Questions tagged [geometry]

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

Filter by
Sorted by
Tagged with
0
votes
0answers
3 views

Show VCdim of (X, R \lor R \lor R) is O(DlogD) when VCdim(X, R) = D

Please help me solve this problem: $(X, R)$ is a range space and $VCdim(X, R) = D$. Show $VCdim(X, R \lor R \lor R) = O(DlogD)$
-1
votes
0answers
21 views

Is it possible to draw several circles on the plane so that each one touches exactly five others? [closed]

I have been trying to solve this for a while. Could someone give me a headstart? Let us assume we have several circles inside a very huge rectangle or square plane, is it possible for each one of the ...
0
votes
1answer
24 views

Representing a hexagon as an intersection of 6 halfplanes

how can I represent a hexagon (6-gon) as an intersection of 6 half planes?
0
votes
0answers
7 views

All boundary points of a Jordan Domain are simple

I have tried many things but I have not succeeded. I am trying to find a topological proof of the fact that all boundary points of a simply connected, bounded Jordan Domain (i.e, the bounded interior ...
1
vote
2answers
29 views

Partition the remaining rectangle into equal parts.

There’s a rectangle. A small rectangle is cut from the bigger rectangle ( not necessarily from the center). How will you partition the original rectangle after removing the cut such that the remaining ...
2
votes
1answer
32 views

Determining all triples $(a,b,c)$ of positive integers that are sides of a triangle inscribed in a circle of diameter $6.25$

An Olympiad Geometry question Determine all triples $(a, b, c)$ of positive integers which are the lengths of the sides of a triangle inscribed in a circle of diameter $6.25$ units. So, in this, ...
4
votes
0answers
44 views

The slope of special diagonal line in ellipse is $b^2/a^2$ - Geometric Proof

Purely geometrically prove that diagonal line in ellipse connecting points of normal vectors in 45° inclination has slope of ratio of Pythagorean squares of lengths of minor and major axes $\frac{b^2}{...
2
votes
0answers
46 views

What is the name of this arc in English?

In geometry, for any line segment AB and angle $\theta < \pi$, the locus of points $C$ on one side of line $AB$ such that angle $ACB$ equals θ is an arc of a circle. Points outside this arc form ...
1
vote
0answers
15 views

Can you derive a parametric function which describes a crystallographic screw axis?

A $2_{1}$ screw axis is defined as a 180-degree rotation followed by a translation of $\frac{1}{2}$ along a particular unit cell vector. In matrix form: \begin{equation} \begin{bmatrix} -1 & ...
2
votes
1answer
31 views

How many elements does the intersection of $n$ circles contain?

For the real problem that I'm solving is For given three circles there are seven elements, then how many elements that 6 circles have? For the first approche I just draw the picture and count all ...
3
votes
3answers
58 views

SUM OF A SET: Find an example of a set $A\subset \mathbb R^2$ such that A+A does not equal 2A

Please am new to discrete geometry, I am finding it difficult to identify what this set could be. Please I need an insight. THANKS! \ QUESTION: Find an example of a set $A\subset \mathbb R^2$ such ...
-1
votes
0answers
25 views

Side Lengths of a Triangle using its Height and Hypotenuse

Given the height and the hypotenuse of a right triangle, find the side lengths a and b, I did some research and I couldn't find much on this, so I decided to show how to find it, which I noticed while ...
2
votes
1answer
33 views

Is this system of geometric points solvable?

Apologies for the vague title, but I am not sure how otherwise to explain my question with a title. I have a set of 3 known points (x, y), and a set of 3 unknown points and a few known relationships ...
4
votes
1answer
54 views

Is it possible/meaningful to have a right triangle with sides $0$, $1$, and $i$?

If $i^2 = -1$, does that mean you could have a triangle with side lengths $0$, $1$, and $i$? But if you draw such as triangle on a complex number grid, the hypotenuse length is $\sqrt 2$, not $0$. ...
1
vote
1answer
12 views

Different representations of hyperbolic space

Two equivalent representations (not quite sure if that's the right word) of hyperbolic space $\mathcal{H}^n$ are the zero set of $- x_0^2 + x_1^2 + \ldots x_n^2 =-1 $ the quadratic space: vector ...
2
votes
1answer
39 views

Missing Quadrilateral Angle

Please find the missing green angle for the quadrilateral using simple geometry and explain your steps. I am not able to use trigonometry for this problem. Thank you.
0
votes
0answers
19 views

Is there a common name for the shape described as a segment of a circle or ellipse?

A circular segment is a region of the area inside a circle partitioned from the rest of the circular area by a chord. Is there a common name for this shape, other than "circular segment"? If ...
1
vote
0answers
29 views

Symmetric vs Symmetrical

I was reading an engineering book. It says " A turbomachine with symmetrical velocity triangles...". I personally felt more naturally right away to say symmetric velocity triangles. What is ...
0
votes
0answers
22 views

Proving a relation between the ordinates of point of contact of a line on a circle

If the tangents at $(h,k)$ to the ellipse $x²/a² + y²/b² = 1$ , cuts the auxillary circle in the point whose ordinates are $p$ and $q$ , then show that $1/p + 1/q = 2/k$ . I found this question while ...
-6
votes
0answers
31 views

how to make an angle that is both greater than and less than 90 degrees [closed]

I need to see how to make the angle both greater than and less than 90 Degrees and what angle shos that it is both greater and less that 90 degrees
1
vote
0answers
27 views

I have two asymptotic triangles that are equivalent

I am trying to prove that two triangles that are asymptotic are congruent. Given that they both have a side that is congruent and, but their angles are not congruent. SO, for example, $\triangle ABC$ ...
0
votes
0answers
26 views

Why is this affine transformation legal?

If $K$ is a centrally symmetric body, and $\varepsilon$ is its maximal ellipsoid, then $K \subset \sqrt{n}\varepsilon$. To check this, we may assume $\varepsilon = B^n_2$, i.e. the unit ball of ...
-1
votes
1answer
25 views

How to find the area of triangle ABC?

How to find the area of triangle ABC if BP is an angle bisector?
0
votes
0answers
22 views

Finding the shortest distance between two skew lines—what does the 'projection' of a vector onto another mean?

In my textbook, it says the following about finding the shortest distance between two skew lines $l_1$ and $l_2$: If $P$ is an arbitrary point on $l_1$, and $Q$ is an arbitrary point on $l_2$, then ...
1
vote
1answer
39 views

Shape of locus of point R

AO and BO are two fixed straight rods. PQ is a straight rod such that P and Q slide respectively on AO and BO. At each position of P and Q lines PR and QR are drawn perpendicular to AO and BO ...
2
votes
1answer
27 views

How to prove geometrically that anticorrelated Gaussians are separated?

I am trying to prove the following theorem: There exists a universal constant $K>0$ such that if $g,h$ are standard Gaussians with $\mathsf{E} gh=1-\alpha$, $$\mathsf{P}\left(g< -1,h> 1\...
0
votes
1answer
49 views

Creating an algebraic formula

I need to create a formula for a piece of software and can't quite work out how to form it as my Maths is a little rusty. I would appreciate any help. I have two values X & Y where each can be ...
1
vote
2answers
44 views

Calculate rotation matrix that flips the frame up

Let's start with the standard basis frame: [1, 0, 0], [0, 1, 0], and [0, 0, 1]. Imagine this frame goes through some arbitrary rotation R, with one constraint, that we know that after the R is applied ...
0
votes
0answers
16 views

flattening part of a cone

I am a design student, and I have recently been 3d modeling an ornament for the heel of a shoe. I have a nice round cone, but unfortunately I am having a lot of trouble turning it into a flat sheet. ...
1
vote
0answers
86 views

How many circles of 6 cm radius can be cut from a piece of paper 100 cm by 80 cm [closed]

I would like to know how this can be solved with formula as well so i may answer furthermore with questions similar to this
3
votes
0answers
63 views

Ellipse inscribed in square and its circumscribed circle

How geometrically can you prove that radius of the circle circumscribing square that is circumscribing ellipse is $$ R=\sqrt{a^2+b^2} $$ where $a$ and $b$ are major and minor axes of ellipse? Note ...
0
votes
1answer
21 views

Points in space

Let $P =\left \{ A_{1}, A_{2} \cdots A_{n} : A \in \mathbb{R}^{3}\right \}$ (where $A_{0}=A_n, A_{1}=A_{n+1})$. By middling of a point $A_{i+1}$ we mean setting it's value to a rectangular projection ...
1
vote
0answers
25 views

Extend ellipsoid by given radius

I have a parameterization of an ellipsoid, given by \begin{align} x &= a\sin(\theta)\cos(\phi)\\ y &= b\sin(\theta)\sin(\phi)\\ z &= c\cos(\theta)\,, \end{align} where $\theta$ is the ...
-1
votes
0answers
27 views

Maximal Genus of Plane Curve [closed]

In website, it is written that plane curve $C$ of degree $n$ inside ${\Bbb P}_{\Bbb C}^2$ satisfies the following equality$\colon$ \begin{equation*} g_{C} \leq \begin{cases} & \!\!\!\! \frac{(n - ...
0
votes
2answers
29 views

Find equation that denotes straight line that intersects middle of chord that is expressed by another equation

$(x-2)^2 + (y + 1)^2 = 16$ is circle $x - 2y - 3 = 0$ is equation that denotes chord of this circle How do I find equation of straight line that intersects middle of this chord?
1
vote
1answer
42 views

Equation for orthocentre in argand plane

I would like to know the general equation for orthocentre (and other centres of the triangle as well, excluding the centroid, if possible) in the argand plane. In my case, I faced some difficulty in a ...
0
votes
0answers
20 views

Using the Cayley-Menger determinant to determine coplanarity in 3-dimensional space

I'm attempting to use the Cayley-Menger determinant to solve the following problem: Given three points in a plane, the velocity of some signal, and the time at which the signal arrived at each of ...
0
votes
0answers
16 views

Get the “furthest point away” along a B-Spline in a segment

Given a B-Spline define by n + 1 control points and degree p, and a specific "t" value segment between knots e.g. 0.6 <= t <+ 0.7, I need to find the point at which the B-Spline "...
0
votes
0answers
12 views

Calculating position of moving point (of 3D object) in circumference

I'm making a 3D game where I rotate a stick around a player. I am given the position of the starting point of the stick, and how much I want to rotate it by. Using these two points how can I calculate ...
0
votes
2answers
37 views

How to find the shaded angle of a right angled isosceles triangle?

Hey everyone, Just another question. I’m trying to figure out how to find the shaded angle of an isoceles triangle. All I know is the ratios between the sides and of course the value of the angles (as ...
0
votes
3answers
55 views

Maximizing the area of a cyclic pentagon made up of triangle centres.

Triangle $ABC$ has $\angle BAC=60^\circ$, $\angle CBA \le 90^\circ$, $BC=1$, and $AC \ge AB$. Let $H$, $I$, and $O$ be the orthocenter, incenter, and circumcenter of $\triangle ABC$, respectively. ...
1
vote
1answer
23 views

Effect of transformation on a point.

What is the effect of the transformation $$A(x,y)=(0.6x-0.8y, 0.8x+0.6y)\quad ?$$ I understand how transformations work when the variables are not in the same coordinate. I do not understand how I ...
2
votes
2answers
91 views

Finding Pythagorean triples, with a conjecture.

A right triangle with integer side lengths ($a , b , c$ where $a < b < c$) can be found (to a certain degree) with the inner radius ($r$), the formulas for the area of a triangle and Pythagoras ...
0
votes
1answer
47 views

Proving two versions of Pasch's Axiom are equivalent

I am trying to show that these two versions of Pasch's axiom are the same. A1. If a line enters a triangle at a vertex, then the line intersects the opposite side. A2. If a line enters a triangle at a ...
1
vote
4answers
77 views

Why can we not evaluate $1+2+\cdots+n$ using a triangle?

Consider the right angled equilateral triangle with the right angle at $(0,0)$. The $i$th row for $0\leq i \leq n-1$ has $n-i$ points (suppose we denote by balls). The area of the triangle is supposed ...
0
votes
1answer
31 views

How do I calculate the number of elements that fit into a container on average?

This is a geometry question. Given that I pour a bucket of small items with a given shape into a smaller bucket, how do I know how many will fit in there on average (obviously depends on how they fall ...
0
votes
1answer
19 views

Angle of an ellipse point shifted up in respect to a similar at origin

I have an ellipse $(E): x = a\cdot \cos(\theta), y = b\cdot \sin(\theta)$ then I move this ellipse upwards along the y-axis (semi-minor axis) so the ellipse $E$ become an ellipse $E'$ (in green) not ...
1
vote
0answers
25 views

Self-intersecting colored polyline

A few days ago I got a problem like this at a math Olympiad. I have some ideas, but I can't seem to complete the proof. Tim draws polylines, and then colors their sides as follows: vertical lines ...
0
votes
0answers
18 views

Projective line $P_{1}$ as bivariate family

Is a projective line $P_{1}$ (brought about by 2 projective points in projective space $P_{n}$ ) a bivariate parametric family? The aim of the question is to get the concept of a basis in a n-...
13
votes
2answers
272 views

Number of grid points outside a rook circuit

When I draw a circuit on a 8x8 chess board that passes through all squares, no matter how many turns I draw, I always end up with 18 grid points outside my circuit (and 31 grid point inside). It looks ...

1
2 3 4 5
808