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

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0answers
7 views

What is number of faces in a k-ary n-dim cube?

What is the number of $(n-r)$ dim faces for a $k$-ary $n$-dim cube ? Definition of k-ary cube: In a $k$- ary $n$- cube , each node is identified by an $n$-bit base-$k$ address $b_{n − ...
1
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1answer
15 views

An inequality about the areas of two triangles

There is point $P$ in a triangle $ABC$. $Q,R,S$ are the symmetric of $P$ with respect to the sides $AB,BC,CA$ respectively. I have to prove that the area of $ABC$ is $\geq$ than the area of $QRS$. ...
0
votes
0answers
8 views

Stellating the Octahedron

I am trying to create a very primitive animation/demonstration that shows the stellation of an octahedron to yield the stella octangula. Unfortunately, it seems that the mental image I have for ...
7
votes
2answers
120 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 ...
0
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0answers
4 views

What is the perspective projection of a 3d point relative to a quarternion encoded camera?

I'm representing a camera on the cartesian space as a tuple of a 3d point (position) and a quarternion (rotation). I get the front, right and up vectors of the camera by applying the quaternion to the ...
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0answers
10 views

About the stable/invariant point sets in a plane with respect to shift/linear transformation

I'm reading Vlademir A. Zorich's Mathmatical Analysis I, meeting exercise question as following: a) A set $S \subset X$ is stable with respect to a mapping $f:X \rightarrow X$ if $f(S) \subset ...
1
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1answer
28 views

Find cartesian coordinates of the incenter

$A(a_1,a_2)$, $B(b_1,b_2)$ and $C(c_1,c_2)$ form the triangle $ABC$. What are the cartesian coordinates of the incenter and why?
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1answer
30 views

Distance from point to sides of a quadrangle

$A(a_1,a_2)$ , $B(b_1,b_2)$ , $C(c_1,c_2)$ and $D(d_1,d_2)$ form a quadrangle. What is the sum of (perpendicular) distances from point $P(p_1,p_2)$ (inside the quadrangle) to all the four sides? I ...
1
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1answer
36 views

Geometry ( dividing a circumference in 360 equal parts)

Is it possible to divide a circumference 360 shares using only ruler and compass? That is, the former (ancients) did so (like this) ? To my knowledge it is possible through exact processes divide it ...
6
votes
2answers
75 views

Sphere packing question

I'm a secondary school maths teacher, currently on my holidays working through some maths problems for fun. Here is one I have done, but it felt too easy, so if you could check if there's any ...
2
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2answers
34 views

Prove that $\Delta BPQ$ is an isosceles triangle

Given was the following figure: Also the following were given: $M_1$ and $M_2$ are the centres of the two circles The two circles have the same radius First, I added an other line through the ...
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1answer
53 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 ...
0
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0answers
6 views

Prove that all hyperbolic straight lines are congruent to $x$-axis

I have the notes on the proof but I cannot fully understand the proof. Let $C$ be a hyperbolic straight line through $z_o\in \mathbb{D}$ and $z^*_o$ the point symmetric to $z_o$ wrt the unit circle ...
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0answers
25 views

Triangular Identity. [on hold]

I have an equation $f(x)=5x+2$.I know the slope is 5 and I take the $5^2$ which is 25. I add $25+1=26$ and take the inverse of 26 which is$\frac{1}{26}$ and subtract it from 1, which is the ...
-4
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1answer
93 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 ...
0
votes
2answers
87 views

Geometric locus of points.

The vertices of triangles having a common base and congruent altitudes. I came up with the picture below. I we consider the segment AB as our common base, and all altitudes length congruent the ...
1
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1answer
53 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 ...
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0answers
16 views

How to calculate optimal sizes of rectangles for this type of array visualization?

Given array of positive numbers, I would like to draw this diagram and be able to put descriptions inside: There should be no empty space left, consider that these numbers represent % of total. Do ...
2
votes
1answer
28 views

Circle Packing, Estimate only of number of smaller circles in a circle.

Given x number of circles of radius r what is a good approximate size Radius for a bigger circle which they fit in. To explain in actual problem terms. I want to move units in a video games which ...
1
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0answers
22 views

determine point in triangle

How can I determine the point of X on the map, or the distance between X and either end point. The dashed line from X to point is perpendicular. The distance between each point is on the map, and the ...
5
votes
3answers
38 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 ...
3
votes
3answers
56 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 ...
6
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3answers
174 views

Let $M$ be an arbitrary point located inside the triangle $ABC$. Prove that $\cot\angle MAB + \cot\angle MBC + \cot\angle MCA \geq 3\sqrt{3}$

Let $M$ be an arbitrary point located inside the triangle $ABC$. Prove that $$\cot\measuredangle MAB + \cot\measuredangle MBC + \cot\measuredangle MCA \geq 3\sqrt{3}$$
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2answers
59 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 ...
5
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3answers
135 views
+100

Let $ABC$ be an acute angled scalene triangle.

Let $ABC$ be an acute angled scalene triangle. Let $P$ be a point on the extension of $AB$ past $B$, and $Q$ a point on the extension of $AC$ past $C$ such that $BPQC$ is a cyclic quadrilateral. Let ...
3
votes
0answers
17 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 ...
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votes
0answers
23 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 $AB$ ?
0
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0answers
21 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} = ...
-2
votes
0answers
21 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
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0answers
27 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, ...
6
votes
2answers
233 views

Hexagon packing in a circle

Suppose I want to pack hexagons in a circle, as on the drawing below (red indicates "packed" hexagons). I am wondering what is known about this problem. Specifically, I am interested in an ...
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votes
2answers
35 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?
1
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8answers
118 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
1
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1answer
40 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 ...
8
votes
1answer
236 views

The case of Captain America's shield: a variation of Alhazen's Billard problem

I'm sure a lot of you are acquainted with Alhazen's Billiard problem, which involves finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in ...
2
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0answers
22 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: ...
0
votes
2answers
290 views

Proof of Alternate, Corresponding and Co-interior Angles

During school our teacher always explains the proof for all theorems even simple ones such as why does the angles in a triangle of add up to $180$ and they all involve alternate, corresponding or ...
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0answers
25 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.
3
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3answers
18k views

Find the volume of the largest right circular cone that can be inscribed in a sphere of radius r?

I checked this question but didn't fully understand it. I know that the volume of a right circular cone is $V = \frac{1}{3}\pi x^2h$ I know that I must take the first derivative and set it equal to ...
3
votes
0answers
54 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?
0
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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 = ...
1
vote
1answer
402 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 ...
1
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3answers
65 views

Find $LK_1^2 + LK_2^2 + \dots + LK_{11}^2$.

$K_1 K_2 \dotsb K_{11}$ is a regular $11$-gon inscribed in a circle, which has a radius of $2$. Let $L$ be a point, where the distance from $L$ to the circle's center is $3$. Find $LK_1^2 + LK_2^2 + ...
0
votes
1answer
776 views

Formula to find the Angle between two slopes

I have given two slopes $m_1 = \frac{1}{2}$ and $m_2 = 1$ While finding the angle I made use of the formula $\tan(\theta) = \frac{m_1-m_2}{1+m_1m_2}$ answer is : $\theta = \arctan(\frac{-1}{3})$ ...
2
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1answer
64 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?
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0answers
40 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
25 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 ...
60
votes
1answer
3k views

About Euclid's Elements and modern video games

Update (6/19/2014) $\;$ Just wanted to say that this idea that I posted more than a year ago, has now become reality at: http://euclidthegame.com/ 12.292 users have played it in 96 different ...
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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 ...
-2
votes
1answer
20 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 + ...