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

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0answers
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Perimeter and Circumference of n-sided polygon

Given the sidelength, number of vertices and vertex angle in the polygon, how can one calculates the perimeter of an n-sided polygon that circumscribes a circle of radius r. And how can they use that ...
1
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1answer
51 views

Dimensions of a sphere and a ball

The volume of the unit ball in $\mathbb{R}^n$ is denoted by $v_{n}$ and the surface area of the unit sphere $S^{n-1}$ is denoted by $\omega_{n-1}$. What is the importance of writing $n-1$ and $n$?
0
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0answers
23 views

Good book on non-Eucledian geometry with linear algebra approach

Does anyone know of a good textbook on non-Eucledian geometry, which approaches geometry by using mostly linear algebra (e.g., projections, dot product, cross product, etc.)? I've looked at the ...
0
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0answers
31 views

Boundary vs. Boundary??

I was reading from a text earlier and the author made the statement: "For a closed surface (that is, the boundary of a solid region)" and although it was not incredibly important for what I was ...
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1answer
13 views

The center of a circle is (5,3) and its radius is 4. Which point lies OUTSIDE of the circle? A) (4,2) B) (6,0) C) (4,5) D) (-1,-4) [on hold]

The center of a circle is (5,-3) and its radius is 4. Which point lies OUTSIDE of the circle? A) (4,-2) B) (6,0) C) (4,-5) D) (-1,-4) Please show work.
2
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1answer
36 views

Problem solving $\int_{1}^{2}\int_{x}^{2x}\int_{\sqrt{1-x^{2}-y^{2}}}^{\sqrt{2xy}}\frac{zdzdydx}{x^{2}+y^{2}+z^{2}} $

Good night, i have a problem solving this integral: $$\int_{1}^{2}\int_{x}^{2x}\int_{\sqrt{1-x^{2}-y^{2}}}^{\sqrt{2xy}}\frac{zdzdydx}{x^{2}+y^{2}+z^{2}}$$ I think make a change to spherical ...
8
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2answers
126 views

New very simple golden ratio construction incorporating a triangle, square, and pentagon all with sides of equal length. Is there any prior art?

Consider three regular polygons with 3, 4, and 5 sides wherein all the polygons have sides of equal length X throughout, as illustrated below. The ratio of the red line segment a to the blue line ...
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1answer
23 views

Cone under similarity transformation

Suppose we have a cone passing through the origin of $xyz$ coordinate system. Now, the question is that whether we can find a similarity transformation on this coordinate system that turns the cone ...
1
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1answer
45 views

How can I calculate $\int_1^2 \int_{\sqrt{x}}^x \sin\left(\frac{\pi x}{2y}\right) \,dy \, dx$?

Good night i have problem solving this integral. $$\int_1^2 \int_{\sqrt{x}}^x \sin\left(\frac{\pi x}{2y}\right) \,dy \, dx$$ I make the area of integration, but i cannot solve the integrat, i don't ...
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4answers
46 views

A cube and a sphere have equal volume. What is the ratio of their surface areas?

The answer is supposed to be $$ \sqrt[3]{6} : \sqrt[3]{\pi} $$ Since $$ \ a^3 = \frac{4}{3} \pi r^3 $$ I have expressed it as: $$ \ a = \sqrt[3]{ \frac{4}{3} \pi r^3} $$ and, $$ \ 6 \left( ...
9
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1answer
51 views

How do you calculate the smallest cycle possible for a given tile shape?

If you connect together a bunch of regular hexagons, they neatly fit together (as everyone knows), each tile having six neighbors. Making a graph of the connectivity of these tiles, you can see that ...
1
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1answer
9 views

Lines intersections distance on the asymptotes

Like in picture we have two lines. Lenght of one of them is 2E and other's lenght 2C and also ellipse asymptotes are A and B and its center is on origin(0,0) I want to find D and F How can I ...
2
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2answers
74 views

Am I correct that the quadrilaterals in this textbook exercise aren't necessarily squares?

Most people when they look at this problem immediately assume that the quadrilaterals are square but there is no mathematical evidence of this. Am I going insane and seeing things or am correct to ...
0
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0answers
15 views

Calculate the percentage of a triangle inside a cuboid?

I have a large (order 10^7) collection of triangles in 3D space. I also have a cuboidal mesh also of order 10^7. For each triangle I need to calculate the area of that triangle which is inside any of ...
4
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0answers
59 views

minimize the area of convex hull of sum of 3 balls

How should we place 3 balls $B_1,B_2,B_3$ on the plane, if we want to minimize the area of convex hull of $B_1\cup B_2\cup B_3$ ? Balls can have boundary common points only -- the intersection of any ...
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2answers
78 views

Problem about a goat, a small house, and some grass [on hold]

A goat is tied to the corner of a small house, with a 6 m long rope . The house is 3 m wide by 4 m long its rektanguler house. There is grass around the house. On how much property can the goat graze? ...
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2answers
19 views

Calculating the angle in which surfaces meet

We have a L-shaped house. Both sides have gable roof. For one side, the inside angle is $45$ degrees and for the second one, $40$ degrees. Question is, how many degrees is the line, in which both ...
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0answers
50 views

Isoperimetric hexagon and triangle ; comparing their areas. [on hold]

A regular hexagon ( all sides of equal length and all angles equal ) and an equilateral triangle is equal circumference. What percent larger is the largest area ??
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1answer
16 views

Two collineations

Give collineations to prove the following (in the extended projective plane): a, One cannot contruct the midpoint of two points using a straightedge only. b, One cannot construct the reflection of a ...
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0answers
51 views

About a geometric algorithm to compute $\sin$ based on the unit circle

In an old post I have found a user which claims to have a geometric algorithm to compute trigonometric  functions for an angle between $0^\circ$ and $90^\circ$ based on the unit circle. Here's the ...
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0answers
17 views

Finding the number of integer points inside a sphere of radius R and dimension D centered at the Origin

I am writing a computer program to count the number of integer points inside a sphere of radius R and Dimension D centered at the origin. In essence, if we have a sphere of dimension 2 (circle) and ...
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1answer
12 views

Get the width and height of the inner well aligned rectangle after rotation

I'd like to get the width and height of the red rectangle with this constraints: Maximize the area of the red rectangle The center of the rotation is the center of the original (dotted) rectangle. ...
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14answers
10k views

Why is radian so common in maths?

I have learned about the correspondence of radians and degrees so 360° degress equals $2\pi$ rad. Now we mostly use radians (integrals and so on) My question: Is it just mathematical convention that ...
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0answers
19 views

Constant of proportionality for the following

Could somebody explain to me what is meant by the constant of proportionality and then show me how I would find it for the following polygons: Pentagon. Hexagon. Decagon. Kilogon. and Megagon. ...
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0answers
51 views

Is there a way to determine the cheapest way to cut a line if each cut costs the current length of a line?

I was reading through an example question for the UNSW Computing ProgComp and found a question they claimed to be impossible to solve without going through all possible solutions. From ...
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0answers
31 views

Problem finding the tangent plane and the normal line of an surface [on hold]

Good night, I have a serious problem when I try to find a tangent plane for the following surface at the point $P$: $$x^{2}+y^{2}+z^{2}=6, \hspace{4mm} P=(-1,-2,3).$$ I make this: $\nabla ...
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4answers
32 views

How to calculate point 90 degrees from ray [on hold]

Say I have a point at (3,3), as in the picture below, and there is a ray that comes in from an unspecified point. What is the formula to calculate the point at 90 degrees in either direction from ...
0
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1answer
32 views

How to find equidistance from 4 points

So, for instance if we have 4 friends at 4 different cities and they want to walk in a straight lines and meet with each of them covering the same distance, how would we calculate it? For 2 people ...
9
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3answers
237 views

New, extremely simple golden ratio construction with two identical circles and line. Is there any prior art? [duplicate]

This question is different from a previously asked question (linked above) as this golden ratio construction only utilizes two circles and a line, and is thus far simpler than the golden ratio ...
0
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1answer
15 views

How to points of line in ellipse when it's moved as ellipse tangent [on hold]

Ellipse Picture In the picture minor and minor asymptote and points of line (X&Y) are known, when we move the line new position is X' and Y'. How can be calculated new position of line or is ...
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0answers
11 views

Same Center Ellipse Major and Minor Axes

Ellipse Picture I have two same center ellipses A, B, and C are known values X and Y arent known values and I need to obtain these values. How can it be calculated?
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2answers
24 views

Calculate the plane equation of 2 vectors. [on hold]

Which type should I use in order to calculate the plane equation that is defined by 2 vectors, let's say V1 $\langle{1,2,3}\rangle$ V2 $\langle{4,5,6}\rangle$.
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0answers
11 views

Propagation of a volume element along a (pseudo) Riemannian metric?

I am considering the propagation of a volume element $\delta V$ along a (probably pseudo)Riemannian manifold. For example, consider the volume element at $\delta V(x_{0}^{\mu})$ . Utilizing the ...
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0answers
28 views

How to find the Coordinate equation of a curve which bends all the parallel rays from infinity towards a single point

How should I proceed on to find the coordinate equation of a curve such that it bends all the parallel rays coming from infinity towards a single point. Yes I know that it would be a 2nd degree ...
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2answers
128 views

New Golden Ratio Construction with Two Adjacent Squares and Circle. Have you seen anything similar?

The below Golden Ratio Construction results in a ratio of PHI (1.6180...) between the blue line and red line, as found in Geogebra. This seems like a simple construction of the golden ratio, yet so ...
2
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0answers
13 views

Describe the position of $w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}$ w.r.t. $B_R(0)$ and $B_r(z_0)$

I am working with two circles $B_R(0)$ and $B_r(z_0)$ and want to describe the position of the point given by $$w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}.$$ First I would like to know whether my ...
3
votes
1answer
27 views

Shapes described by a homogeneous quadratic equation

Suppose we have a homogeneous quadratic equation of three variables $w_1$, $w_2$, and $w_3 \in \mathbb{R}$ as follows: $$W^TAW=0.$$ where $W=[w_1,w_2,w_3]^T$ and $A$ is a non-singular $3\times 3$ ...
0
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2answers
24 views

Angle between the plane of an ellipse and the axis of the conic

Is there a way to determine the angle between the plane of the ellipse and the axis of the conic?
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1answer
20 views

Find the surface area of the shape formed by the boundary of $\frac{z^2}{4}=\frac{x^2}{2}+\frac{y^2}{4},z=2x+4y, z\geq 0$

$$\frac{z^2}{4}=\frac{x^2}{2}+\frac{y^2}{4},z=2x+4y, z\geq 0$$ I know that this is a cone that is cut by a plane, but I do not know how to find the projection onto $xOy$. I need this because then I ...
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0answers
21 views

Reflection is not a collineation

Could you give me a collineation that proves that you can't construct the reflection of a line $e$ across a parallel line $f$ with a straightedge only? (That is, a collineation that maps $e$ and $f$ ...
0
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1answer
26 views

Maximum area of a triangle when perimeter is fixed.

I can't solve the following problem: Show that amongst all triangles with perimeter $3p,$ the equilateral triangle with side $p$ has the largest area. Further show that $9p^2\ge 12\sqrt{3}\Delta.$ ...
0
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1answer
21 views

Point of intersection of ellipses

If two ellipses are intersecting at a point,is it necessary that the line drawn joining the centre of those two ellipses should also pass through the point of intersection (of ellipse)? (if yes,how to ...
0
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1answer
25 views

Can point in 3D space be represented as vector?

If yes, then such vector is just displacement from origin in coordinate system? Also, I have another(optional) question, how to name variable that represnts particular point using vector? Position or ...
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0answers
14 views

How to construct the circumcenter of a triangle using a compass ONLY.

I just figured out how to find the midpoint between two points using just a compass and no straight edge. A similar approach can be found in this question: Constructing the midpoint of a segment by ...
0
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4answers
34 views

Determining the radius of a circle to fit a specific region

Imagine I have two identical circles of radius 1, placed side-by-side so they touch at one point, and a tangent line that touches both circles at one point each, like so: There's a vaguely ...
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0answers
23 views

The set $S = \{(x,y,z) \in \mathbb{R}^3: y^2=4x, z=2\}$ represents a? [on hold]

The set $S = \{(x,y,z) \in \mathbb{R}^3: y^2=4x, z=2\}$ represents a ? $1$) Parabola $2$) Cylinder $3$) Plane $4$) Empty set
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2answers
44 views

Can a 2d shape have more vertices than edges? [on hold]

Can a 2 dimensional shape have more vertices than its edges, if there are no curved edges? For example, a hexagon has 6 edges, and 6 vertices. However, is there any shape, open or closed, where the ...
2
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1answer
45 views

Have you seen this golden ratio construction before? Three squares (or just two) and circle. Geogebra gives PHI or 1.6180.. exactly

Have you seen the attached golden ratio construction before? Three squares (or just two) and circle. For the ratio of segment t to segment a, Geogebra gives PHI or 1.6180.. exactly. Geometric and ...
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0answers
9 views

What is an orthogonal monometric system?

I am reading a journal paper. In that I have chosen a flat slab as a reference geometry for some object. Then they have placed a orthogonal monometric system x,y,z with the plan of xy coinciding with ...
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0answers
47 views

Surface area of cone without calculus

Let $l$ be the length of a cone's lateral and $r$ be the radius of its base. The cone's surface area (excluding the base) is $\pi rl$. Briefly googling, most proofs I see simply claim that if you ...