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

0
votes
0answers
17 views

Find 3D axis parallel to given vector passing through given point

Doing some university study and I'm stumped on the proper way to find a 3D axis (which will be used later for a rotation transformation). For example: How do I find an axis that is parallel to n = 2i ...
0
votes
0answers
21 views

Distance between triangles in a pattern

Lets say you have a triangle similar to the one below, with each triangle numbered $(N, i) $ where $N$ is the row number and $i$ is the position within the row. From any triangle, you are allowed ...
-1
votes
2answers
40 views

Circle in Triangle Help! [on hold]

P is the center of the inscribed circle of right triangle ABC. If AB=4 and AC=2 , find AP.
-2
votes
1answer
35 views

Circle Geometry Help! [on hold]

In the figure BEC=86 and arc AB=140. Find the measure of arc CD.
0
votes
1answer
37 views

If 51 mosquitoes are sitting on a square with side 1m, are at least 3 of them within a disk of radius 1/7?

There are 51 mosquitoes on a square-shaped window with side 1 m. Can Stephen kill 3 mosquitoes with a circular plastic disk of radius 1/7 m in a single strike? I know this can be solved by ...
-2
votes
1answer
20 views

Circle Angle Help! [on hold]

In the figure below, XY, YZ, and XZ are chords and WV is tangent to the circle at X. If the measure if angle Z=38, find the measure of angle YXV.
1
vote
0answers
30 views

Proof of whether the ships will collide?

My first sailing instructor had a rule of thumb that if another vessel appeared to be moving forwards across the background, then it would pass in front of our own vessel. And if it appeared to be ...
0
votes
2answers
19 views

What is the value of length D -Triangle

How can I get D? I know that the triangle right has the measure $1, 1, \sqrt2-1$. But how can i find out the other?
0
votes
0answers
9 views

The Whitehouse simplicial complexes and compositional (Lagrange) inversion

Associahedra and Lagrange inversion of ordinary generating functions (OEIS A133437): For an o.g.f $ f(x)= a_1x+a_2x^2 + \cdots$ with inverse $f^{(-1)}(x)= b_1x+b_2x^2 + \cdots$, the compositional ...
0
votes
0answers
30 views

Area of similar triangle

Suppose that we are given a triangle whose area is known. put a circle C of radius r inside that triangle. How can we find the area of a triangle similar to the first one and whose inscribed circle is ...
-2
votes
1answer
30 views

Triangle Geometry Help! [on hold]

A square is inscribed in a triangle with $\angle A=30^\circ$. What is the ratio of the area of $\triangle EFC$ to the area of $\triangle ADE$?
0
votes
2answers
17 views

comparing areas of unstructured shapes

I want to know, which area is greater? A or B? I know counting squares is an estimation for areas, but I want to know is there any other way to solve this problem?
0
votes
1answer
17 views

Length of tangent line segment to 2 circles

https://drive.google.com/file/d/0B-4lJHUDH1P5UEZ4QzNYcTNYQWs/edit?usp=sharing The image of the problem can be accessed in the above website. Two semicircles are tangent to each other. The ...
1
vote
0answers
28 views

Count balls to put in triangle

Given balls of radius $R$ we need to find how many balls can be put into a triangular container with sides $a,b$ and $c$. Example : Let $R=1$ and $a=3,b=4$ and $c=5$ then answer is $1$, as only one ...
0
votes
1answer
48 views

Fourth grade geometry problem

I found this problem at an elementary school festival and I've spent the last 30min making no progress whatsoever. I have a suspicion that the solution involves cleverly adding a line to the diagram, ...
0
votes
0answers
24 views

The Stable Table

Consider a square table with four legs whose lengths are equal. Suppose that the ground is not smooth , flat surface , but wavy, bumpy one. ( not too much relative to the length of the table legs). ...
2
votes
2answers
49 views

Alternate proof for $a^2+b^2+c^2\le 9R^2$

As I studying geometric inequalities, one of those famous inequalities is $$a^2+b^2+c^2\le 9R^2$$ I did some research and I found that there is a proof (not exactly the this inequality but an useful ...
1
vote
0answers
22 views

How prove: for every convex polygon there exist three consecutive vertices which their circumcircle include all polygon?

How prove that for every convex polygon there exist three consecutive vertices which their circumcircle include all poligon?
2
votes
1answer
43 views

euler triangle inequality proof without words

today i was studying geometric inequalities and I saw this inequality $$R \ge 2r$$ unfortunately the book did not provided any prove or further explanations. So I just did a little research about it. ...
1
vote
2answers
53 views

How can I prove this problem on geometry?

I need to prove the following: If $P$ is an inner point of $\triangle ABC$, then there is a single transverse $EF$ of $\overleftrightarrow{AB}$ and $\overleftrightarrow{AC}$, where $E$ is on ...
0
votes
1answer
11 views

parallelepiped volume with a variable

Giving this three vectors : $$ \vec{a} = \vec{i} + \vec{j} - \vec{k}$$$$\vec{b}=2\vec{i}+\vec{j}-\vec{k}$$ $$\vec{c} = m\vec{i} - \vec{j} + m\vec{k} $$ What value must have $m$, if the volume of the ...
0
votes
1answer
18 views

Name for shape defined by volume between two concentric spheres

Is there a proper name for a shape defined by the volume between two concentric spheres? My understanding is that, formally, a "sphere" is strictly a 2D surface and there's a formal term for volume ...
0
votes
0answers
12 views

Topological conjugacy in Hénon map

$\textbf{Definition:}$ $\textit{(Topologically conjugate)}$ Let $f:A\rightarrow A$ and $g:B\rightarrow B$ be two maps. $f$ and %g% are said to be topologically conjugate if there exists a ...
0
votes
1answer
14 views

triangles and convex quadrilaterals

I've just finished a 5 hour long regional programming competition at my university, and there was one question in particular that had me particularly stumped. It is as follows: Given two parallel ...
0
votes
0answers
11 views

Turning a point in 3d space to a point on the surface of an object

guys. I'm feeling really stupid, but I'm unsure how to do this. Basically, imagine you have a box in a 10x10x10 grid. You can look at it from any angle in the room, and calculate exactly where in the ...
4
votes
4answers
285 views

How to show that these two lines are perpendicular?

Let $AEE'$ be an isoceles triangle with $\angle EAE'=90^\circ$ such that $AE=AE'$ and such that $A$, $E$ and $E'$ lie on the circle $c_1$. Let $ADD'$ be an isoceles triangle with $\angle ...
0
votes
0answers
21 views

HyperCube questions

I have three hypercube questions. 1) How many nodes does a d-dimensional HyperRing have (as a function of d) ? 2) How many edges ? 3)What is the degree of each node in a HyperRing with n nodes ? I ...
2
votes
1answer
68 views

How to prove that $r\geq\frac {1}{2(1+\sqrt 3)}$?

Each interior point of an equilateral triangle of side $1$ lies in one of six congruent circles of radius $r$. How to prove that $r\geq\frac {1}{2(1+\sqrt 3)}$?
2
votes
2answers
31 views

In $\triangle ABC$, $D$ is a point on side $BC$ that $\angle BAD = \angle CAD =\angle ABC$. If $BD=1$ and $DC=2$, what would be the length of $AB$?

In $\triangle ABC$, $D$ is a point on side $\overline{BC}$ that $\angle BAD = \angle CAD =\angle ABC$. If $\overline{BD}=1$ and $\overline{DC}=2$, what would be the length of $\overline{AB}$ ? ...
1
vote
2answers
40 views

How do you solve this trig/geometry question?

In a quadrilateral $ABCD$, if $\sin\left(\frac{A+B}2\right)\cos\left(\frac{A-B}2\right) + \sin\left(\frac{C+D}2\right)\cos\left(\frac{C-D}2\right) = 2$ then $\sin\left(\frac A 2\right) ...
-1
votes
0answers
16 views

What is the convex hull of three vertices of a triangle? What if I add a point inside the triangle?

What is the convex hull of three vertices of a triangle? What if I add a point inside the triangle? What about outside? What can we infer about the properties of convex hull from these examples?
0
votes
0answers
8 views

Move a distance $d$ from $x_i, y_i, z_i$ using yaw, pitch, roll angles as 'headings'

I'm trying to write some code for 3D turtle graphics for a Lindenmayer System, which is similar to how a plane moves. I have a current position in Cartesian coordinates. I know a set of current ...
0
votes
1answer
49 views

Why geometric median cannot be solved analytically

$\DeclareMathOperator*{\argmin}{argmin}$ For a given set of $m$ points $x_1,...,x_m$ with each $x_i\in \mathbb{R}^n$, the geometric median (or the weber point) is defined as $$\argmin\limits_{y \in ...
0
votes
2answers
30 views

Giving two equal line segments AC and BD so that they bisect each other at E. Prove that quadrilateral ABCD is a Rectangle.

Given AC=BD so angle AED= angle CEB by Prop I.15 AE+EC and BE=DE by definition of bisect So by SAS triangle AED is congruent to triangle BEC (postulate 12) Therefor AD=BC Then by Prop I. 15 ...
0
votes
0answers
42 views

P-norm Unit Ball

Proof that for $0<p<1$, $p\in \Bbb{R}$ $$\|(x,y)\|_p=(|x|^p+|y|^p)^{\frac{1}{p}}$$ doesn't define a norm in $\Bbb{R}^2$. However, $$d_p((x_1,x_2),(y_1,y_2))=\sum_{i=1}^2|x_i-y_i|^p$$ defines a ...
0
votes
0answers
11 views

Finding plane from corners of a rectangle

I have a structure with 2 3D coordinates, each a corner of a rectangle. While they're co-linear, I also know that they will never be the adjacent corners, e.g. they always lie on the diagonal of the ...
0
votes
0answers
25 views

Analog clock problem [duplicate]

The hour and minute hands on a clock line up at noon. How many more times do they line up BEFORE midnight, and where are they pointing at each of these times? Empirically, it occurs 10 times after ...
1
vote
1answer
14 views

Application of Desargues' theorem for constructions

I found this interesting document (german) on the internet. On page 8 it says: "Draw a line segment between two given points only using compass and ruler, while the distance between the two points is ...
3
votes
0answers
31 views

Generalized triangle with negative angle?

In approaching triangle problems, it is often convenient to assume there is a triangle with twice a given angle. This usually means splitting up the proof into acute and obtuse cases. I was wondering ...
1
vote
0answers
41 views

Game idea “square or not”

I have an idea of a quadrilateral / square game, and am looking for help. For the moment lets call it the "Square or Not " game. Imagine we have a big stack of cards with on each card some property ...
2
votes
0answers
60 views

Prove that $3$ points are collinear

$\triangle ABC$ is any triangle, $BD$ is its angle bisector. Everything else on the diagram is as you see it, except we are not sure if $I,K,D$ are collinear. How to prove it? Of course, $E$ is not ...
0
votes
0answers
23 views

Significance of Orthocenter in real life

I have found that the circumcenter, incenter, and centroid have some connection with real life, for example centroid is used to find the center of mass of a 2d object.. however I am unable to find the ...
2
votes
3answers
62 views

How to determine if a triangle can be drawn with the given points.

Given $3$ points $$(x_1, y_1), (x_2, y_2), (x_3, y_3),$$ how does one determine whether they are vertices of a triangle? Thanks.
1
vote
0answers
12 views

Recovering 3D point from perspective projection.

Say I have a point $(X,Y,Z)$ and that point lines in a plane with gradient $(A,B,C,)^T.$ If I know the perspective projection of that point onto an image plane has the coordinates $(x,y)$ and the ...
1
vote
1answer
13 views

What is the plane gradient?

My professor recently used the following phrase "the unknown 3D point is in a plane whose gradient is $(a,b,c)^T$". I can't seem to place his terminology anywhere on the internet. What does he mean by ...
-2
votes
5answers
19 views

Find point on a line, given the line equation and distance from the origin [on hold]

Given the line $y=3x+6$, how to find the coordinates of the points on the line which are $9$ units from the origin?
1
vote
0answers
19 views

Determining 3D position of point from 2D projection.

Say I have a 3D point $p$ and I project this point (using perspective projection) onto the image plane at 2D point $u$. Knowing that $p$ is on a plane with gradient $(a,b,c)^T$, how can I express the ...
0
votes
1answer
11 views

Showing angles are preserved by isometry.

Im trying to show that a rigid transformation (isometry) preserves angles. Here is my approach so far. Let $x,y \in \mathbb{R}^n$ and $f: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}$ be a rigid motion ...
0
votes
2answers
16 views

Prove that every set of n points in R3 with diameter L can be covered by a cube with side length L.

Prove that every set of n points in R^3(3 dimension) with diameter L can be covered by a cube with side length L. Can someone show me the picture of draw it? I can't figure it out in picture.
-1
votes
0answers
36 views

Trigonometry problem - No right angles triangle [on hold]

I got a trigo problem I need to solve asap :p I've got a triangle, with no right angle. 1 of the side length is know, and the opposite angle is known too. I am spliting the triangle with a line ...