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

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2answers
43 views

A triangle in a circle

According to the following picture $E$ is the midpoint of $BD$ and $DC=BD$. If measure of $\angle EGF$ is equals to $90$ degrees then find the value of $\frac {DE} {EF}$.(point A is the center and BC ...
1
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1answer
30 views

Vector Fields on $\mathbf R^2$ [on hold]

Let $X : \mathbf R^2 \to \mathbf R^2$ be a no-zero smooth vector field. I want to show (without background about vector bundles or manifolds, just if possible differentiable calculus in $\mathbf R^n$) ...
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1answer
11 views

On the isometries of $D_8$ (i.e isometries of the square)

The group of the isometries of the square (the dihedral group $D_8$) is generated by the rotation $\rho$ and the reflection $\sigma$. Now I have no problem with understanding the rotation but the ...
3
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0answers
31 views

Why does the coordinate transformation from Cartesian coordinates leads to an additional term in the biharmonic operator in spherical coordinates

I am trying to solve a problem in physics where the biharmonic operator is involved. I think that the bihahmonic operator can be obtained by taking twice the Laplace operator, such that $\nabla^4 f = ...
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1answer
36 views

Circle tangent to three tangent circles (without the Soddy/Descartes formula)

We have three circles tangent to each other with radii $1$, $2$, and $3$. Another circle is tangent to the other circles; find the radius of that circle using elementary geometry, without the Soddy ...
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0answers
21 views

The precise definition of Cartesian coordinate and Euclidean space?

I'd searched them for a while, but still have not found a clear and unity definition on it. The problem really confused me. What is the precise definition of Cartesian coordinate and Euclidean space? ...
0
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1answer
50 views

New Golden Ratio Conjecture with Triangle and Square: It is very close, but is it really the golden ratio?

Geogebra gives me 1.616 for the ratio of the blue segment p to the red segment q instead of the golden ratio 1.618 for the construction shown below, so it could be close to PHI, but no cigar. This ...
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1answer
11 views

Alternative Method To Looking For Equation Of A Tangent And Normal At A Point On A Parabola

Like my previous question, I'm looking for an alternate method to calculus in looking for the equation of the tangent and normal at a point on a parabola.
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0answers
24 views

Parametric Equation of Elliptical Cycloidal Sine Curve

I am trying to find the parametric equations of a cycloidal curve, which, instead of using a circle, uses an ellipse to oscillate around a base circle. Below are equations of the standard, circular ...
2
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2answers
65 views

Prove that Triangle ABC is an equilateral triangle iff $\tan{A}+\tan{B}+\tan{C} = 3^\frac32$.

This question is picked from AM GM HM inequalities, so this is to be proved form that concept only, I think it isn't possible because there is no inequality, but if it is please tell me how.
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2answers
26 views

Need help with alternative method to equation of a tangent at the point of a circle

so I know a simpler of looking for the equation of a tangent at the point of a circle is to differentiate, my lecturer would rather we not use calculus and has charged us with looking for an alternate ...
2
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1answer
28 views

Question regarding curl in dimensions higher than 3

According to the wikipedia page about curl curl can be defined implicily as $$(\nabla \times \textbf{F} ) \scriptsize{\bullet} \normalsize{\hat{n}} = \lim_{A \rightarrow 0} \frac{1}{|A|} \oint_C ...
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0answers
11 views

Differentiation between the unit spheres and the hypersurfaces in $\mathbb C^n$

Let $\Sigma ^{n-1}$ be the complex unit sphere in $\mathbb C^n$, $$\Sigma^{n-1}=\{(z_1,...,z_n)\in \mathbb C^n; z_1\bar {z_1}+...+z_n\bar {z_n}=1\}$$ and let $S^{n-1}_{\mathbb C}$ be the hypersurface, ...
1
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2answers
27 views

The number of intersection points between a trivial loop and a meridian in the torus

Let A and B be two closed curves intersect on the torus transversally at a point, the intersection index of the crossing point is defined to be positive if the tangent vectors to A and B form an ...
12
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1answer
301 views

Can any higher-dimensional Spheres be rotated everywhere equally?

You can rotate a circle so that every point on it (just the perimeter, not the interior) moves "equally". That is, every point moves with the same speed and even has the same "acceleration" ...
2
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0answers
28 views

Inverse points concurrence on the circumcircle

Let $ABC$ be a triangle, and $P,Q$ two inverse points with respect to its circumcircle. Let the circle through $A,P,Q$ meet $AB,AC$ at $A_c,A_b$ respectively. Analogously define $B_a,B_c,C_a,C_b$. ...
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1answer
39 views

Is these angles 90 degrees?

If I have the following triangle: Where $\angle B=\angle C = O$ And $AP$ bisects $\angle A$ so essentially $\angle BAP = \angle CAP = \frac12 \angle A$ We can prove that $\angle APB = \angle APC$ but ...
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0answers
10 views

Gradient and Laplacian of a submanifold

let $M^n$ be a smooth an $n$-dimensional sub-manifold of a $\mathbb{R}^{m}$. Denote by $\nabla^{M}$ and $\nabla^{\mathbb{R}^{m}}$ be the gradient of $M$ and $\mathbb{R}^{m}$ respectively. Similarly ...
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0answers
10 views

Obtain the set of points from Voronoi diagram

Given a planar infinite two dimensional mesh graph such that each small polygon of the mesh is convex, is it correct to assume for any such mesh there exists a set of points such that the these ...
4
votes
2answers
81 views

placing balls inside ball

Is it possible to put pairwise disjoint open 3d-balls with radii $\frac{1}{2},\frac{1}{3},\frac{1}{4},\dots$ inside a unit ball? not an original question, I found it somewhere in the internet ...
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0answers
14 views

Finding centriod given circumcenter, orthocenter, and direction from the origin.

I pose this problem to figure complete a answer on a problem with I have gotten far in but I am stuck here. I don't want to delete my answer because of how far I gotten anyways here is the issue I'm ...
1
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1answer
27 views

Geometric generation principle form constructing the Hilbert Curve

I have some questions on the generation of the Hilbert's space-filling curve. Any help to clarify doubts a-e would be very appreciated. The Hilbert's space-filling curve is a function ...
1
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2answers
34 views

Find the equation of tangent line passing $(2,3)$ and perpendicular to $3x+4y=8$.

I need to find the equation of tangent line passing $(2,3)$ and perpendicular to $3x+4y=8$. Need help in this and also show me how you got the answer. I will be very thankful.
1
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1answer
10 views

Finding the Centre of an Abritary Set of Points in Two Dimensions

I am currently working on a program that needs to transform one set of coordinates by shifting them to the center of the screen. The points are offset from the middle of the screen - either to the ...
1
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1answer
22 views

Why/What is this shape possible/classified as?

From supernatural season 9 episode 23. Circle is divided to 6 parts with a hexagram(? I guess), but then each line is divided to 5 parts with kissing circles, the fact that all the circles are ...
1
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1answer
20 views

Given a right triangle's perimeter and difference between median and height to the hypotenuse, find it's area.

I have been trying to solve the following problem for a while: You are given a right triangle ABC (angle C is right). The perimeter ABC is 72. CK is the median, and CM is the height to the ...
4
votes
3answers
94 views

The value of $(a+b)$, according to the question.

My friend gave me a question I tried my best, but I'm low on triangle concept. Points $ O, A, B, C... $ are shown in the figure where $ OA=2AB=4BC=...$ and so on. Let $A$ be the centroid of a ...
1
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1answer
25 views

Support of a clamped B-spline

Let a B-spline of degree $p$ be defined by its parametric equation $$ \mathbf{r}(t) = \sum_{i=0}^n N_i^p(t)\mathbf{P}_i$$ where the $n+1$ control points are denoted by $\mathbf{P}_i$. The basis ...
3
votes
0answers
25 views

Surface of the intersection of $n$ balls

Suppose there are $n$ balls (possibly, of different sizes) in $\mathbb R^3$ such that their intersection $\mathfrak C$ is non-empty and has a positive volume (i.e. is not a single point). Apparently, ...
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0answers
22 views

What is the name of a “polygon” with piece-wise polynomial boundary?

I would like to know if somebody knows the name of these objects. Given a set of $N$ vertices $\{(x_i, y_i)\}_{i=1,\ldots,N}$ (points in $\mathbb{R}^2$) we create a closed curve, defined piece-wise, ...
1
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2answers
41 views

Geometry construction

I appreciate any help. I want to find the angle $ADC$. I have drawn the circle in Geogebra, and the angle $ADC=120^\circ.$ But how can I give an argument that is always will be $120^\circ$ if angle ...
1
vote
1answer
29 views

Geometry (Locus and constructions)

I want to find the equation for the locus that is at the same distance from the point $(2,3)$ to the line $x=1$. Im not sure if I am right or wrong? Is the locus just the two point at a distance=1 ...
1
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1answer
43 views

Conics and conics of the form $ax^2+by^2+c=0$

The problem of finding rational points on conics is usually discussed (for example in the book of Silverman and Tate) for conics of the form $ax^2+by^2+c=0$. I assume that those conics are in ...
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0answers
13 views

Converting a Parametric with trig and inverse trig functions to Rectangular form

I came up with a parametric equation for rotating a function $f(t)$ on a graph in three dimensions $$y=\sqrt{f(t)^2+t^2}\sin{\left(\beta+\arctan{\frac{f(t)}{t}}\right)}\cos{\alpha}$$ ...
0
votes
1answer
31 views

Voronoi edges example

I have 4 line segments: 0 0 2 0 // 1st line segment 2 0 2 1 // 2nd line segment 2 1 0 1 0 1 0 0 and I wrote some CGAL code to print the Voronoi edges. However, ...
-1
votes
2answers
52 views

Proof that the area of a rectangle is $\ell\times b$ [on hold]

Can anybody prove that the area of a rectangle is length * width
1
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1answer
37 views

How to find the sides of a triangle if all angles of the triangle are known

In a triangle, if all angles are known, how is it possible to find all the 3 sides, using just this much information?
-1
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2answers
43 views

olypiad mathematics rmo 1999 .geometry question [on hold]

Prove that the radius of the incircle of a right angles triangle with integer sides is an integer.
-1
votes
1answer
15 views

Limit through a figure

If a circular arc of radius 1 subtends an angle of x radians . The centre of the circle is o and the point c is the intersection of two tangents lines at a and b . Now let T(x) be the area of the ...
-6
votes
1answer
33 views

Simplifying basic algebraic expressions [on hold]

$$\frac{1}{h\left(\frac{1}{x+h}-\frac{1}{h} \right)} $$ please help I'm about to take a final. I've got to study so in just gonna type till this things let's me submit my question but please don't ...
0
votes
1answer
20 views

The Locus Of M (Repeated Questuon) [duplicate]

Let A and B be two fixed points on a straight line. Two circles touch this line at A and B respectively and the tangent to each other at M, when the circles vary the locus of M is? This question has ...
1
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1answer
45 views

Area of triangle which hypotenuse=10 [duplicate]

A right triangle has a hypotenuse equal to 10 and an altitude to the hypotenuse equal to 6. Find the area of the triangle.
0
votes
0answers
42 views

Dual of a maximization problem

We have a positive, smooth, increasing concave function $f:\mathbf{R}^n\to \mathbf{R}^+$ and $k$ smooth, increasing constraint functions $f_i:\mathbf{R}^n\to\mathbf{R}$. I've recently encountered two ...
0
votes
1answer
17 views

How to find this angle isos triangle? [on hold]

$$\text{Point }A = (-4,3)$$ $$\text{Point }B = (2,1)$$ $$\text{Point }C = (-2,-3)$$ Find the angle $BAC$.
1
vote
3answers
73 views

New very simple Golden Number Ratio PHI construction with Circle and Two Equal Segments of Circle Diameter. Is there prior art? Proofs?

Geogebra gives me the golden number PHI to fifteen decimal places for this simple construction illustrated below wherein the ratio of the blue line i to the red line h is PHI or 1.6180.... The golden ...
0
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1answer
11 views

how do i do this similarity question

olivia wants to find the the height of a building. She stands so that the top of her shadow hits the same spot as the top of the buildings shadow. Olivia is $1.6\mathrm m$ tall and her shadow is ...
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votes
2answers
45 views

Measuring water in a pool [on hold]

The edge of a swimming pool is composed of two equal arcs as in the picture below. The pool is 1.8 meters deep over all, and the pool is filled with water to 20 cm from the top. How many gallons of ...
0
votes
1answer
16 views

How to find coordinates of $D$

How can I find the coordinates $D$ if I have the other coordinates of a parallelogram $A(-3/-2)$, $B(4/1)$, $C(6/5)$, $D(?/?)$. Thanks in advance
1
vote
2answers
25 views

Converting the Great Circle distance to direct distance between two points on earth?

Apologies if this question has been asked before. Across the surface of the Earth, the distance between London and New York is 5567 km. Given that the earth has a radius of 6371 km, what is the ...
1
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1answer
20 views

Coordinates along lines in a Triangle

I've just lumbered myself with a bit of a maths problem. I have the triangle below Its 3 points are at these coordinates - $(-4.2,0),\,(0, 2.7),\,(5, 0)$. I know all of my coordinates along the ...