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

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2
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0answers
8 views

Intersections of Planes, Points…

I'm in sixth grade and learning geometry. Can someone tell me if I'm correct? The intersection of a point and a point is a point. The intersection of a point and a line is a point. The intersection ...
1
vote
0answers
9 views

Iterated circumcenters - proving collinearity and establishing distance ratios

Let $P_0, P_1, P_2$ be three points on the circumference of a circle with radius $1$, where $P_1P_2 = t < 2$. For each $i \ge 3$, define $P_i$ to be the centre of the circumcircle of $\triangle ...
-2
votes
0answers
17 views

Distance between point and line with cartesian coordinates

$A(a_1,a_2)$, $B(b_1,b_2)$ and $C(c_1,c_2)$ are points. $A$ and $B$ form a line $AB$. What the distance between $C$ and $AB$ ?
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0answers
14 views

How to find location - multilateration

I have this data: $$ {x1} = 473463,100288[m]\\ {y1} = 5924242,046998[m]\\ {z1} = 0[m]\\ {t1} = 41919,84025[s]\\ {x2} = 473483,237020[m]\\ {y2} = 5924212,730018[m]\\ {z2} = 0[m]\\ {t2} = ...
0
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0answers
23 views

Number of polyhedron diagonals

Suppose that I have a polyhedron with given number of faces, edges and vertices are given. Is there a formula that gives me the number of polyhedron diagonals, ...
-2
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0answers
20 views

Geometry midpoint [on hold]

John wants to center a canvas which is 8 ft wide on his living room wall which is 17 ft wide. Where on the wall should John mark the location of nails if the canvas requires nails every 1/5 of its ...
0
votes
2answers
49 views

Probability that distance of two random points within a sphere is less than a constant

Two points are chosen at random within a sphere of radius $r$. How to calculate the probability that the distance of these two points is $< d$? My first approach was to divide the volume of a ...
1
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1answer
36 views

Geometry question, prove that $\angle APB = \frac12 (\angle AMB + \angle CMD)$

I got the following question: Prove that $\angle APB = \frac12 (\angle AMB + \angle CMD)$, with the following figure given: Also, the following information is given: $M$ is the centre of the ...
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vote
8answers
117 views

How can I parametrize $|x|+|y|=1$

I need parametrize $|x|+|y|=1$ but I don't know how to parametrize. I know that it is a rotated square, I would like understand so if you can explain to me like if I was still, thanks
2
votes
3answers
42 views

Geometric interpretation of inverse complex function?

Function $f\colon\mathbb{R}\to\mathbb{R}$ and its inverse $f^{-1}$ are symmetric over line $y=x$. It's easy to imagine inverse of real function, we just have to "flip" the plot over $y=x$. But what ...
-3
votes
0answers
23 views

area of intersection between 2 circles [on hold]

could you please tell me how you solved 1/2(R)2 sin 120' Area of intersection between two circles Thanks.
2
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0answers
20 views

Multiplicative version of convex hull

The convex hull of a finite set of points, $(x_i,y_i) \in \mathbb{R_+}^2$ ($i=1,...,n$), is defined as: $$\left\{(\sum_{i=1}^{n} \alpha_i x_i,\sum_{i=1}^{n} \alpha_i y_i) \mathrel{\Bigg|} (\forall i: ...
2
votes
0answers
49 views

how many spheres can all touch a single one?

In Euclidian space, one sphere can be touched by how many equal-sized spheres simultaneously? Intuitively, the answer is 12. Is there a (geometrical) proof of this?
1
vote
1answer
360 views

Which Area of mathematics can explain this?

http://i.stack.imgur.com/rij3X.png As in the image we can see that ray of light is bouncing off objects. Black ones are opaque objects and white ones are transparent objects. I want to calculate how ...
0
votes
1answer
12 views

Show that a line is tangent to a circle in the extended complex plane.

The straight line $l$ in the extended-complex plane pasess through $2+i,2+2i$.The circle $C$ centered at $-1-2i$ with radius $3$. First, I find the parametrization of the straight line which is $$z = ...
2
votes
1answer
59 views

Is angle an instance of something more abstract than angle? [on hold]

Is an angle (as generally understood) best described as a relation or a quantity?
1
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1answer
24 views

Half secant in Circle

OT and OQP are tangent and secant respectively drawn from external point $O$ of a circle centered at $C$. Mid-point M of the secant is joined to center $C$,an arc is drawn with center $O$ to be ...
0
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0answers
9 views

Minimum Curvature for Circular Trapezoids? [on hold]

I am thinking any shape that can be close to circular trapezoid having the surface curvature less than circular trapezoid. About the minimum curvature here. About the naming of circular trapezoids in ...
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votes
1answer
89 views

Whats the size of the X angle? [on hold]

In this question, we have no information about line. we just know that we have some angels and we need X. Please solve this question by geometry. http://borjianamin.persiangig.com/File1.jpg the ...
-2
votes
1answer
19 views

Relations involving the altitudes and orthocenter of a triangle [on hold]

For acute $\triangle ABC$ with altitudes $AD$, $BE$, $CF$, orthocenter $H$, and area $S$, I have to prove that: $$AB^2 + HC^2 = BC^2 + HA^2 = AC^2 + HB^2 \tag{a}$$ $$AB \cdot HC + BC \cdot HA + ...
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votes
1answer
27 views

$ DB\cdot DC = HA\cdot HB + KA\cdot KC.$ [on hold]

We have a point $D$ on the hypotenuse $BC$ of a right triangle $ABC$. $H$ and $K$ are the projections of $D$ on $AB$ and $AC$, respectively. I have to prove that: $$ DB\cdot DC = HA\cdot HB + ...
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votes
0answers
36 views

Geometry - points on a sphere [on hold]

Is there a way, or is it possible to describe a set of points on a sphere so that the they are distributed over the surface with maximal symmetry (or just evenly distributed)?
1
vote
1answer
31 views

Maximum number of equilateral triangles in a circle

I am stuck with a question. Given a circle with radius $x$ cm, what is the maximum number of equilateral triangles of side length 1 cm that can fit in the circle without overlapping or ...
0
votes
0answers
9 views

polar moment of area for nonplaner circle (cup)

Can somebody tell me the polar moment of area of chord for a sphere. for example when you cut a sphere at a point other than from center? Also polar moment of area for curved axis symmetry ?
8
votes
0answers
42 views

Congruent quadrilaterals in a tri-colored $72$-gon

I recently watched a movie (A Brilliant Young Mind) in which this problem appeared: Let the vertices of a regular $72$-gon be colored red, blue, and green in equal parts. Show that there are $4$ ...
1
vote
1answer
23 views

Selecting a basis such that the orientation is preserved

I need to map a polygon from a 3D plane to a 2-dimensional basis, do some processing, and project the result back to 3D. The vertices in the polygon is always ordered counterclockwise and this ...
-4
votes
0answers
15 views

What are the possible applications of homothety? [on hold]

What are the possible applications of homothety? Give me some examples, please. I know it can be used to proof coincidence of lines but what else?
0
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1answer
9 views

Isometries and Orthogonal Matrices

I know how to show that multiplying by an orthogonal matrix preserves the angle and distance between two vectors. I have seen everywhere that Orthogonal matrices are kind of related to rotations and ...
3
votes
4answers
25 views

Euclidean Geometry Quadrilateral Problem

When the quadrilateral is a square, rectangle, or parallelogram, the problem is very simple since X1Y1=X2Y2=X3Y3=a=b, but this falls apart when the quadrilateral is something like a trapezoid. How ...
0
votes
3answers
36 views

What is the relationship between the two radii and the two volumes? [on hold]

I don't understand this question, as it says to use the formulas for the volume and radius of a sphere. Formulas are $V=\frac43 \pi r^3$ $r=\sqrt[3]{3V/4\pi}$ Volume for the first sphere is ...
3
votes
1answer
31 views

How do I represent a Mobius Band Triangle Parametrically

I am trying to describe a Mobius band in the shape of a triangle like this: parametrically in terms of its $x$, $y$, and $z$ functions. Is this even possible? I know a basic mobius strip can be ...
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0answers
13 views

Is there any mathematical significance of the set-theoretic union of the hemispheric middle thirds of an oriented (e.g., rotating) sphere?

The title says it all, but we can add a synonymous formulation: Is there any mathematical significance of the region of an oriented (e.g., rotating) sphere whose latitudes are neither small nor large? ...
2
votes
0answers
15 views

Area of a sphere bounded by hyperplanes

Say we have a sphere in d-dimensional space, and k hyperplanes (d-1 dimensional) all passing through the origin. Is there a way to calculate (or approximate) the area of the surface of the sphere ...
0
votes
1answer
25 views

Dividing a Triangle by Connecting the Midpoints of its Sides

If $T$ is any triangle. Suppose we connect the midpoints of its sides forming four triangles. Does these four triangles have the same angles?
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votes
1answer
20 views

Rotated parabola 2d vertex

I'm implementing an application where I need to get the vertex of a parabola, the parabola might be tilted; so it can have an angle with the x-axis not necessarily vertical or horizontal. Can I get ...
4
votes
3answers
63 views

Motivations for Hyperbolic Geometry

Why would one study hyperbolic geometry? I am only aware of the motivation where you give axioms for elementary euclidean geometry and then start to wonder wether the parallel axiom is necessary. You ...
0
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0answers
11 views

Solid Angle Formula Derivation

How to derive the formula for solid angle that is $2\pi(1-cos \theta)$ ? I searched on Wikipedia but could'nt understand the double integral method they provided.I searched Wikipedia:Solid Angle Can ...
0
votes
1answer
30 views

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

If you could arrange building blocks for example toy cubes so that every next cube was tilted over its base by 20 degrees and rotated to it's right by 15 degrees, it would form a helical structure. ...
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0answers
21 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 ...
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0answers
21 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: $$\ker (\bar{m}-\bar{id})^2 \cap \{x_0=1\}$$ ...
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votes
0answers
43 views

Neccesary condition for perpendicularity [on hold]

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
8 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
36 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
30 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
54 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 ...
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votes
2answers
43 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
56 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), ...
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votes
0answers
26 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)