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

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0
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3answers
30 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 ...
0
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1answer
25 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 ...
1
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2answers
25 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 ...
1
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2answers
12 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 ...
0
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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
10 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 ...
-4
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1answer
22 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?
0
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1answer
18 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
34 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 ...
3
votes
2answers
105 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: ...
1
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1answer
13 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
12 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?
4
votes
2answers
469 views

Find the area of a cyclic octagon

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 ...
1
vote
1answer
37 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
23 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
vote
1answer
21 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 ...
1
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2answers
41 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
36 views

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

Question asks how to find out Cheryl's birthday??
2
votes
1answer
49 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?
3
votes
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 ...
1
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0answers
24 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
vote
1answer
42 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 ...
0
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0answers
27 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 ...
5
votes
2answers
123 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, ...
1
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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 ...
1
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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 ...
1
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1answer
41 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
votes
3answers
89 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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votes
1answer
21 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
71 views

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
votes
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 ...
-4
votes
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 ...
1
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 ...
-5
votes
1answer
55 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 ...
6
votes
4answers
211 views

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. Why? [on hold]

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse. A statement from the trigonometry section of Simmons' Precalculus in a nutshell. Please ...
2
votes
2answers
58 views

Volume of a parallelepiped, given 8 vertices

Given the eight vertices $(0,0,0)$, $(3,0,0)$, $(0,5,1)$, $(3,5,1)$, $(2,0,5)$, $(5,0,5)$, $(2,5,6)$, and $(5,5,6)$, find the volume of the parallelepiped. I'm having trouble finding the 1 vertex ...
0
votes
0answers
36 views

Proj of some ring.

Let $R= \mathbb C[x_1,x_2,x_3,x_4,x_5,y_1,y_2,y_3,y_4,y_5]$ be the polynomial ring and let $S$ be the subalgebra generated by $x_1x_2x_3x_4x_5, x_1x_2x_3x_4y_5, \cdots ,y_1y_2y_3y_4y_5$ (the ...
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votes
0answers
38 views

Why does this proof by bashing not work?

Given is a triangle $ABC$ with circumcenter $O$ and orthocenter $H$. The feet of the perpendiculars from $C$, $B$, and $A$ to the opposite sides are $F$, $E$, and $D$ respectively. Prove that ...
8
votes
4answers
363 views

How to construct a line with a given equal distance from 3 Points in 3 Dimensions?

Important: I'm now convinced that 4 points are needes in order to reduce the solutions to a finite number. (Which is necessary because I need ALL solutions) In a computer science context I need to ...
-1
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0answers
20 views

angle between two lines on a sphere

What happen to the angle between two lines inscribed on a sphere of radius $1$ when its radius grows to $R>1$? My first thought is that it doesn't change at all..but i'm not sure, any suggestion ...
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votes
0answers
23 views

Linear Operator in Euclidean Space

In oriented Euclidean space $E_3$ consider the following linear operator $$A(x) = x − a × (a × x)$$ where vector $a = e + 2f + 2g$. Here $\{e,f, g\}$ is an orthonormal basis in $E_3$ defining ...
0
votes
1answer
35 views

What is the height of this pyramid?

Let $W$ be the point in the base $(XYZ)$ of the pyramid such that $VW$ and $WZ$ are perpendicular. $XYZ$ is a right triangle and $XZ$ is perpendicular to $YZ$. What is the height of the pyramid? ...
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votes
1answer
84 views

Why a line is said to have infinite number of points? [duplicate]

Why a line is said to have infinite number of points? Is this so because a line is ever lasting or we can not count how many points does it have? Finite means: Having an end. Infinite means: No end! ...
3
votes
1answer
15 views

Let $R$ be any rotation and $P$ any reflection then $R \circ P$ and $P \circ R$ are both glide reflections

Let $R$ be any rotation and $P$ any reflection then $R \circ P$ and $P \circ R$ are both glide reflections I am having trouble showing $P \circ R$ is a glide reflection, I manage to get $R \circ P$, ...
-1
votes
1answer
21 views

sum of the squares of the reciprocals of the two parts of the focal chord of a parabola

Find the sum of the squares of the reciprocals of the two parts of the focal chord of a parabola. My attempt: Let $y^2=4ax$ be a parabola. Let PQ be the focal chord through the focus S$(a, 0)$ ...
2
votes
0answers
19 views

Proof: The inverse of the translation $T_{AB}$ is the translation $T_{BA}$

Prove: The inverse of the translation $T_{AB}$ is the translation $T_{BA}$ This is my work so far: Let P be any point of the plane and set: $P'=T_{AB} (P)$ We want to show ...