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

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1answer
27 views

Geometry problem; right triangles in a square

Given square ABCD with E the midpoint of CD. Join A to E and drop a perpendicular from B to AE at F. Assign coordinates D(0,0), C(20,0), B(20,20) and A(0,20). Find the coordinates of F. If ...
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0answers
8 views

Source sound position mutiple point

i want find sound source position like this picture : ![find source][1] But i just konw the delay I know the delay for position 2 and 3 (or more) from source after hits the first point. I don't ...
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1answer
5 views

Finding the euclidean centers of the geodesics AB, AC, and BC

I am trying to learn about finding the angles in hyperbolic geometry and I am trying to understand this example given in Stahl's Introduction to topology and geometry. You can notice that there is a ...
3
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2answers
45 views

Dihedral angles of a pentakis dodecahedron

I'm new to the world of mathematical descriptions of polyhedra, and I'm wondering if, for a Pentakis Dodecahedron, the dihedral angles are uniform at each vertex. The visualization of the P.D. on the ...
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2answers
15 views

Barycentric Coordinates of Orthocenter question

this page describes the barycentric coordinates of the orthocenter as $(\tan A : \tan B : \tan C)$. How would you prove this using the areal definition of barycentric coordinates? Thank you. EDIT: ...
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3answers
43 views

Find circle radius by given triangle inside

So the triangle inside the circle: $AB = 9$cm $CB = 6$cm $CH = 5$cm I think solving this problem involves similar triangles. Thanks in advance, I'd like to have a solution suitable for 9th ...
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0answers
18 views

How to write explicity a curve on $S^n$?

I considered the $n$-sphere $S^n=\{x\in \mathbb{R}^{n+1}| \space ||x||=1 \}$ and $p\in S^n$. I want to write down explicity a curve $\sigma$ on $S^n$ passing through $p$ (for example one of the ...
2
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1answer
21 views

Can an isometry of the hyperbolic plane that maps a circle to a disjoint circle have a fixed point?

Can an isometry of the hyperbolic plane that maps a circle (centred on the real line) to a disjoint circle (also centred on the real line) have a fixed point? By disjoint, I mean that the two circles ...
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2answers
35 views

Affine transformation that sends a conic to itself but does not preserve the focci or the axes [on hold]

So I'm trying to find an affine transformation that sends a conic to itself but does not preserve the foci or the axes. I don't know if this can be done. I'm pretty sure that if it is possible then I ...
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0answers
12 views

How prove $S_{ABC}S_{XYZ}\ge S_{MNP}^2$ for an acute-angled triangle and $M, N, P$ are points from the segments $AB, BC, CA$ respectively

Let $ABC$ is an acute-angled triangle and $M, N, P$ are points from the segments $AB, BC, CA$ respectively. Let $CM\cup NP=X, AN\cup MP=Y, BP\cup NM=Z$. How prove $S_{ABC}S_{XYZ}\ge S_{MNP}^2$? ...
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0answers
23 views

How to obtain a rectangle's side's positions if its origin isn't in its middle? [on hold]

Basically I have an algorithm which generates rooms and corridors randomly and each time a room is made, a new corridor is placed on $1/4$ of the room's sides and its origin point is set to that ...
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1answer
61 views

Is $a \sin x + b \sin y \leq \sin(ax + by)$ true?

Studying math essay exam, I saw the following strange formula $$ a \sin x + b \sin y \leq \sin(ax + by), $$ where $x, y$ are arbitrary angles and $a + b = 1.$ Is the above inequality true, and can it ...
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3answers
34 views

How can I find the minimum value of this expression?

A straight line $L$ with negative slope passes through point $(8,2)$ and cuts the positive coordinate axis at $P$ and $Q$. As $L$ varies, what is the absolute minimum value of $OP+OQ$? ($O$ is ...
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2answers
33 views

Geometric and algebraic aspects of geometric vectors

I'm writing some notes for a honors physics class and I am having some trouble with some proofs. Say $\vec{A}$ and $\vec{B}$ are some geometric vectors. Then we defined the dot product ...
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2answers
43 views

Show that the Möbius band has its central circle $C$ as a deformation retract

I have started this problem by using the planar representation of the Möbius band and noted that a line down the middle is probably what is meant by the central circle, since travelling from top to ...
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2answers
19 views

Approximating length of a curved line based on Begining and End points of line

I have two points, a known distance apart. At each of these points I have a sensor that gives me flow speed and direction. I originally assumed the flow path between the first point and second point ...
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2answers
26 views

Center of mass of a wire frame?

I have this question on centers of mass which I'm trying to solve, I managed to get a value for both $x$ and $y$ of $(0.3,0.4)$ but apparently it's $0.5$ from $AD$? A uniform square frame ...
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0answers
16 views

Every tetrahedron has a vertex whose adjacent edges can form a triangle

Prove that in every tetrahedron there exists a vertex $v$ such that the three edges incident at $v$ have lengths that can form a triangle. It can be proved using a tedious casework: assume by ...
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1answer
30 views

Find out point coordinates [on hold]

In the following image all the variables are known except the point (x3,y3): How to find the coordinate of that point using other variables?
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1answer
19 views

Which points lie on the prependicular bisector of (-1,-6) and (5,-8)

$A$ and $B$ are the points $(-1,-6)$ and $(5,-8)$, respectively. Which of the following points lie on the perpendicular bisector of AB? $P(3,-4)$ $Q(4,0)$ $R(5,2)$ $S(6,5)$ Midpoint of $ AB = ...
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2answers
37 views

Find the height of statue.

Standing on one side of a 10 meter wide straight road, a man finds that the angle of elevation of a statue located on the same side of the road is X. After crossing the road by the shortest possible ...
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2answers
113 views

maximum area of semi-circle in square

I'm struggling the with the following question: Given is a square with length $a$. Now I want to find a semi-circle with the max. area. Looks like this: ...
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1answer
14 views

Extermal curve for specific problems?

I ran into a quiz question last month. how we can find the Extermal curve for following problem. $$ \int_1^2 \frac {\dot {x}^2}{t^3} dt $$ where $x(1)=2, \ x(2)=17$
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0answers
13 views

What is the isotomic conjugate version of the six point circle of isogonal conjugates?

As it is well known, the pedal triangles of a pair of isogonal conjugates in a triangle share a circumcircle. This is a nice theorem, but is there an analogous version of it for a pair of isotomic ...
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2answers
22 views

Is there a term for an “unbounded simplex”?

Is there a general term for regions like $\{(x,y):x>y\}$ and $\{(x,y,z): x>y>z\}$, i.e., regions which are simplexes with one open?
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2answers
576 views

Find the area of this irregular octagon inscribed in a circle [on hold]

Find the area of the octagon pictured here I do have some ideas how to solve it, but do not want to write them down here, because I'm hoping to find some different approaches. Also, see 1978 ...
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1answer
39 views

Is absolute value an one dimensional circle?

A circle is the set of all points that are at the same distance r from a given point in a plane (two dimensions). Similarly, a sphere is the set of all points that are at the same distance r from a ...
2
votes
1answer
24 views

Projected Area of Circle onto the Side of a Cylinder

I have encountered a problem that requires me to find the projected area of a beam of light (circular cross-section, with radius R1) vertically onto the side of a cylinder with R2 as its ...
1
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1answer
25 views

Dense basic open set contained in dense open subset

For an affine variety $X$ with coordinate ring $A$ it is not hard to see that for $g\in A$ the basic open set (or distinguished open set) $$D(g):=\{ P\in X | g(P)\neq 0\}$$ is dense in $X$ if and only ...
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2answers
43 views

Find distance between two poles.

2 poles, AB of length 2 metres and CD of length 20 metres are erected vertically with bases at B and D. The two poles are at a distance not less than twenty metres. It is observed that tan(angle(ACB)) ...
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0answers
38 views

question asks when is the birthday??? [duplicate]

Question asks how to find out Cheryl's birthday??
2
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1answer
54 views

Unit square in a 2-sided square

Let ABCD be a square, |AB|=2. Let EFGH be a unit square included in ABCD (every point of EFGH is inside ABCD). If O is the center of ABCD, is it possible for O to stay outside EFGH?
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3answers
90 views

Weird Al revolution

Observe, Weird Al on a Thing; http://imgur.com/gallery/LBg2rYR I tried posting this as an image, but it's a .webm file. This motion is also found in coins or tires or other circular objects as they ...
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0answers
25 views

Tangent plane of a convex set.

Given a convex set $\Omega$ in $\mathbb{R}^n$ with smooth boundary, is $\Omega$ contained completely on one side of it's tangent plane at any point on the boundary? If so, how can we prove this? ...
1
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1answer
46 views

The approximate value of the angle in a right-angled triangle

If we have a right-angled triangle $c^2$=$a^2$+$b^2$ and if we assume $a<b$ and We have the formula $ \frac {180}{pi}\cdot\frac{(\frac43\cdot(2\cdot\sqrt{\frac{(c-b)\cdot ...
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0answers
30 views

Congruent Angles with Condition [on hold]

Let A be a point in the interior of triangle BCD such that $AB · CD = AD · BC$. Point P is the reflection of point A with respect to BD. Prove that $\angle PCB = \angle ACD$. I don't know how to ...
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2answers
124 views

Sierpinski (Triangle) for Other Polygons

The Sierpinski triangle can be "generated" by the algorihm where you start in the triangle, pick a vertex at random, then move half the distant towards it, draw a dot and then repeat this. I wasn't ...
2
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1answer
22 views

$2D$ plane geometry inequality

I am trying to shade a region on the $2D$ plane that can satisfy $$1-x-y \leq 0$$ What region would that be? Am I even drawing the line correct? thank you for any help.
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0answers
28 views

An orthogonal transformation with determinant 1 rotate $\mathbb{R^3}$ around an axis.

I'm studying differential geometry and need confirmation on the solution of the following problem. A rotation is an orthogonal transformation $C$ such that det $C=+1$. Prove that $C$ does, in fact, ...
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1answer
25 views

Need Assistance with Calculating the Area of a Square when given the diagonal.

It's been several years since I've done this stuff---I'm trying to brush up for a Praxis exam in a few weeks. I've come across a problem I'm having a lot of trouble with. I'm given a square. The ...
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1answer
52 views

A simple to explain solution to this kids' geometry puzzle

A smart 10 year old asked me basically this question. Consider a rectangle with both diagonals drawn in. Now ask if you can visit all the edges by travelling from some starting vertex and only ...
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1answer
42 views

How to find the focus of a parabola

To find the center of a circle, it's enough to choose three points on the circle and find the circumcenter of a triangle with those three points. When a parabola is drawn and the formula is not ...
2
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3answers
90 views

Proving $ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context

Prove or disprove $$ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}. $$ I have no idea where to start, but it must be a simple proof. Trivia. This fact was used for determination of resistance of two ...
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1answer
22 views

Intersection between plane and circle

I have plane $$z = c$$ $$c - constant$$ and circle with center in $(0, 0, 0)$ and two points on circle $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. How can I calculate coordinates of points of ...
3
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0answers
90 views
+50

Laplace's equation in Polar coordinate, an example?

Consider Laplace's equation in Polar coordinate $ \frac {1}{r} \frac {\partial} {\partial r} (r \frac {\partial u} {\partial r}) + \frac {1} {r^2} \frac {\partial^2 u} {\partial \theta^2}$ with ...
2
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1answer
13 views

Identifying translations and rotations as compositions.

I am having trouble understanding the below which are the ones underline in red and blue. For the red: Why is that $R_{A,90}(A)=A$ and that $\tau_{AB}(A)=B$ As for the blue: Why is that ...
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1answer
45 views

Circle sandwiched between two squares problem

Can anyone help with the problem attached? Many thanks in advance! Regards, P. This is what I've done so far a) The perimeter of square PQRS is 4 x 10 cm = 40 cm. The diagonal of square ABCD = ...
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2answers
14 views

Vector proof to show the line connecting two points on a triangle is parallel to a side.

If X and Y are points on sides AB and AC of triangle ABC, and $\frac{AX}{AB}=\frac{AY}{AC}$, the $XY||BC$. I'm supposed to prove this using vectors, but we haven't done too much of this yet, and I'm ...
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vote
1answer
12 views

How can I find the inner limit of a line passing through a lune?

I have a crescent defined by two offset circles with different radii: a small one (let's call it outer circle) centered at (0,0) with radius ...
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1answer
57 views

Geometry question, very tricky! Any help appreciated [on hold]

I have another one, sorry! Can you help with this one at all? Thanks! All four sides of a rhombus are equal. a Taking this as a starting point and using congruent triangles, prove that the opposite ...