shape, congruence, similarity, transformations, properties of classes of figures, points, lines, angles
1
vote
1answer
71 views
circle of inversion
Determine the equation of the circle reflection of the line $x = 2$ if the
circle of reflection is $x^2 + y^2 + 2x = 0$ which in standard form is $(x+1)^2+y^2=1$ where $radius=1$ and center is ...
2
votes
1answer
52 views
Center of circle that has two points on its circumference and a known tangent
I've found a related question, which helped me get started on this. I can get it to work for the example on the question, but I'm running into an issue when the tangent is not y = 0.
Other question ...
0
votes
1answer
21 views
Condition for a quadrilateral to be tangential
Define a quadrilateral to be tangential iff all four of its internal angle bisectors meet a a single point. Prove the following:
A quadrilateral is tangential if and only if three of of its ...
-1
votes
1answer
22 views
Pascal's theorem in geometry
We denote $P= WX \cap YZ$ to mean point $P$ is the intersection of lines $WX$ and $YZ$.
The problem is about pascal's theorem: Let $ABCD$ be a cyclic quadrilateral. Let the tangent lines at A and at ...
2
votes
1answer
37 views
Can one use Pick's theorm to prove that area size 5 covers at least 6 grid points?
According to Pick's Theorem, the size of an area $A$ can be calculated by the sum of
the interior lattice points located in the polygon $i$ and the number of lattice points on the boundary placed on ...
2
votes
1answer
84 views
help on a geometry problem
$ABCD$ is a convex quadrilaterial such that $AC=BD$. $AC$ and $BD$ intersect at $E$ and $\angle AEB=66^{\circ}$. $F$ and $G$ are the midpoints of $AD$ and $BC$, respectively. $FG$ intersects $AC$ ...
1
vote
2answers
18 views
What's the geometric interpretation of a semidenifite matrix smaller than identity matrix?
What's the geometric interpretation of a semidenifite matrix in terms of eigenvalues/eigenvectors with the condition:
$$
0 \preceq W \preceq I
$$
3
votes
4answers
143 views
What's the best 3D angular co-ordinate system for working with smartfone apps
This is very much an applied maths question. I'm having trouble with Euler angles in the context of smartphone apps. I've been working with Android, but I would guess that the same problem arises ...
5
votes
1answer
56 views
Inscribing equilateral triangle in rectangle
Problem: What is the area of the largest equilateral triangle that can be inscribed in a rectangle with sides $10$ and $11$?
(The problem comes from an old high school math contest. I believe it's ...
3
votes
0answers
46 views
Maxmin sum of squares construction
In triangle ABC construct thru B a line so that the sum of squared
distances from A and C to this line was MAX, MIN, or a given p*p.
How to do this construction?
1
vote
1answer
27 views
Change in angle due to rotation in another plane
I hope someone can help me figure this out.
Step 1: We are looking at the ZX plane (front view). I have two lines, which have been rotated 15 degrees around the Y axis. At this step both lines are ...
2
votes
1answer
57 views
$Pic(\mathbb{C}P^1)$
I have to explain the Picard group to some people that doesn't know the concept of sheaf. So is there a method to calculate $Pic(\mathbb{C}P^1)$ without sheaf theory? Is there a simple and easy proof ...
1
vote
0answers
24 views
Relation between triangle and its circumscribed circle, on the surface of a sphere. Generalizations to higher dimensions.
Consider the unit sphere in $R^3$ and an equilateral triangle of side length 1, with all vertices on the surface of the sphere. Now project (from the center of the sphere outward) the triangle and its ...
0
votes
3answers
48 views
Given a line segment. Construct an equilateral triangle with one side the given line segment.
I found this problem in a website, but I don't know how to solve it.
Given a line segment $AB$. Construct an equilateral triangle with one side being $AB$.
3
votes
1answer
37 views
area of trapezium
A trapezium has perpendicular diagonals and altitude 4. If one of the diagonals has length 5, find the area of the trapezium
A 12
B 50/3
C 25/2
D 40/5
I guess the answer is C. I divided the ...
0
votes
0answers
21 views
How can I align the angle between points with the magnetic heading as the points move?
I have 3 robots which must track a point. The distance between all the robots and the point is known so a triangle can be formed between any 2 robots and the point.
If I find the angles in the ...
1
vote
0answers
26 views
Calculating sheet size required for creating a cubic corrugated box
Basically I am developing a software for Corrugated Box Manufacturing Industry, but stumbled upon the calculations regarding the initial sheet size and weight required to create box of a particular ...
4
votes
1answer
48 views
dividing planar regions into congruent parts
I've been looking for counterexamples, with no success, to this for a few days running:
Suppose for a planar region $R$ with finite positive area, there is a
point $x$ where all lines of ...
1
vote
1answer
90 views
Identify the curve from the sample points
I am writing a script which will identify the patterns drawn on the touch-pad of the laptop. I have generated all the points where user moved his finger over the touch-pad using synclient.
Now i ...
0
votes
1answer
46 views
A question about definition of hyperplane
In a course I took, the instructor gave a definition of hyperplane as follows:
Let $X$ be a vector space and $f:X\to\mathbb{R}$ a linear function. Then $M_a=\{x\in X|f(x)=a\}$ is called a hyperplane. ...
1
vote
1answer
73 views
Trig, matrix transform, or…?
I am working on an app that will transform a figure such as this:
Into this:
In short, the grey "canvas" is deformed so that the inner black quadrangle is as close to a rectangle as possible, ...
0
votes
0answers
30 views
Mymultiple image geometry
I have to work with multiple aerial images. the objective is to reconstruct 3d features.
For a particular object, i want to find the images which are giving good viewing geometry than others. so ...
2
votes
1answer
18 views
Non-singular-non-redundent representation of rotations and scaling in 3 dimensions
First, lets pin down what singularities mean.
We define two mappings of vectors $M$ and $N$ as close if
$|M(v)-N(v)|\le\epsilon|v|$ for all $v$ (at least for linear mappings).
We define two ...
0
votes
2answers
82 views
hyperbolic triangles angle sum
In the accompanying figure M and N are the respective (hyperbolic) midpoints of AB and AC. $\phi$ and $\theta$ are indicated angle measures. Determine, with proof, which of the following is true: (1) ...
3
votes
1answer
115 views
Cutting a cube by plane cuts
This is an extension of a 3rd grade problem.
How many pieces can one get at most if one cut a unit cube with n plane cuts?
1,2,4,8, ???
And assuming cutting through an area 1 takes time t, what is ...
0
votes
0answers
21 views
a simple goemetric inspection which I cannot get it
Given two rectangles(in $R^2$)$A,B$ which have the same size $\alpha_1\times\alpha_2$($\alpha_1>\alpha_2$), suppose the anlge(here angle is less then $\pi/2$) between the long sides of any two ...
4
votes
1answer
93 views
Trisecting a paper using hand and without using a ruler or compass
This is a practical problem born while folding a paper.
We can bisect a paper by using only hand.
$\star$ Easy, fold it so that the two ends (of the length) coincide and press
the paper to get ...
2
votes
1answer
30 views
How can I find the shortes path on square prism?
My boss ask us a geometry question a few hours ago, but we can't find a solution at all..
We have a square prism that long edge is 12 cm and short (base) edges are 4 cm.
We have 2 points (A and ...
0
votes
0answers
28 views
Geometry Question with irregular hexagons
Suppose you have a rectangle with sides x and y and both numbers are integers and have no factors. now draw lines inside this rectangle starting with a line at 45 degrees coming out of a corner and ...
4
votes
1answer
31 views
Geometry question with rectangles purely out of curiosity
Apologies in advance, I really cannot think of an intelligent or easy way to explain this.
You start out with a rectangle. Then you draw a straight line out of a right angled corner at 45 degrees ...
1
vote
2answers
48 views
triangles in hyperbolic geometry
I have to prove which of the following is true: (1) DC = AB,(2) DC < AB, or (3) DC > AB (all hyperbolic length).
The only thing that im not sure about is whether vertical angles would work here. ...
0
votes
0answers
28 views
Properties of some hypersurface
$S$ is a compact surface in $\mathbb{R}^n$ of positive definite second fundamental form.
$V= span \left\lbrace e_1, \dots , e_m\right\rbrace .$
$S^\prime \subset S$ is the preimage of $V\cap ...
0
votes
0answers
71 views
Overlapping Areas
Knowing the areas of A, B and C, is there an analytical way to find out if two arbitrary shapes overlap each other in the plane? (See image here: http://i.imgur.com/RWsqysT.jpg)
More formally, I'm ...
0
votes
0answers
14 views
How to reduce loops of prolate cycloid
I am trying to reduce the loops of a prolate cycloid in my code. I also want the $x$-value to increase significantly faster than the $y$. I used the parametric equations to write the code. I have been ...
0
votes
1answer
14 views
Which point on or inside or outside the frame move in a circular trajectory?
Which point on or inside or outside the frame move in a circular trajectory?
0
votes
1answer
23 views
Unique sets of angles?
Consider shapes composed of isosceles right triangles of a unit size and joined at edges of equal length, with the restriction that any such shape must have a perimeter edge count of n+2, where n is ...
4
votes
0answers
48 views
Invariant of matrix under elementary transformations
$\DeclareMathOperator{\rank}{rank}$
Let $A \in \mathbb R^{n \times n}$, $b \in \mathbb R^n$, $c \in \mathbb R$. Consider the following matrix
$$
B = \begin{bmatrix} A & b \\ b^T & c ...
0
votes
1answer
34 views
Isometries to prove rhombus?
Suppose that the diagonals of a quadrilateral are perpendicular bisectors of each other. Use isometries to prove that the quadrilateral must be a rhombus.
Im unsure how to use isometries to prove this
...
1
vote
1answer
17 views
2D triangulation
I understood what it is from the following link:
http://electronics.howstuffworks.com/gadgets/travel/gps1.htm
But I want to know :
In a 2D plane, if we know the (x, y) positions of three “guard” ...
0
votes
2answers
35 views
split irregular line in equal parts
I have this irregular line and I want to split it in, for example, ten equal parts. How can I do that?
Thank you!
0
votes
1answer
21 views
Let $f$ be glide reflection, proove $\frac{1}{2}(\vec x + f(\vec x)) \in g$
Let $f$ be a glide reflection with $\sigma_{\lambda,g}=\vec x + 2 (d-\vec n \bullet \vec x) \vec n+\lambda \vec{n_r}=A\vec x + 2 d\vec n + \lambda \vec{n_r}$ with $g=\lbrace \vec x:\vec n \bullet \vec ...
1
vote
1answer
53 views
Two sticks between two concentric circles
Let's start with two concentric circles of radii $r<R$. Then we put two sticks inside the outer circle while avoiding the inner circle, say $AB$ and $CD$.
Then we compare the length of inner ...
0
votes
1answer
24 views
Finding point in two parallel lines in 3d?
The line $L_1$ that goes through the point $A(4,3,-2)$ and its parallel to the line $(x=1+3t, y=2-4t, z= 3-t)$, if $P(m,n,-5)$ belongs to $L_1$, determine the values for $m$ and $n$
I really don't ...
1
vote
1answer
49 views
Meaning and types of geometry
I heard that there's several kind of geometries for instance projective geometry and non euclidean geometry besides the euclidean geometry. So the question is what do you mean by a geometry, do you ...
0
votes
1answer
17 views
Isometries of two dimensional space
I know that isometries of R^n are composed of orthogonal transformations followed by translation. My questions are:
In 2-D space, there are glide reflections, but why must the glide be according to ...
4
votes
1answer
41 views
Optimal rotation to align a circle with external points
I have a circle $C$ with radius $r$ and a set of finite points $P=\left \{ p_1,p_2,\ldots,p_n \right \}$ are identified external to the circle $C$. These points may lie on the exterior or the interior ...
0
votes
0answers
46 views
What's the difference between a 2-sided and 2-sided strip polytan
There are 14 2-sided tetratans and 13 2-sided strip tetratans. The sets are identical, except the square is missing in the strip version. My best guess is that for strips, no vertex can have an edge ...
1
vote
1answer
60 views
finding Length of a diagonal
Given Quadrilateral ABCD in such that $AB<BC<CD$ creating increasing arithmetic progression with sum of $27$ cm.
$\measuredangle BCD=60^{0}$. the diagonal $BD=\sqrt{133}$ cm, and it divided ...
0
votes
2answers
124 views
Calculating circle radius from two points and arc length
For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius.
I have 2 way points the ...
4
votes
1answer
61 views
Angular alignment of points on two concentric circles
I have two concentric circles $C_1$ and $C_2$ with radii $r_1,r_2$ such that $r_1< r_2$and a set of finite points $P=\left \{ p_1,p_2...p_n \right \}$ and $Q=\left \{ q_1,q_2...q_n \right \}$ are ...
