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
vote
1answer
62 views
+50

What rotation rules can be applied to stacked cubes to make a 3D spirograph?

If you arrange building blocks for example toy cubes so that every next cube is tilted over its base by 30 degrees and rotated to it's right by 12 degrees, it would wind through space in a helical ...
0
votes
0answers
22 views

Geometry rotation and common points

The equation of the rotation surface S which is created by the rotation of the hyperbola t: { $\frac{x^2}{9}-\frac{z^2}{4}=1$ ; $y=0$} is S:$\frac{x^2}{9}+\frac{y^2}{4} -\frac{z^2}{4}=1$,right? and ...
1
vote
0answers
23 views

Explanation of $\ker (\bar{m}-\bar{id})^2 \cap \{x_0=1\}$

Let $m$ be an isometry on $\mathbb{R}^2$ which is a composition of a reflection and a translation. The way to find the axis of the isomtry is by solving: $$\ker (\bar{m}-\bar{id})^2 \cap \{x_0=1\}$$ ...
-1
votes
0answers
44 views

Neccesary condition for perpendicularity [closed]

Triangle $\mathit{BCD}$ lies in plane $P$ and $\mathit{AD}$ and $\mathit{DC}$ are perpendicular ($A$ is the top of the prism $\mathit{ABCD}$) $\mathit{AD}$ is perpendicular to $P$ if which of the ...
0
votes
0answers
9 views

Shear Stress of Circular non-planer plate

Shear Stress of plan circular plate is given by T = M/($2*t*$Pi*r^2) What will be Shear stress of non-Planer circular plate? For example chord of shpere or any other circular plate but curved in ...
0
votes
0answers
41 views

How to derive parametric equations of a curve from its geometric property?

A straight segment of line of variable length $h$ is attached to the origin $O$ and to the other free end $M$ another straight segment of variable length $a$ is attached . Its endpoint $P$ has two ...
0
votes
1answer
32 views

What is the radius of smallest circular disk large enough to cover every acute isosceles triangle of a given perimeter $L$?

What is the radius of smallest circular disk large enough to cover every acute isosceles triangle of a given perimeter $L$? Let $a,a,b$ are the sides of the isosceles triangle whose perimeter is ...
2
votes
2answers
55 views

How to determine a kind of distance between two permutations?

Let's define a distance between two permutation of length $N$: it is the minimum steps to change one to be another. "A step of change" means that exchanging any two elements' location. For example, ...
0
votes
1answer
38 views

Find the cosine of the angle at the vertex of an isosceles triangle having the greatest area

Find the cosine of the angle at the vertex of an isosceles triangle having the greatest area for the given constant length $l$ of the median drawn to its lateral side. I tried to solve this ...
0
votes
2answers
47 views

Two circle intersection: help on understanding a specific explanation

As someone with basic algebra knowledge, I am having trouble understanding Paul Bourke's explanation on "Intersection of two circles" on this page. The specific part that I don't understand is where ...
6
votes
1answer
61 views

Is this GRE math problem wrong?

I'm working out of the Manhattan GRE test prep book and I've come across a question that I can't figure out why they chose the answer they did. "Perpendicular lines m and n intersect at point (a,b), ...
0
votes
0answers
27 views

Find the maximum volume of the cylinder.

A cylinder is obtained by revolving a rectangle about the $x-$axis,the base of the rectangle lying on the $x-$axis and the entire rectangle lying in the region between the curve $y=\frac{x}{x^2+1}$ ...
1
vote
1answer
28 views

Equation to get the center point of the union of n ellipses?

If I have 3 ellipses that all intersect such as in image. How can I get the center point of the Union of all three ellipses? (Basically the center point of the red area in the image)
0
votes
0answers
5 views

Get LWH with volume ≥ X and smallest possible surface area

The formula for volume of a rectangular prism is $l\cdot w\cdot h$, and surface area is $2(wl + hl + wh)$. If I already have the volume (ie 20m²) as $X$, what are the optimal values for $l$, $w$, and ...
-3
votes
1answer
65 views

Find x in the triangle [closed]

Find x, even if I turn out not
1
vote
1answer
24 views

Expression of reflection isometry in the complex plane

Using the fact that an anti-displacement in the plan has the form $$f(z) = a \overline{z} + b$$ I have done some computation to find the reflection about the line passing through two points $P$ and ...
1
vote
1answer
69 views
+200

3D projection coordinates onto 2D plane to determine transformation matrix?

I'm not sure if there is an actual solution to this problem or not, but thought I would give it a shot here to see if anyone has any ideas. So here goes: I basically have three vertices of a rigid ...
1
vote
1answer
33 views

Surface area of circle extracted from a tube wall

I have made a hollow tube (thickness $1$mm) having inner radius $89$ mm and outer radius $90$ mm (length $400$ mm, can be higher). then I made a circular (circle radius $25$ mm) cut perpendicular to ...
0
votes
1answer
30 views

If $AD=999$ and $PQ=200$, find the sum of the radii of those incircles.

Let $ABCD$ be a convex quadrilateral with $\angle DAB =\angle BDC=90° $. Let the incircles of $\Delta ABD $ and $ \Delta BCD $ touch $BD$ at $P$ and $Q$, respectively with $P$ between $Q$ and $B$. If ...
-2
votes
1answer
30 views

Finding a point along a circle a certain distance away from another point [closed]

How do I find the point(s) C (and C') which: lies on a circle centered at a point B with radius r is at distance d from point A A specific case would be: A = (0,0) B = (5,7) r=5 d=5
1
vote
3answers
37 views

Chords $AB$ and $AC$ divide the area of the circle into three equal parts.If the angle $BAC$ is the root of the equation,$f(x)=0$,then find $f(x)$

$A$ is a point on the circumference of a circle.Chords $AB$ and $AC$ divide the area of the circle into three equal parts.If the angle $BAC$ is the root of the equation,$f(x)=0$,then find $f(x).$ I ...
-2
votes
1answer
32 views

Geometry-Is this a correct question?

ABis parallel to CD.The values of the angles are a,3x,2x and z as shown in the figure.Also,2x+z=100 degrees.Now it is required to find the value of angle a.I tried hard but could not solve it.I ...
-3
votes
1answer
22 views

how to find the locus when distance from the origin is defined as d(x,y) = max { |x|,|y|},d(x,y) =a (where 'a ' is a non zero constant ) [closed]

How to find the locus when distance of any point from the origin is defined as d(x,y) = max {|x| |y|} where d(x,y) = a ( where is a non zero constant) I have a very long list of questions like these ...
1
vote
1answer
21 views

When is a quadratic Bézier curve nearest the origin?

Consider a planet moving along a quadratic Bézier curve through points A B C, with $t$ = time: $\qquad \operatorname{curve}( t, A, B, C ) \equiv t' (t' A + t (2B - A)) \ + \ t (t' (2B - C) + t C ) $, ...
0
votes
0answers
17 views

Inverse curve fitting to a regular grid

Given a fixed grid of regular polygons (square, trianglular or hexagonal) and a curved path, (imagine a river), how do you generate or select the set of grid links that most closely matches the curved ...
3
votes
3answers
28 views

change of basis and inner product in non orthogonal basis

I have some vector, originally expressed in the standard coordinates system, and want to perform a change of basis and find coordinates in another basis, this basis being non-orthogonal. It's ...
1
vote
1answer
28 views

Maximum no. of laddoos of diameter $6$cm in a box of given dimension

What is the maximum number of laddoos having diameter of $6\text{ cm}$ that can be packed in a box whose inner dimensions are $24\times 18\times 17\text{ cm$^3$}$. I found that at the lower label ...
5
votes
2answers
66 views

Trapezoids in a square

Good day As part of a problem I need to show that AB is parallel to CD, with the given info on the image. All the segments marked red are equal, all 1-stripe grey equal etc. I'd like to prove ...
-4
votes
0answers
67 views

Locus of points on a curve for constant segment lengths squared sum $ OM^2 + MP^2 $ [closed]

EDIT : This edit supersedes the post and edits before it as it is simplified and freshly done once again. After sometime they would be deleted if ok. Anyway: Two points M and P in a plane (Origin ...
1
vote
0answers
30 views

How many discs necessary to cover a big circle?

Let be a circle a radius R,and other discs of radius r,palpable. I can cover the circle,completly, with a minimum number of discs,N.I can't cut any disc. What is the value of N,according to R and r? ...
0
votes
1answer
41 views

Transform square to rectangle with natural sizes.

I'm newbie in math, in my play with math, I came across the following problem: Let $A$ the area of square with sizes: $(l_1 = l_2) = \sqrt A$ How transform $(l_1,l_2)$ to $(l_1',l_2')$ where ...
0
votes
2answers
27 views

How many face we could make regular convex polyhedron

I want to tile the sphere as many face as possible. And I want every face be the same size and shape. Is it possible to generate more than 100 or 1000 faces of regular convex polyhedron?
2
votes
1answer
67 views

Find quickest line of interception to a moving object

First, a visual illustration of the problem: http://tube.geogebra.org/m/1512793 The goal is to mathematically predict the direction in which the player need to run to intercept the ball as fast as ...
5
votes
1answer
62 views

Arranging circles around a circle

$N$ circles are given by their radii: $r_1$, $r_2$,..., $r_N$. They are arranged around another circle so that they pack, like in this picture (order of $N$ circles should be preserved): What is ...
8
votes
2answers
132 views

What hyperbolic space *really* looks like

There are several models of hyperbolic space that are embedded in Euclidean space. For example, the following image depicts the Beltrami-Klein model of a hyperbolic plane: where geodesics are ...
-1
votes
2answers
36 views

Finding equation for hyperbola given 2 points and center [closed]

A hyperbola passes through (3,−2), (7,6) , its focal axis is on OX and its center is (0, 0). How can I write the equation for this hyperbola?
2
votes
2answers
48 views

Determining the minimum dimension required for embedding a finite group

Consider the groups $S_3$ and $S_4$ which are the symmetric groups on 3 and 4 elements respectively. We note that $S_3$ can be realized geometrically as the set of all rotations and reflections of a ...
0
votes
1answer
28 views

Is there proof anywhere of the continuity of spherical coordinates and cylindrical coordinates?

Im thinking they are continuous as a composition of continuous functions, but then again. I don't know exactly which specific(precisely speeking) functions are in question.. Any thoughts on this?
4
votes
1answer
44 views

Determining the angle of a photograph containing known parallel objects/lines.

I have a photograph of a house and a window taken at an angle. I'm trying to determine the angle at which the photograph was taken. The house has wooden siding that can be safely assumed to be ...
0
votes
1answer
23 views

How would I make continuous functions to form these sets? Parametarizing of sets

How would I make continuous functions to form these sets?(So the domain is connected) I need continuous functions that map connected sets to these in question. $1. \text{Cone}$ $$(x,y,z)| \ ...
1
vote
0answers
13 views

Given a point and figure, how can I find the distance?

I have this two formulas in Matlab: the_p=atan2((-y(2)+obs(2)),(-y(1)+obs(1))); phi_p=acos((y(3)-obs(3))/(norm(y-obs))); ... where y is a 3d point and obs is a ...
1
vote
1answer
33 views

Two cevians divide a triangle into 4 parts. Calculate the area of the 4th part, given the other 3.

Good day Here is the question: Connecting $AF$ and setting areas $\triangle ADF = x$ and $\triangle AFE = y$: $\frac {9+x}{12} =\frac y{15}$ $\frac{15+y}{12} =\frac x9$ from the ratios of the ...
2
votes
1answer
44 views

Non-orientable submanifolds

Let $M$ be a $n$-manifold and let $S \subset M$ be a non-orientable $n$-dimensional submanifold possibly with boundary. Under what conditions can I conclude that $M$ is also non-orientable? Is ...
0
votes
0answers
23 views

sqrt(bc) inversion problems

Can anyone explain to me what $\sqrt{bc}$ inversion is? A problem on that topic would be helpful too. I know the basis of geometric inversion and I'm searching for methods to solve Olympiad geometry ...
2
votes
0answers
33 views

Invariant points and lines under homography

Given a matrix representation of an homography in a real projective space $P(\mathbb{R^3})$, what is the general procedure to calcule the invariant subspaces? A brief description would be enough.
0
votes
0answers
15 views

Determining the octet in Bresenham's Line Drawing Algorithm.

First question, I have tried to calculate the expression, $d_{i+1} = d_i + 2 * \Delta y - 2 * \Delta x (y_{i+1}-y_i)$ for the four quadrants. Irrespective of the quadrant, the expression was found to ...
0
votes
0answers
42 views

Isometries of hyperbolic space

The metric tensor for the Poincaré ball model of hyperbolic geometry is $$ g_{ij} = \frac{\delta_{ij}}{(1 - \lvert \mathbf{r} \rvert^2)^2} $$ where $\mathbf{r}$ is the position in the ambient ...
1
vote
0answers
23 views

Line tangent to circle inside an isosceles triangle

If you take a circle enclosed inside an isosceles triangle, and then draw a line which is tangent to the circle and which intersects with the two equal sides, is that line parallel to the triangle's ...
0
votes
1answer
11 views

Write the co-ordinates of E such that the parallelogram ABCE is a rhombus.

I'm unsure how to do this and it's always in my exams. (The original shape was a triangle and E was originally not a point) A:(1,0) B:(0,8) C(7,4) Gradient of AC:2/3 AC equation:2x - 3y - 2 = 0 ...
1
vote
1answer
40 views

Constant rank theorem: intuition?

Let $f: \mathbb R^n \to \mathbb R^m$ be smooth and let $x_0 \in \mathbb R^n$ be such that $\operatorname{rank}{(J_f(x_0))} = k $. Then there exists a neighboudhood of $x_0$ and diffeomorphisms $\phi, ...