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
35 views

finding out the chord length

Let there are given that. Radius of the circle is 2 and CD= 1.5 = CB . Now how to find out the arc length of CD or CB? In this case we know the all length but not any angle. EDIT:Calculator is ...
1
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1answer
24 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
0
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1answer
20 views

How can I find the intersection length of a circle and a rectangle?

I have the following information: The coordinates of the vertices of the rectangle. The radius and center position of the circle. How can I find the length of the red line in the picture? (The ...
1
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1answer
16 views

Confusion with Bolyai-Gerwien theorem

The Bolyai-Gerwien theorem states: Given two polygons with the same area, it is possible to cut up one polygon into a finite number of smaller polygonal pieces and from those pieces assemble into ...
0
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1answer
35 views

Central angle of an ellipse

If I have an ellipse centered at the origin and know the length of $a$ and $b$ and was given the length of an arc, how can I find the angle that is between the two radius from the center of the ...
2
votes
1answer
52 views

Neighbour Points in N-Dimensional Space

if you got a integer point in the n-dimensional space how many neighbor integer points does it have? 1D you have 2 2D you have 8 3D you have 26 i came to the formula $$n_i = 2*(n_{i-1}+1)+n_{i-1} ...
1
vote
1answer
24 views

Find the value of area of trinagle ADF by AG and AE

Consider a triangle ABC where angle A = 60. Let O be the inscribed circle of triangle ABC, as shown in the figure. Let D, E, F be the points at which circle O is tangent to the sides AB, BC and CA. ...
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0answers
31 views

Determine parametric equations [closed]

The data point A(3,4, -2) and the line determine parametric equations of the line through A and is perpendicular to l.
1
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0answers
11 views

Decompose distortion affected homography matrix

I am working on a system that finds homography between images taken by moving (shaking) camera with rolling shutter and map. The map is orthogonal image of flat 2D plane and the camera images are ...
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1answer
15 views

Preserving incidence relation proof

How can one prove via analytic method that projective map preserves incidence relation?
2
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1answer
34 views

Calculating a specific point on a circle

I am looking for a formula to calculate the point of intersection where the arc crosses the angled line (designated by the letter 'X' in the example below), only from the dimensions given. I am ...
0
votes
0answers
25 views

Modelling 3 dimensions embedded in 1 dimension [closed]

Are there any methods to model 3 dimensional space compressed/embedded down into 1 dimension of space.
0
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1answer
39 views

Is there a mathematical method to draw a circle tangent to three other circles and give it's equation?

I was curious as to whether there is a mathematical method by which one can draw a circle which is tangent to three other circles and give it's equation. Thanks for your time.
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0answers
20 views

Seams/net of curved surfaces

Like with the seams of a piece of clothing or inflatable, what would the methodology be to creating a flat net of a curved 3d object? I would like to create a model of a mobius torus, and would like ...
5
votes
1answer
67 views

Find all such functions defined on the space

$f:\mathbb{R}^3\to \mathbb{R}^{\ast}$ is such that for any non-degenerate tetrahedron $ABCD$ with $O$ the center of the inscribed sphere, we have : $$f(O)=f(A)f(B)f(C)f(D) $$ Prove that $f(X)=1$ for ...
0
votes
1answer
38 views

A line going through a point, how to find it's touching point with a circle.

I have a circle and a point outside of it. I need to find a line passing through this point and only touching the perimeter of the circle (my intuition tells me that there are always two lines like ...
0
votes
1answer
32 views

Circles and tangents

3 circles of radius 3 cm, 4cm, 5 cm touch each other externally at $A$, $B$, $C$. Tangents drawn at $A$, $B$, $C$ intersect at $P$. Find $ PA + PB + PC$ . Thanks. My thoughts and approach: ...
6
votes
2answers
175 views

Formula for adjusting font height

INTRODUCTION AND RELEVANT INFORMATION: I am a software developer that needs to implement printing in my application. In my application user can choose different paper sizes ( A3, A4, A5 ...) which ...
0
votes
1answer
27 views

A square pool is surrounded by a concrete deck

A square pool of area $144 \, \text{m}^2$ is surrounded by a concrete deck of area $25 \, \text{m}^2$. What is the perimeter of the outside of the deck?
1
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2answers
27 views

Stuck on triangle geometry problem

The answer is 378 but I can't seem to get it. I know that the triangles are similar, but I can't get past that. Any help is appreciated! Thanks!
-1
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1answer
90 views

What proportion of the circle is covered by the square?

Or what is the combined area of the circle segments (chords)? Picture a circle which is covered by a square, where the bottom vertices of the square are inscribed within the circle (so that the ...
2
votes
2answers
41 views

What are a geometric system and a finite geometry?

Wikipedia says A finite geometry is any geometric system that has only a finite number of points. I wonder what a geometric system is? Is it some set system $(E, F)$, where $E$ is a set and $F ...
6
votes
1answer
61 views

Name of a shape that is intersected once by each ray that starts at a given point

Is there a particular name for a shape that is intersected exactly once by each ray that starts at a given point? To illustrate: I'm looking for a name for shapes like the left one in this image: ...
3
votes
2answers
202 views

what is the limit of $\theta$ if $r\to 0$ when we have these conditions?

the problem is based on this picture. at beginning or we say $t=0$, $P$ is a circle of which the center is at the point $(0,r)$, $r_0=1$ is the initial radius of this circle. $AB$ is a vector which ...
0
votes
0answers
13 views

radon transformation backprojection

I am working on image recontruction and I try to find out how the radon transformation works. I have benn using mainly Natterer, F. and Wubbeling, F.: Mathematical Methods in Image ...
0
votes
2answers
33 views

Locus of the Orthocenter of the Traingle

Coordinates of $\Delta ABC$ are $A(3,4)$, $B(5 \cos\theta, 5 \sin\theta)$ and $C(5 \sin\theta,-5 \cos\theta)$. Find the locus of its orthocenter. My idea: It is clear that $(0,0)$ is equidistant ...
0
votes
1answer
19 views

Determine Center Point based on 2 separate elipses

First timer here. I've been digging back into my good old maths days but am extremely rusty (beyond belief). I got a really tricky question that i want to determine formula for so that my mate can ...
0
votes
1answer
29 views

How to normalize a slope?

Say I have two slopes and two averages for a sample: $m=4{,}000$ dollars/day, average $a=50{,}000$ $n=80{,}000$ dollars/day, average $b=700{,}000$ Graphically, $n$ is very ‘steep’ compared to $m$. ...
1
vote
1answer
26 views

Surface area of lateral section of paraboloid

Here is my 2D parabola curve. The x,y locations of each point of interest are displayed, and the equation of the parabola and the line are given as well. I want to create a hollow 3D Paraboloid by ...
2
votes
1answer
26 views

Does symmetry maximize area for a given nonconstant diameter of a convex subset of the plane?

Let $A$ be a nonempty convex subset of the Euclidean plane. For each direction $\theta$, let $d_A(\theta)$ be the diameter of $A$ in that direction. That is, $d_A(\theta)$ is the distance between the ...
-2
votes
1answer
73 views

Cw complex $\Sigma_g$

Consider the oriented connected compact surface $\Sigma_g$ of genus $g$ with its standard CW structure. How do I write down the attaching map for the single $2$-cell and how can it be proven that it ...
1
vote
1answer
35 views

The max arc length for 3 symmetrical circles to intersect

Consider the following: 3 Identical circles, intersecting in a way so that all 3 arc lengths outside are the same length. Now here is a similar situation: The arc length for the circles got ...
4
votes
3answers
99 views

Hyperplanes and Support Vector Machines

I have the following question regarding support vector machines: So we are given a set of training points $\{x_i\}$ and a set of binary labels $\{y_i\}$. Now usually the hyperplane classifying the ...
-1
votes
4answers
52 views

Find the line through $(-1,4)$ for which the distance to $(6,3)$ is 5

This is the question: Find the line through $(-1,4)$ for which the distance to $(6,3)$ is $5$ The answer is: $y-4=-4/3(x+1)$ and $y-4=3/4(x+1)$ I do not know how to get this answer. ...
1
vote
1answer
43 views

minimizing squared distance for point to a set of lines

I have this problem that I cannot figure out how to solve. It is from Szeliski's computer vision book (http://szeliski.org/Book/drafts/SzeliskiBook_20100903_draft.pdf) p.94 (electronic version) and is ...
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votes
0answers
14 views

Shortest path over polygons with different cost of travel

The real world problem I'm trying to solve: A road has to be built over a terrain. The terrain have areas that are more costly to build over. Those areas can have complex shapes. How do I build the ...
0
votes
0answers
15 views

Linear speed on a sphere with severals axis of rotation

I want to calculate linear speed of a unit sphere rotating around different axis over time. I have 3D coordinates of points on the sphere surface. I saw that linear speed $s = rw$ with $w$=angular ...
0
votes
1answer
25 views

Geometric proof with a isosceles triangle

Given is $\triangle ABC$ with the medians $AD$, $BE$ with $|AD|=|BE|$. The medians intersect in $S$. a. Use similar triangles to show that $|AS|:|SD|=|BS|:|SE|=2:1$. b. Prove that $\triangle ABC$ is ...
2
votes
1answer
27 views

Definition of (hyper)planes

I know the definition of a plane to be: $(r-r_0)\cdot n = 0$ where $n$ is the vector perpendicular to the plane, $r$ the vector to a given point and $r_0$ the vectors to the points which constitute ...
0
votes
1answer
31 views

How can I calculate the angles of two RA triangles with a shared common hypotenuse?

I have two RA triangles with a shared common hypotenuse. Given the lengths of the adjacent sides of the two right angle triangles, a1 and a2, and the sum of both angles, theta, how can I calculate ...
3
votes
1answer
40 views

Does a pseudo-Anosov homeomorphism of a punctured surface possess infinitely many periodic points?

In A Primer on Mapping Class Groups by Farb and Margalit theorem 14.19 implies that every pseudo-Anosov homeomorphism $f:S \rightarrow S$ on a compact surface $S$ possesses infinitely many periodic ...
0
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0answers
34 views

Proving the 3-d pythagorean theorem on surface areas of oblique triangular pyramid

I would like suggestions if possible, other than the really sloppy picture, I'll edit that once my dad gets me Microsoft office. I got a snip of the shape, and edited it as best as I could. The ...
8
votes
1answer
95 views

How does the area of $A+A$ compare to the area of $A-A$?

The Minkowski sum of two sets $A$ and $B$ in the plane is defined as $$A+B = \{ a + b \mid a \in A, b \in B \}.$$ The Minkowski difference $A-B$ is defined similarly. For any convex set $A$, is ...
2
votes
1answer
54 views

Find this angle, in terms of variables

I have a geometry question. Take a look at this figure: It is 3 circles, symmetrically placed so that the arc length that is outside is equal for all sides. I tried to determine the angle that is ...
0
votes
2answers
37 views

How can I find the smallest enclosing circle for a rectangle?

I have the four vertices of a rectangle. I need to find it's smallest enclosing circle. For example: I need to find the radius of the circle.
0
votes
1answer
26 views

SAT geometry and drawing lines

The black color represents the original problem. Q: In the figure above, line "l" (not shown) is another line in the plane. What is the maximum number of pieces the shaded area can be divided into if ...
3
votes
0answers
28 views

determining orientation of a sphere

I have a sphere and I am trying to find out its orientation with respect to ground frame. The sphere is as follows:- As can be seen from the image, different colors are painted on the sphere with ...
0
votes
1answer
14 views

Triangular pyramid proof about incenter

Suppose that the lateral faces $VAB, VBC,$ and $VCA$ of triangular pyramid $VABC$ all have the same height drawn from $V$. Let $F$ be the point in plane $ABC$ that is closest to $V$, so that $VF$ is ...
0
votes
1answer
20 views

monotonically reducing euclidean distance

In the given image, if $a<\frac{\pi}{2}$ how can I prove that the distance to $T$ from any point $Q$ on $PX$ is less than $TX$? i.e. given $ a<\frac{\pi}{2}-XTP/2$, $|QT|<|TX|$ for all $Q ...
72
votes
18answers
7k views

How to distinguish walking on a sphere or on a torus?

Imagine that you're a flatlander walking in your world. How could you distinguish if the world is a sphere or a torus ? I can't see the difference from this point of view. If you are interested, this ...