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
17 views

Some help needed with a geometry question

What is a formula for all integers n for which a regular polygon with n sides can be constructed using a ruler and compass construction?
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0answers
34 views

Two touching circles inscribed in an angle

There are two touching circles inscribed in a $60^\circ$ angle. The distance between the vertex of angle and the center of smaller circle is $5j$. What is the ratio of the surfaces of two circles?
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0answers
26 views

Rectangle with side length of integer value. [duplicate]

There is a rectangle $D=[a,b]\times [c,d]$. This rectangle has finite partition with smaller rectangles with parallel sides $\{D_i\}_{i=1}^n$ $(n\in\mathbb{N})$. Let's put these rectangles as ...
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2answers
23 views

Find the value of EF and AC.

In the figure given below, BA, FE and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate EF and AC. I think the answer is EF= 8.66 and AC = 25.66 but I ...
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1answer
40 views

Classical geometry statement in modern terminology

Given two line segments $\overline{AB}$ and $\overline{CD}$, it's always possible to find a third line segment whose length divides evenly into the first two. In modern terminology, if we assign $x = ...
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2answers
26 views

Unusual 3D Packing Problem

I made up this interesting problem playing with wire sculptures: If I have a $10 \times 10 \times 10$ clear box and inside I can put wireframe unit cubes, what's the maximum number of unit edges (or ...
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1answer
17 views

Is there a smooth map from the square to the deltoid?

Is there a $C^\infty$ map between a unit square in $\mathbb R^2$ and a deltoid like this one The deltoid is obtained by varying the angles $\theta_1$, $\theta_2$ in the equations \begin{align} x_2 ...
4
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1answer
37 views

Calculate depth using triginometry

I was asked a question like this on an exam today and I'm wondering if I got it right or not. ...
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0answers
5 views

Generate X, Y, Z coordinates of 3D triangular prism with Edge Rounding

I'm trying to create an interactive 3D visualization with Python and Mayavi for inputs to an analysis program. The program accepts certain primitive shapes which it combines (constructive solid ...
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0answers
15 views

Solving for and x,y,z coordinate in a 3D plane

This is hard for me to explain, but basically I am making a game and I want a 3rd person like camera. I have a lot of information about how the camera should be but I can't seem to get the camera to ...
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1answer
12 views

Centroid of contiguous polygons

Say that I know which are the centroids of two polygons. These polygons share a number of edges (they belong to a planar subdivision). I want to compute the union of the two polygons and also to know ...
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2answers
31 views

Angle between two vectors, where am I wrong?

I am facing a problem, I want to find the angle between the vector u and the vector v, here is what I am doing to get this angle (I used this method) : So what I am finding is an angle that is about ...
2
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2answers
39 views

Geometric intuition: Seeing the regions in double integrals

Context: solving double integrals. I had the formula $$x^2+y^2=1-x-y$$ yet I could not see what shape it had. This is even more true with 3D pictures like $$2x^2+2y^2 \le 1+z^2.$$ Is there a summary ...
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1answer
26 views

Is there a way to find a point on a circle, given another point and an arc length without using trig functions?

Emphasis on not using the trig functions. For example, the problem would be something like find the point $\pi/3$ units counterclockwise from the point $(1,0)$ on the unit circle, without using trig ...
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1answer
47 views

Radius of the circle…

can you please give an idea of how can I solve the following problem. Given that $|AO|=\sqrt5$ and that $|OC|=\sqrt10$ find the length of the circle with the center in point $O$. Here's a picture ...
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4answers
36 views

How to determine the side on which a point lies?

Suppose we have a linear equation and a point in the plane, then how can one determine on which side of the line the point lies?
2
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0answers
11 views

action of symmetry group of cube on pairs of opposite faces.

I want to solve the following problem from Dummit & Foote's Abstract Algebra: Explain why the action of the group of rigid motions of a cube on the set of three pairs of opposite faces is not ...
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3answers
21 views

Standard equation of a line

I'm a bit confused. I read in many places that the standard equation of a line in $R^2$ is the following: $w_1 x_1 + w_2 x_2 = d$ but I found a resource that mentions it as: $w_1 x_1 + w_2 x_2 + d ...
2
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1answer
27 views

Common perpendicular

In the Poincare plane $\mathbb{H}$ show that two distinct type $1$ lines are parallel but do not have a common perpendicular. Let $\mathbb{H}= \{(x,y) \in \mathbb{R}^2 | y > 0 \}.$ A type ...
2
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0answers
15 views

Oblique Pyramids

(1) Can we have a rectangle cross-section (doesn't need to be parallel to the base) in an oblique square pyramid? (2) Can we have a square cross-section (doesn't need to be parallel to the base) in ...
2
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1answer
34 views

Intersection coordinates of a parabola with a circle

One point$(x_{0},y_{0})$ on parabola is given, the distance between the given point with two other points is $r^{2}$, $r^{2}$ is given. So this problem can also be described as: The circle equation ...
0
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1answer
12 views

How to identify any point inside or outside the given cone?

The equation of a double circular cone with a vertex $p=(a,b,c)$ with the generating angle $t$ is given by $(x-a)^2+(y-b)^2= \frac{(z-c)^2}{t^2}$ How do I identify the point ...
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0answers
17 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
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1answer
33 views

Isosceles triangle proof

In a neutral geometry, given $\triangle{ABC}$ with $A-D-B,$ $\ A-E-C,$ $\angle{ABE}\cong \angle{ACD},$ $\angle{BDC}\cong \angle{BEC}$ and the line segment $\overline{BE}\cong \overline{CD}$, then ...
0
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0answers
21 views

max and min values on symmetric polytope

Let $-N\leq t \leq N$. Let $A$ be regular $(N-1)$-dimensional simplex with vertices $(t,0, \ldots, 0)\ldots (0, 0,\ldots, t)$ and $B$ be regular $(N-1)$-dimensional simplex with vertices $(t-N+1,1, ...
0
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0answers
29 views

Calculate rotation given Points of a Triangle, Rectangle etc

If I have the all the points of a rectangle or a triangle, how do I calculate it's rotation ? EDIT : I meant the rotation of the whole rectangle or a triangle
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1answer
30 views

terms/names for these *things* [on hold]

So I am having difficulty finding the correct terms to describe the following things. multiple planes make up a space multiple spaces make up a universe (maybe? if not, what is it?) multiple ...
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0answers
50 views

A book suggestion -Algebraic geometry. (Arf rings and Hilbert Function)

I am studying algebraic geoemtry. And I need to learn Arf Ring & Hilbert funciton. Please suggest me books / lecture notes...etc. that explains this topic in detail. Thank you.
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1answer
42 views

What is the nature of this surface?

What is the nature of the surface whose equation is (it depends on $m$) $$x^2+2y^2+(m+1)z^2+2xy-2yz-2x+2y-4z+m^2+4=0$$
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0answers
10 views

Scalar Curvature of a metric on the hemisphere, from a paper on the Min-Oo Conjecture

I'm reading a paper on the Min-Oo Conjecture (http://arxiv.org/abs/1004.3088), and I'm stuck on the following step in a proposition: Given a metric $g_0(t)$ on the upper hemisphere $\mathbb{S}^n_+$, ...
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0answers
16 views

Approximating shapes using a predefined set of geometric shapes

Suppose I have a predefined set of geometric shapes.Is there a certain shape that has an advantage in approximating "constructing" arbitrary shapes "models" from mathematical "best fit & ...
0
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1answer
47 views

Parabolas intersection

We can get parabolic equation by using only focus and diretrix of parabola: $y^2 = 2px$, where p is a shortest distance between focus and directrix. But this equation defines parabola in coordinate ...
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2answers
35 views

Given a 2D integer grid, how to choose three points (x,y), (2x,2y) and (3x,3y) such that their distance to the integer grid is maximal?

Given an integer grid $\mathbb{Z}^2=\{...,(0,0), (1,0), (2,0),...,(1,1),(1,2),...\}$, choose $x,y \in \mathbb{R}$ such that the points $(x,y)$, $(2x,2y)$, $(3x, 3y)$ have maximal (Euclidean) distance ...
2
votes
3answers
39 views

Maximum volume of a box given perimeter and surface area

What would be maximum volume of a rectangular box with a given perimeter $P$ and surface area $S$? I tried to solve following equations, where $l$ is length, $b$ is base, $h$ is height, $P$ is the ...
1
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2answers
36 views

the geometric explain of $t = x-\frac{a}{3}$ in the simplify of cubic equation $x^3+ax^2+bx+c=0$

Assume $$f(x) = x^3+ax^2+bx+c$$ we have $$f''(x)=2a+6x$$. we get $x = -\frac{a}{3}$ Magically, If we take the transformation: $$t = x -\left(-\frac{a}{3}\right)$$. we can transform the above ...
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0answers
15 views

Fit cartesian coordinate system to point cloud

I have a cloud of points that initially lie in a plane and have a coordinate system attached to them. I then displace the points slightly, and I want to find how a 'best fit' of the coordinate system ...
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0answers
15 views

Finding area and perimeter with linear scale factor information

If the perimeter of a Figure A is p and the linear scale factor is r, what is the perimeter of Figure B?
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0answers
26 views

volume,area,circumference and their differences for a sphere and a circle. [on hold]

I posted the following examples and a student in mathematics said that it's nonsense using a diameter of one instead of 0.5 radius. Constant of the volume of a sphere for a diameter of one unit. ...
0
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1answer
50 views

Geometry, Find sides of a triangle

I have this equilateral triangle. The sun shaped object is a sound source. I know the difference of time between the arrival of the sound at the 2 vertices of the triangle. I need to find the angle ...
3
votes
3answers
40 views

Show that two points from four are at a distance $\leq \sqrt{3}$ in an equilateral triangle.

In a given equilateral triangle of sides length $3$, we locate 4 points. Prove that there are two of them are located at a distance less or equal to $\sqrt{3}$. I arranged the four points in this ...
3
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0answers
77 views
+50

Set geometry and inclusion

I would like to prove that the set of the symmetric positive semi-definite matrices which is defined as $\Delta_2= \{S\in\mathbb{S}_{m,m} \quad \text{s.t.}\quad ...
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0answers
15 views

Bézier curve limits

Can be any curve of any shape (without sharp edges) described by Bézier curve with unlimited (but finite) number of control points? The answer to the question above would probably be no, because I ...
0
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2answers
22 views

Distance from a point on a circle to another when the angle between them is given

There are two points on a circle and the angle between them is known, as well as the radius of the circle. What I want to do is find the horizontal and vertical distance between these points. Is ...
1
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0answers
18 views

Show an immersion is locally one to one using the inverse function theorem

Using the inverse function theorem, show that an immersion is locally one to one. I am really struggling with this homework question can anyone give me a hint?
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1answer
30 views

Draw a picture of a cube with edges a+b, and show it cut by planes that divide each edge into a segment of length a and a segment of length b.

I am reading through 4 pillars of geometry and I need some help with this question. Draw a picture of a cube with edges a+b, and show it cut by planes (parallel to its faces) that divide each edge ...
2
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1answer
40 views

The relation between principal curvature and curvature tensor?

To me, there are two systems of curvature of a surface, one is consist of 'principal curvature, mean curvature, Guass curvature, normal curvature' while the other is consist of 'curvature tensor'. I ...
3
votes
3answers
77 views

Why do we use $cm^2$?

I can't seem to wrap my head around why we should use $cm^2$ for area. According to my textbook we use it for converting units of area but I don't understand how $1cm$ is any different from $1cm^2$. ...
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3answers
64 views

Prove that this triangle is equilateral?

Given $\triangle ABC$ . Let $D$ be the point where the altitude form the $A$ vertex intersect $\overline{BC}$ and the point $E$ is the intersect between the bisector of $\angle ABC$ with ...
0
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0answers
21 views

Proving Relationships between Tangents and Secants

Prove (EA)^2 = EC*ED given that segment AE is tangent, segment Ed is a secant, and that C is the point of which the secant intersects the circle.
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3answers
38 views

Use algebra to write an equation of a circle that contains 3 points

Use algebra to write an equation of the circle that contains the following set of points: (2,1), (-3,-4), and (4,-4).