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

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2answers
23 views

Given 4 points with 2 on different radius. Obtain the center of the circle.

I'm struggle on a math question that states the following: Black holes have an overwhelming gravity, such that the nearest stars begin spinning around them (Example). Every affected star keeps ...
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1answer
17 views

What is the name for the image form you get you take a line segment and sweep it through a region of space?

For instance, if you were to take a line segment and translate it along a coplanar path, then you'd get a plane. If the path is cyclic and on that path you rotate the line segment on the axis ...
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2answers
35 views

Finding a triangle ABC if $2\prod (\cos \angle A+1)=\sum \cos(\angle A-\angle B)+\sum \cos \angle A+2$

Find $\triangle ABC$ if $\angle B=2\angle C$ and $$2(\cos\angle A+1)(\cos\angle B+1)(\cos\angle C+1)=\cos(\angle A-\angle B)+\cos(\angle B-\angle C)+\cos(\angle C-\angle A)+\cos\angle A+\cos\angle ...
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1answer
24 views

Generalization of Cantor Pairing function to triples and n-tuples

Is there a generalization for the Cantor Pairing function to (ordered) triples and ultimately to (ordered) n-tuples? It's however important that the there exists an inverse function: computing z from ...
1
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1answer
35 views

Stadium Seating - Geometric Sequences

A circular stadium consists of sections as illustrated, with aisles in between. The diagram show the tiers of concrete steps for the final section, Section K. Seats are to be place along every step, ...
3
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1answer
33 views

Does the centroid of a triangle ever fall outside of its Morley's triangle?

Let $T$ be a triangle, and $M$ its (first) Morley triangle:                     (Image from Bruce Shawyer web page.) Q1. Does the ...
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2answers
17 views

Having 2 independent segments made by 4 cartesian points, calculating x points of a smooth curve connecting the two segments

Drawing with an example of what Im trying to do I'm trying to make a sort of turtle program as a toy programming project. I can send instruction to go from A to B straight giving direction and ...
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0answers
28 views

Calculating amount of cubes that fit in a sphere

I know that the problem of finding out how many spheres can fit in a cube is a commly asked and well documentted ons, but I am struggling to find anything on the inverse of the problem, namely: How ...
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4answers
760 views

Two circles inside a semi-circle

Two circles of radius 8 are placed inside a semi-circle of radius 25.The two circles are each tangent to the diameter and to the semi-circle.If the distance between the centers of the two circles is ...
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0answers
18 views

Need help with a design calculations equal spacing of circles

I need the spacing between the circles to match. Design need 6 circles, their diameter is not fixed, but the spacing between circles need to be identical. As the circles are moved up and down their ...
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0answers
16 views

Analytic Center of Convex Polytope

I have a convex polytope defined by $Ax \leq b$. I want to know how to find the "analytic center" of my convex polytope, because my goal is to sample from the polytope using Monte-Carlo Markov ...
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2answers
27 views

Show that an order relation can be defined for the set of points $(x,y)$ of a coordinate plane.

I Think I have to show that the following two axioms hold, I have already shown that multiplication of ordered pairs can be defined (as well as other axioms) showing that it is a field. Although I ...
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1answer
16 views

new plane equation after transformation of coordinates

I have a plane equation $ax + by + cz + d = 0$ w.r.t to a particular coordinate frame. this coordinate frame w.r.t to the world coordinate frame is $$\begin{vmatrix} r_1 & r_2 & r_3 & ...
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0answers
23 views

equally spaced on circle question

Define $$\|\vec{x}\|:=\sqrt{\alpha^2+\beta^2},$$ where $\vec{x}:=(\alpha,\beta)\in \mathbb{R}^2.$ Set $$\mathbb{S}^1:=\{\vec{x}\in \mathbb{R}^2: \|\vec{x}\|=1\}\quad \quad and\quad \quad ...
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0answers
29 views

For what hexagon size can I pack $n$ hexagons into a rectangle of $s$ area?

I have a fixed number of identical regular hexagons I use to build a honeycomb looking grid of hexagons. I have a rectangular container of known dimensions. My job is to figure out how big the ...
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1answer
12 views

Finding the equation for the tangent plane to earth given latitude and longtiude

I'm creating a program where I need to calculate the equation of the plane tangent to the earth at a given latitude and longitude. I used Projecting an Arbitrary Latitude and Longitude onto a Tangent ...
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3answers
17 views

Determine if 2 points are horizontal without trigonometry

Let's say that I have 2 points: (c1X, c1Y) and (c2X, c2Y). I would like to consider these 2 points horizontal as long as their angle is below 45 degrees. I could accomplish this with trigonometry. ...
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0answers
39 views

What's a good book on geometry to read after Kiselev?

I have finished reading both books on geometry by Kiselev and now look to move on but can't find any book to let me do so. Which book would you suggest that one may read after finishing Kiselev?
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0answers
31 views

Demonstrative geometry around the world and its significance.

This is not exactly a mathematical question. I am from Pakistan; and over here students are taught a subject 'demonstrative geometry' (as a part of mathematics) from secondary level education. ...
2
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4answers
69 views

Find $x$ in the triangle

the triangle without point F is drawn on scale, while I made the point F is explained below So, I have used $\sin, \cos, \tan$ to calculate it Let $\angle ACB = \theta$, $\angle DFC = \angle ...
0
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1answer
41 views

A triangle ABC with the internal bisector of $\angle A$, the median drawn from B and the altitude drawn from C meet at the same point.

A triangle $ABC$ with the internal bisector of $\angle A$, the median drawn from $B$ and the altitude drawn from $C$ meet at the same point. Prove that $$\tan A = \dfrac{\sin C}{\cos B}$$ I try to ...
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0answers
29 views

Translate a geometric theorem into polynomial equations — Theorem of the orthocenter of a triangle

This is Exercise 13 of Chapter 6 of Ideals, Varieties, and Algorithms by Cox et al. The problem asks to translate the following geometric theorem into polynomials and using Groebner basis to test ...
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1answer
39 views

Geometric problem based on angle bisectors

I am not asking a question,i just want to conform,is my method of solving problem correct? Given a triangle ABC.It is known that AB=4,AC=2,and BC=3.The bisector of angle A intersects the side BC at ...
1
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1answer
48 views

Given an acute triangle ABC with altitudes AH, BK. Let M be the midpoint of AB

Given an acute triangle ABC with altitudes AH, BK. Let M be the midpoint of AB. The line through CM intersect HK at D. Draw AL perpendicular to BD at L. Prove that the circle containing C, K and L is ...
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1answer
84 views

Is the area of this pentagon $4-\sqrt 5$?

Consider a regular pentagon with vertices (in clockwise order) $A, B, C, D, E$, let $A'$ be the point of intersection of $BD$ and $CE$, let $B'$ be the point of intersection of $CE$ and $DA$, and ...
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2answers
22 views

Similarity conditions of two right trapezoid with similar angles

We have $2$ right trapezoid for example two trapezoid with angles $90^{\circ},90^{\circ},80^{\circ},100^{\circ}$. do we need to all the sides proportionality or less is enough ?
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2answers
59 views

Is the Dikin Ellipsoid actually a ball?

I have the inequality (row wise): $Ax \leq b$ The Dikin ellipsoid centered at $x_0$ with radius $r$ is: $$\{z \quad | \quad (z-x_0)^T(z-x_0) \leq \frac{r^2}{H(x_0)}\}$$ where, $$H(x_0) = \sum ...
0
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0answers
25 views

Find distance between a plane and some points [on hold]

Consider points $x_1,\ldots,x_n$ and plane $w\cdot x-\gamma=0$ in $\mathbb{R}^n$ and let $A=[x_1,x_2,\ldots,x_n]^T$. Is correct following formula to find the distance between these points and the ...
2
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2answers
57 views

Question based on triangle inscribed in unit circle

$ \bigtriangleup ABC $is inscribed in a unit circle.If angle bisectors of internal angles at A,B and C meet the circle at D,E and F respectively then value of $\frac{AD \cos\frac{A}{2}+BE ...
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1answer
20 views

Intersection of Cut Locuses

If $C_p(M)$ is the cut locus of some $p\in M$ in some Riemannian Manifold $M$, then when is: \begin{equation} \bigcap_{p\in M} C_p(M)=\emptyset\text{ ?} \end{equation}
3
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1answer
84 views

Prove that $\tan\alpha =\tan^{2}\frac{A}{2}.\tan\frac{B-C}{2}$

Given a triangle ABC with the sides $AB < AC$ and $AM, AD$ respectively median and bisector of angle $A$. Let $\angle MAD = \alpha$. Prove that $$\tan\alpha =\tan^{2}\frac{A}{2}\cdot ...
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0answers
19 views

Find the best trapezoidal fitted in an irregular shape [on hold]

I am working with some earth irrigation canals. Irrigation canals are usually in trapezoidal shape. These trapezoidal canals are defined by the width of bottom of canal (B) and high of depth of canal ...
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3answers
73 views

what is the definition of cosine , sine [duplicate]

I know that sine is the ratio of the perpendicular to the hypotenuse of an acute angle. Similarly cosine is the ratio of the base and hypotenuse . But now I found that there is sine and cosine of an ...
4
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0answers
59 views

How is it that $\pi$ appears in so many formulas that seem to be in no way geometric. [duplicate]

When I first saw: $$\frac{\pi}{4}=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}\mp\cdots.$$ I was puzzled that such an expression could have anything to do with circles. There are tons more and ...
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2answers
44 views

Find a plane with distance $3$ from $3x-y-z = 0$

I need to find a plane such that its distance from the plane $3x-y-z = 0$ is $3$. Since distance is defined only for parallel planes, I already know that they have to be parallel, and then, the ...
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0answers
25 views

Is there a theory for cellular automata propagating signals in straight lines?

Is there a theory explaining how a cellular automata can propagate signals in straight lines? For example, this video shows how some "signals" travel down at a diagonal, even though they are composed ...
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0answers
43 views

Beyond Pythagoras [on hold]

Draw an arbitrary triangle $\triangle ABC$. Measure its sides. Draw a ray, $BC$. Draw a circle with radius $AB$. Find the point of intersection, $D$. Measure segment $\overline{CD}$. ...
1
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2answers
64 views

Triangle Geometry and Circles Problem

I have discovered something using Geogebra and I am positive it is true. I have tried to prove and my solution works but it is extremley convoluted. I'm hoping someone can provide a simple proof of ...
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5answers
44 views

co-ordinate geometry question 3 [on hold]

Find intercept of the line whose intercept of $x$-axis and $y$-axis are respectively twice and thrice of those by the line $3x+4y=12$ ?
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0answers
21 views

Symmetry of stereographic projections of tangent vector to $S^2$ at equator

There is a vector lying in the tangent plane to a sphere $S^2$ at equator. We take two its "stereographic" projections - one from the south pole and other - from north. Projections to the planes ...
0
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1answer
34 views

Number of triangles having particular area

If $g:R\to \ N\cup\big\{0\big\}$ and $g(x)=n$,where $x$ represents the area of triangle joining the two fixed points and a variable point $R(p,q)$such that $\angle PRQ=\frac{\pi}{2}$ and $n$ ...
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1answer
11 views

Finding $x$ coordinates on a rectangle if Rectangle $a$ was scaled up to Rectangle $b$

I wasn't too sure how to explain the question in the title so i drew up my problem that I am trying to solve: http://i.imgur.com/PyWMh6f.jpg Basically I choose a point on rectangle $A$ and then find ...
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2answers
24 views

A triangle and its median in complex plane.

Let $z_1$, $z_2$, $z_3$ be vertices of the triangle $\triangle ABC$. And given that $|z_1|=|z_2|=|z_3|$. Then the median through $A$ cuts the circumcircle at which point? We need to get the answer in ...
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0answers
32 views

Should I try to figure out geometric construction?

I've been reading and working through the book - Euclid and Beyond by Robin Hartshorne. In the first chapter there are a few constructions that I haven't been taught in school (just finished 11th ...
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3answers
197 views

Finding the area of a square that has a circle inside itself

I tried to solve the following problem: I think the image is self-descriptive. I tried to draw a vertical line from the top-end of $\theta$ angle to the horizontal line, then tried to use the ...
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3answers
33 views

Find more integral points on a hyperbola

Let $\mathcal H$ be a hyperbola (in the affine plane) whose defining equation has integers coefficients. Assume that one knows 2 points of $\mathcal H$ with integral coordinates. Is there a way to ...
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2answers
49 views

Interesting problem in congruence of triangles

While solving the exercises of my book I came across this interesting problem: $\triangle ABC$ is isosceles triangle with $AB=AC$. D is a point on base BC such that $AD$ perpendicular on $BC$. To ...
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1answer
43 views

Is there a specific mathematical term for a shape whose dimensions are defined?

When I say the word "circle", I know that I have described a "shape". Specifically, a "circle" is the shape formed by the set of all points in a plane that are at a given distance from a given point. ...
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0answers
93 views

Penrose's remark on impossible figures

I'd like to think that I understand symmetry groups. I know what the elements of a symmetry group are - they are transformations that preserve an object or its relevant features - and I know what the ...
1
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1answer
65 views

Finding the intersection points of common tangents on a pair of non-intersecting ellipses

I'm having some trouble with this, I don't know why but for some reason it is giving me a lot of trouble. Ultimately I intend to implement it into a program for modelling something, but I cannot even ...