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

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3 views

Line parallel to parallel sides of a trapezium dividing it into equal areas

A trapezium with length of parallel sides $a$ and $b$ is such that a line segment parallel to these parallel sides divides the trapezium into two parts having equal areas. Find the length of this ...
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0answers
14 views

at least how many cube do I need?

at least how many cube do I need to make the below structure?
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1answer
9 views

Find the point in this line such that the distance from $A$ is $\sqrt{3}$

My line: $$r: (0,2,-2) + \lambda (1,-1,2)$$ The point: $$A = (0,2,1)$$ I know that the line has equations: $$x = \lambda \\ y = 2-\lambda\\z = -2+2\lambda$$ But when I use the distance formula ...
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0answers
8 views

Finding the number of Circle or Circles in a Circle

Let a circle $A$ which radius is $10 m$ and another circle is $B$ which radius is $0.2 m$.Is it possible to say that what is the maximum number of circles $B$ can be drawn in circle $A$? I tried much ...
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1answer
26 views

Elementary geometry from a higher perspective

I'm searching for some references that deal with topics from "elementary geometry" analysing them from a "higher" perspective (for example, abstract algebra, linear algebra, and so on).
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2answers
25 views

Geometry , gre problem

Smallest distance from a point P to any point on the circle C is 5 and the largest distance from the the point P to the circle is C is 11 . If point P is situated outside the circle C , then what is ...
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0answers
7 views

Least sum of power of distances

Let $n$ points in a $3$-dimensional space. Are there any general intuitive methods to tackle the problem of finding the point $X$ such that the sum of distances $A_1X^x+ A_2X^x + ... +A_nX^x $ (where ...
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0answers
19 views

Find points that defines the intersection of an ellipse with a plane.

I want to test for the intersection of two ellipses $E_1$ and $E_2$ in $\mathbb{R}^3$ represented on a computer. In some sense, this isn't a hard problem: ...
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2answers
31 views

Differential Geometry: Is a closed disk a surface?

An open disk is clearly a surface, in the sense that it is locally homeomorphic to a part of $\mathbb{R}^2$. But what about a closed disk, even though it still looks like a surface, I am starting to ...
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0answers
10 views

Proof an edge in a geometric graph

Suppose i take two random uniformly distributed points $X_{1},X_{2}$ in $[0,1]^{2}$. In addition i connect $X_{1}$ and $X_{2}$ by an edge if $||X_{1},X_{2}||_{\infty} \leq r$ where $0<r<1$ and ...
2
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0answers
38 views

Historical motivation for Hilbert's Third problem

What was the historical motivation for Hilbert's third problem? Why did Hilbert feel it was worthy of including on his published list? Hilbert's Third problem: Say that two polyhedra are scissors ...
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0answers
35 views

How to draw an ellipse, given its center, its major radius and two arbitrary points from its perimeter?

I'm trying to write as practice a program where I could visualize a circle being freely moved around in space, and long story short is that I ended up with this problem that I could not solve Besides ...
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0answers
24 views

Kauffman Bracket

Can anyone explain or direct me to: . What are the x and y's? Is x cutting the loop? And for the last picture, I don't understand how the Reidemeister moves have been applied there. I would much ...
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1answer
34 views

Assuming an assembly robot arm with various rotation axes, how to find the angles it needs to take to get at (or closest to) a given point?

For each rotation axis, I know its current angle and its angle range (its minimum angle and its maximum angle). Assuming I want a point on its "hand" to be at a given coordinate or as close as ...
3
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0answers
44 views

The number of regions of an $n$ dimensional space

Consider $n$ dimensional Euclidean space. I am interested in the following question. For a $n$ dimensional space, what is the maximum number of $n$ dimensional regions you can get if the space ...
2
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2answers
34 views

High-School level question concerning circle and arcs

This question somehow is unsolvable to me. Any idead/hints wil be much appreciated. $AB$ is a chord which is cut ny the chords $CD$ and $EC$ in the circle. Givens: $\frown{AC} ...
0
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1answer
22 views

Dividing a triangle into seventeen equal parts.

I was trying to solve a problem on Pigeonhole principle from Problem Solving Strategies by Arthur Engel. A target has the form of an equilateral triangle with side 2 units. If it is hit ...
0
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1answer
31 views

Evaluating a sum by applying geometry

This is really an interesting question: Evaluate S, where $$ \large S= \sum_{k=1}^{502} \left\lfloor \frac{305k}{503}\right\rfloor$$
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1answer
18 views

How to derive the standard symplectic form on a 2-sphere in cylindrical polar coordinates?

I have already know that at a point $p\in S^2$ with $u,v$ the tangent vectors at $p$. Then the standard symplectic form is $\omega_p(u,v) :=\langle p,\,u\times v\rangle$ where $u\times v$ is the outer ...
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0answers
23 views

Task with extreme point [on hold]

I have been given $3$ points for a triangle. Three factory problem. $A=(1,5)$ $B=(0,0)$ $C=(8,0)$ I need to find the coordinates that sum of lengths from the points $ABC$ is smallest.
3
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1answer
56 views

Find angle x in the picture [on hold]

This question is in the form of a picture: How long did it take you to find out?
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1answer
22 views

How to prove two triangles have the same centroid?

Suppose you have a triangle ABC and three similar exterior triangles BCX, CAY and ABZ. How can I prove that the centroids of ABC and XYZ are the same point?
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1answer
26 views

eigenfunctions on covering spaces of graphs

I am reading about lifts of graphs in relation to covering spaces. Before I pose my question I will explain some of the terminology. Let $G$ and $H$ be two graphs. We say that a function $f: V(H) ...
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1answer
13 views

Distance from a point to a line

Consider a point $P \,(-6,-5)$, and a line $s$ given by $y=-3x+7$. I have at least two options $A$ and $B$ to compute the distance between them: A.1) Find a line $t$, perpendicular to $s$, that goes ...
-1
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0answers
17 views

Billiard balls in monolayer of a circle. [on hold]

Suppose you pack some billiard balls into a circle so they form a monolayer. If the circle had an area of $320\ \mathrm{cm}^2$, how many billiard balls can fit into the circle? (ignore any empty space ...
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0answers
16 views

Volume of a $n$-dimensional sphere and of the inscribed cube

How can one find a general formula to find what fraction of a $n$-dimensional sphere is the volume of the inscribed cube? Context: the problem emerged out of curiosity starting from the $3$-D case, ...
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0answers
28 views

Enumerating n-gon rings

How many rings can be constructed from a set of regular $n$-gons? For this purpose a ring is planar arrangement of $m \ge 2$ identical non-overlapping regular $n$-gons joined edge to edge, the whole ...
4
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2answers
96 views

Problems in elementary number theory and physics (and other branches)

Yesterday I started wondering if there are problems from number theory (elementary number theory in particular, but also advanced topics) which can be intuitively solved (or at least approached) by ...
0
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1answer
35 views

I'd like a rigorous proof that the dihedral group $D_8$ is the isometry group of the unit square

My geometry is woefully inadequate. Can someone help me show that $D_8 = \langle r, s \mid r^4 = s^2 = 1, rs = sr^{-1} \rangle$ is exactly the group of isometries of $S = [0,1]\times[0,1]$? Of ...
0
votes
1answer
26 views

What is the geometric way of relating zero to infinity?

I once saw (what I think was) a geometric way a relating zero to infinity. Something about a circle with radius 1 around the origin. Can you tell me where to find that? Thanks
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3answers
58 views

How to prove/disprove this? [on hold]

How can I prove or disprove this without using inverse trig functions ?
2
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1answer
20 views

Surface area of quarter of a Sphere

A quarter sphere with a radius of $10 \text{ units}$. Please help, also remember the sides. I used the normal formula of the total surface area of a sphere and divided it by $4$, then added half the ...
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0answers
21 views

Help me understand chained rotations

Ok, so for my thesis I am trying to do some stuff with ellipsoids in 3-dimensional space. I am trying to rotate an ellipsoid to face a certain direction using Tait-Bryan chained rotations. That is, ...
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0answers
9 views

Suppose point j has coordinate of -2 and JK=4. Then what is the possible coordinate(s) for K? [on hold]

Suppose point j has coordinate of -2 and JK=4. Then what is the possible coordinate(s) for K? A. 4 B. 2 or -4 C. -4 D. 2 or -6 Hey, can anybody help and give basic reasoning on why? ...
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2answers
66 views

What are the ranges of triangle angles?

Lets say, that $\alpha \le \beta \le \gamma$. As shown here, $60 \le \gamma \lt 180$. What are the minimum and maximum values of $\alpha$ and $\beta$? The answer: $$0\lt \alpha \le 60 \\ 0 \lt ...
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0answers
24 views

Length of a hyperbola, between two points [on hold]

Given a hyperbola, xy = k Is there a way of determining the length of the hyperbola between two arbitrary points? e.g. Suppose k = 25, what is the length of the hyperbola between (1/25, 625) and (5, ...
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1answer
30 views

What is the range of angle in front of longest triangle edge?

What is the minimum and the maximum values of the angle $\gamma$ in front of the longest triangle edge?
1
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1answer
19 views

Is the perimeter of a nested convex set smaller than the containing set's?

Prove/Disprove: $\forall S' \subset S\subset\mathbb R^2$ such that $S',S$ are convex and have finite area, the perimeter of $S'$ is smaller than the perimeter of $S$. e.g. $S$ could be the unit ...
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2answers
31 views

Prove that a string cant be outside a circle

How can I prove that a chord can't be outside the circle itself. Is there a way to prove that you can't draw a chord outside the circle.
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0answers
22 views

Distance from incenter of Heron triangle to vertex

Given Heron triangle (all sides are integers as well as area) with integral inradius it is needed to find a distance between incenter of that triangle and any of its vertices. Thanks!
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0answers
20 views

3D Vectors and Geometry [on hold]

With the points A = (2, 0, 3), B = (1, 1, 1), C = (0, 1, −1) and D = (1, −1, 2)and using five subtractions, two cross products and one dot products find the distance from point D to the plane through ...
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0answers
30 views

“solve” geometric shape

Well I have some "easy" geometrical shape. However I'm having troubles solving the equations. Basically I have 4 lines, which have a fixed length. Two bars cross each other, one bar is "fixed" in ...
7
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1answer
38 views

Geometry and land

The word "geometry" in Greek means "measurement of Earth/land". This may imply that geometry was originally invented in order to solve problems related to land. Are there historical accounts of ...
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2answers
22 views

Calculate the angle from the given points coordinates.

I'm trying to figure out the way to calculate the a angle value from given coordinates of three points as showed on the illustration below: I know how to ...
1
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0answers
22 views

Calculating point on sphere surface where sun reflection to a target point occurs

Imagine a mirror sphere at position O with radius R, and a target point at position P, at distance d from the sphere origin. There is an unknown point X on the surface of the sphere, where the light ...
2
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2answers
56 views

A Regular Tetrahedron is a special Polyhedron.

A regular tetrahedron has this property: For any two of its vertices exists a third vertex, which forms a regular triangle with these 2 vertices. Are there any other polyhedrons that have the same ...
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0answers
16 views

Finding a function with desirable behaviour

I was playing around with math in my spare time and came up with the following problem. Suppose I have a $1$-parameter family of lines in the plane. Each line is given by the following equation ...
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4answers
76 views

locating any point on a real number line

So my question is really simple (and may be a bit naive): The claim is, I can locate any point in a 2D-plane by recursively applying the following method (possibly infinite number of times): For ...
1
vote
2answers
24 views

Proving a trigonometric relation using circle properties

Hi, I've been having trouble with this question, and would really like some help. What I've done so far is applied the cosine rule in the triangle PQR to find that $PR^2=a^2+c^2+2ac\cos\theta$. ...
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1answer
37 views

Exercise books in linear algebra and geometry

I'm studying Brannan's Geometry and Lang's Introduction to Linear Algebra and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as ...