14answers
9k views

Why is radian so common in maths?

I have learned about the correspondence of radians and degrees so 360° degress equals $2\pi$ rad. Now we mostly use radians (integrals and so on) My question: Is it just mathematical convention that ...
0
votes
0answers
20 views

What is the name of a “polygon” with piece-wise polynomial boundary?

I would like to know if somebody knows the name of these objects. Given a set of $N$ vertices $\{(x_i, y_i)\}_{i=1,\ldots,N}$ (points in $\mathbb{R}^2$) we create a closed curve, defined piece-wise, ...
2
votes
1answer
53 views

Explanation for relationship between hypotenuse segments and leg lengths?

|` | ` x | ` | ` c a | z /` | / ` y |_/ ` |/|_____` b I'm new to this SE, but I have an SO account, so hello! Assume ...
66
votes
2answers
755 views

Modelling the “Moving Sofa”

I believe that many of you know about the moving sofa problem; if not you can find the description of the problem here. In this question I am going to rotate the L shaped hall instead of moving a ...
0
votes
1answer
29 views

Find the point on the plane xOy [closed]

Let $A(x_1; y_1)$, $B(x_2, y_2)$ and $C(x_3, y_3)$ be three points not lying on the same straight line. Find the point on the plane $xOy$ such that the sum of the distances from it to these points is ...
-1
votes
2answers
51 views

Proof that the area of a rectangle is $\ell\times b$ [on hold]

Can anybody prove that the area of a rectangle is length * width
0
votes
0answers
12 views

Converting a Parametric with trig and inverse trig functions to Rectangular form

I came up with a parametric equation for rotating a function $f(t)$ on a graph in three dimensions $$y=\sqrt{f(t)^2+t^2}\sin{\left(\beta+\arctan{\frac{f(t)}{t}}\right)}\cos{\alpha}$$ ...
0
votes
1answer
16 views

Two collineations

Give collineations to prove the following (in the extended projective plane): a, One cannot contruct the midpoint of two points using a straightedge only. b, One cannot construct the reflection of a ...
0
votes
1answer
23 views

Cone under similarity transformation

Suppose we have a cone passing through the origin of $xyz$ coordinate system. Now, the question is that whether we can find a similarity transformation on this coordinate system that turns the cone ...