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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0answers
36 views

Hippocrates trapezoid lune

How can I prove that a lune based on the construction of a constructible isosceles is quadrable? Hippocrates' other squarable lune
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0answers
15 views

Reading a 3d graph to generate a 2d projection.

I know this will sound very dum but I have spent some good time trying to understand before posting this question. Basically, I need some help in understanding how (a) and (b) are being used to ...
0
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0answers
19 views

Calculating fov angle based on distance

I'm trying to calculate the angle between me and the target angle yaw in a 3D game, so that the actual angle is always the same based on distance how far I am from the target. I've tried a few ...
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1answer
41 views

number of rectangles in two superimposed grids

I got two grids consisting of square "pixels", each has a different unit length per pixel though, 1 and $\frac1\xi$. Now I superimpose them as in the following image. The grid sizes differ, as ...
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2answers
47 views

Grid with both squares and equilateral triangles

Is it possible to have a grid that contains both squares and equilateral triangles? By grid I mean any set of the form $M \mathbb Z^2$, with $M \in GL_2\mathbb R$. I think this is impossible, ...
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1answer
11 views

Transitive parallel lines in noneuclidean-geometry

Is it true in neutral geometry that "If a line $m$ parallel to to a line $\ell$ , and line $\ell$ parallel to line $n$ then $m$ parallel to line $n$"? ' where $m\ne n$ I think that this is corrent, ...
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1answer
21 views

Finding the gradient vector of a plane along the plane's surface

How do you find the gradient vector of a plane? I have a plane that passes through the origin with the equation P: 5x + 95y + 46z = 0 whose normal ...
2
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6answers
82 views

Checking nature of angles of a triangle given the equations of the three lines that form a triangle

Suppose we have three lines $\ell_i=a_ix+b_iy=c_i$, $i=1,2,3$ and we are given that they form a triangle. I need to find which angles are acute and which are obtuse without plotting the lines ...
2
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2answers
42 views

Radius of inner circles given radius of outer circle and number of inner circles in circular fractal

I am trying to create a circular fractal in which each circle is composed by a given number $n$ of smaller circles. It would look something like this for $n = 8$: However, I don't know how to ...
0
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1answer
37 views

Finding the overlap between direction of distance in position space and direction of distance in velocity space

There are two objects A and B that can be described in position space and velocity space. The position space describes the instantaneous positions of the objects while the velocity space describes ...
0
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3answers
51 views

Finding ratio of cevian lines

I am preparing for an exam and doing some pratice problems. So I'm having a difficult time with this problem. At first I thought the ratio was 2:1 and then I also thought I would be able to use the ...
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0answers
20 views

Solve linear system with $A_{i,j} = \langle e_i, e_j\rangle^2$, edges of a tetrahedron

I have six vectors in $e_i\in\mathbb{R}^3$ that are the edges of a tetrahedron. Let us consider now the linear equation system $Ax=b$ with $$ A_{i,j} = \langle e_i, e_j\rangle^2,\\ b_i = \langle e_i, ...
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1answer
1k views

IMO 2016 Problem 3

Let $P = A_1 A_2 \cdots A_k$ be a convex polygon in the plane. The vertices $A_1, A_2, \ldots, A_k$ have integral coordinates and lie on a circle. Let $S$ be the area of $P$. An odd positive integer $...
0
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1answer
74 views

Can you Prove or Disprove this?

In $a^n+b^n=c^n$ , $(a<b<c)$ , $a,b,n$ belongs to natural numbers, If $n>=b/2$ , $c$ lies between $(b,b+1)$. Also, only for $n=1,2$ , $c=b+1$.
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1answer
18 views

In flux vs. radius equation, isn't there a mistake in the dimensions?

The video: https://www.youtube.com/watch?v=m13kKLHhN6Y The equations given are: $\frac{Energy}{Seconds} = \frac{L . A}{4 \pi r^2}$ where $L$ is the luminosity, $A$ area and $r$ is the radius. $Flux ...
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2answers
55 views

How to express an angle of 90 degrees between two lines?

If I would extend two lines $l_1$ and $l_2$ they would intersect with an angle of 90 degrees. How should I write with math terms that there would be a 90 degree angle. I assume $l_1 \perp l_2$ is ...
0
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0answers
24 views

Explicitly calculating the group of global isometries of a convex regular polygon (dihedral group)

Instead of an intuitive geometric description of the dihedral groups $D_{2n}$, that one can find in virtually every good book on group theory, I want to calculate the global isometries of a convex ...
0
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1answer
30 views

Parametric equations of an ellipse in an arbitrary plane at an arbitrary orientation?

I have searched both on here and on stackoverflow for answers to this question and I can't seem to find a good answer relating to what I'm doing. I have a center point and two vectors, one that is in ...
0
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1answer
27 views

If we increase the radius of a circle, does the arc's length equal the length of two end points of the arc?

I'm taking an online course and in it, the professor says that if we increase the radius of a circle, the arc's length will be equal to the length of line joining the end points of the arc (https://...
-4
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2answers
83 views

Geometric Implication of 0.9999… =1

I have been taught that $0.\overline9=1$. Now if we think of the finite series' in turn, each closer in turn to $1$ than the previous: 0.9 0.99 0.999 etc. If we called the difference between ...
2
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0answers
45 views

Could Euclid have proven Dedekind's definition of real number multiplication?

In Euclid's day, the modern notion of real number did not exist; Euclid did not believe that the length of a line segment was a quantity measurable by number. But he did think it made sense to talk ...
0
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1answer
22 views

Pair of straight lines problem: Prove that $g (a_1+b_1)=g_1 (a+b) $

If the lines joining the origin and the point of intersection of the curves $ax^2+2hxy+by^2+2gx=0$ and $a_1x^2+2h_1xy+b_1y^2+2g_1x=0$ are mutually perpendicular then prove that $g (a_1+b_1)=g_1 (a+b) $...
2
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1answer
34 views

Identifying a triangle in the 3d-space as acute, obtuse, right or equilateral

Triangle $ABC$ has vertices $A(-1, 1, 3)$, $B(-1, 3, 5)$, and $C(-3, 3, 3)$. What kind of triangle is $ABC$? Justify your answer. So far all I have done is I found the distance between $AB$, $BC$ ...
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1answer
36 views

Show that the reflection of a disc through the origin is a disc

This is a problem from the book "Basic Mathematics" by S.Lang (p.225, exercise 13b). It is similar to the one in my previous question, with the exception that we're considering a reflection instead of ...
2
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1answer
26 views

How can I get the angle on radian on wolfram?

Here, the argument of a complex number in degrees is given. How can I ask wolfram to convert it into radians (they give an approximation).
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3answers
74 views

Motivation for the dot product

We can motivate the cross product by considering a 3D vector perpendicular to two others. This results in 3 equations in 2 unknowns, i.e. a line of solutions, and... $\lambda(u_2 v_3 - v_2 u_3, ...
2
votes
1answer
40 views

Sierpinski triangle formula: How to take into account for 0th power?

The formula to count Sierpinski triangle is 3^k-1 .It is good if you don't take the event when k=0.But how can you write a more ...
4
votes
1answer
69 views

Interesting circles hidden in Poncelet's porism configuration

This question is an investigation starting here, with a straightedge and compass construction of $ABC$ given $(R,r,h_A)$. The key lemma is the following one: Let $\Gamma$ be a circle with centre ...
1
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0answers
14 views

Show that the disc of radius $r$ centered at $A$ is the translation by $A$ of the disc of radius $r$ centered at the origin

This is a problem from the "Basic Mathematics" book by S.Lang (p. 225, exercise 12). My problem: Let $D(r, A)$ denote the disc of radius $r$ centered at $A$. Show that $D(r, A)$ is the translation ...
1
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0answers
44 views

Finding an isometry in $\mathbb R^4$ under some conditions.

This is a follow-up to a previous question of mine that was not fully answered, I tried again my hand at the problem and I think I am close to a solution. In an affine space with the standard ...
0
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1answer
65 views

Area of a quadrilateral in which a circle can be inscribed using algebraic geometry

$\Delta POR $ has vertices $P(0,12),R(5,0)$ and $O(0,0)$. There exists a line $l$ cutting $PR$ and $OP$ at $A$ and $B$ respectively such that circles can be inscribed in $\Delta PAB$ and quadrilateral ...
2
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0answers
30 views

Fitting Rectangles

I have a quantity of small rectangles I need to fit in a larger rectangle frame. I need an equation to figure out what is the maximum size I can make the small rectangles before they are all too big ...
0
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1answer
32 views

Relative speed of minute hand in a clock

In a 12 hours clock: The minute hand has to chase the hour hand with a relative speed of 5.5 degrees/min what is the mathematical derivation of this relative ...
1
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0answers
102 views

Conjecture about circles in plane lattices

A plane lattice $\Lambda$ is a set $\Lambda= \{ mA+nB: m,n \in \mathbb Z \}$, where $A,B$ are linearly independent vectors in $\mathbb R^2$. The set of all circles in $\Lambda$ is $$\mathcal K(\...
0
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1answer
29 views

Proving the concurrency of angle bisectors in a triangle analytically

I'm taking a course at teaching and we have some geometry questions. Among the questions there was one I couldn't solve. I'm trying to prove that angle bisectors in a triangle intersect at a single ...
0
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0answers
30 views

Average distance between two points in a bounded region [duplicate]

How to construct the integral in calculating the average distance between two random points inside a square? Is this the same as asking the average length of all the possible line segments which can ...
0
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1answer
20 views

Show that, if $u,v,w$ are orthogonal two-by-two, then $S = \{ u , v , w\}$ forms a basis which is linearly independent

I am given the following question: Show that, if $u,v,w$ are orthogonal two-by-two, then $S = \{ u , v , w\}$ forms a basis which is linearly independent. My idea to tackle this problem is to ...
0
votes
3answers
39 views

Verify if $\overrightarrow{w}$ is a linear combination of $\overrightarrow{u}$ and $\overrightarrow{v}$

I am given the following question: Let $\Vert \overrightarrow{u} \Vert = \Vert \overrightarrow{v} \Vert = \Vert \overrightarrow{w} \Vert = 1$ and $\overrightarrow{u} \cdot \overrightarrow{v} = \...
1
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2answers
41 views

Circle Geometry Question

1) In triangle $ABC$, $AB = 10$, $AC = 8$, and $BC = 6$. Let $P$ be the point on the circumcircle of triangle $ABC$ so that $\angle PCA = 45^\circ$. Find $CP$. Diagram(1) 2) Let $B$, $C$, and $D$ be ...
4
votes
2answers
65 views

Solve linear system with $A_{i,j} = \langle e_i, e_j\rangle^2$, edges of a triangle

I have three vectors in $e_i\in\mathbb{R}^3$ that form a triangle. Let us consider now the linear equation system $Ax=b$ with $$ A_{i,j} = \langle e_i, e_j\rangle^2,\\ b_i = \langle e_i, e_i\rangle. $$...
3
votes
1answer
37 views

On constructing a triangle given the circumradius, inradius, and altitude .

I was recently pondering about constructing triangles given different attributes of it. I am wondering whether we could construct a triangle given its Circumradius $R$ , Inradius $r$, and length ...
1
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2answers
23 views

Parametrized equation of hyperplane orthogonal to main diagonal

For the hyperplane passing through the origin and orthogonal to the ones vector,$(\underset{n\ \mbox{times}}{\underbrace{1,\dots,1})}$ in $\mathbb{R}^{n}$, what are the $n-1$ remaining orthonormal ...
2
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2answers
37 views

How to find the length of a side in a right triangle

If the length of a side in a right triangle is 8 and the hypothenuse is $\sqrt{113}$, what is the length of the other side ? I tried different formulas but I'm not getting any answer. Answer ...
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1answer
28 views

Average distance (maximum norm) from origin to the nearer of two random points in a unit square

I got a unit square, the origin (0,0) and two random points which are uniformly distributed on the 1x1 unit square. What is the average distance in maximum norm from origin to the nearer of the two ...
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2answers
38 views

What type of triangle is this? [closed]

what type of triangle has side lengths $12,13,2 \sqrt{3}$ A. Acute B. Right C. Obtuse D. not a triangle I tried $a^2 +b^2=c^2$ but that didnt work
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0answers
16 views

How to back calculate x based on a smoothed f(x)

I am trying to develop a widget that helps you define a function visually. So you could add various points on a graph and have the whole function for each x be calculated based on these points. If ...
4
votes
2answers
117 views

The problem of congruent areas in a triangle.

A problem was posed in front of me and I couldn't solve it after multiple attempts-- Consider any triangle and 3 concurent cevians are drawn from each of its 3 points . Now the figure formed has 6 ...
0
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7answers
552 views

Get the equation of a circle when given 30 points [closed]

A similar question has been asked before on this site but that was of getting equation of circle using 3 points. I want my center to be more accurate So my question is how can i get the center of ...
1
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0answers
20 views

How to Compute peak point form polygon object

I have to transform the first object (Polygon object) to the second. In order to transform the object to flat surface I need to compute the Height $H$ from the curved line. I am looking for the ...
1
vote
2answers
51 views

In $ABC$, $D$ is the feet of the angle bisector of $\widehat{BAC}$. Prove $AB\times AC=BD\times DC+AD^2$

In $ABC$, $D$ is the feet of the angle bisector of $\widehat{BAC}$. Prove that $AB\times AC=BD\times DC+AD^2$. I have proved triangles $ABD$ and $ABC$ similar then I am confused.