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

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1
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0answers
25 views

How to compute the volume of such a triangular prism shaped object

like this : where $z_i$ are not equal.
-2
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0answers
21 views

circles word problems! geometry section [on hold]

In the given figure, triangle $ABC$ is inscribed in a circle with center $O$. if angle $\angle ACB$ equals 65 degree then what is angle $\angle ABC$?
0
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1answer
31 views

The equation of a 3D surface bounded by 3 known elliptical curves

I am trying to find the equation of a 3D surface as illustrated below. The boundaries of this surface is comprised of two planar elliptical arcs $AB$ and $AC$ as well as a 3D arc $BC$ which is a 3D ...
0
votes
1answer
25 views

Linear bound on angles in an euclidean triangle.

I am trying to understand a proof in the book of Burago "A Course in metric geometry" (Lemma 10.8.13 page 383). I have difficulties with a certain inequality for the angle of euclidean triangles: ...
0
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0answers
21 views

Arrow Space Construction

Is there a paper or book that has rigorously constructed the space of "arrow vectors" and shown that it is a vector space? I'm just wondering how far anyone has followed the heuristic.
0
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0answers
19 views

How can we split a single rotation into two along orthogonal axes?

I have the following axis system, where the X-Y plane is horizontal and Z points 'up': I have a horizontal plane that I want to rotate so that the angle between it and the XY plane is theta. I ...
4
votes
2answers
111 views

Find the ratio between $|AB|$ and $|BC|$

I have this problem, which is about this right triangle below. It says that $|AB|$ and $|BD|$ (which is the diameter of the circle) are equal and that the circle is touching the side $|AC|$. Now I ...
-2
votes
0answers
21 views

circles and points on a grid [on hold]

An infinite number of points are marked on the coordinate grid such that there is no circle that passes by 1000 of them. Is there necessarily a circle of radius 20 that does not contain any of those ...
0
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0answers
33 views

Trying to prove concurrence of altitudes of a triangle.

I know that this question had been asked before, but I am not exactly following what the answers say. Doing my own way here: I am puuzzled how to continue? I named the points A,B,C, and the foot of ...
2
votes
2answers
16 views

Find the area of the cyclic quadrilateral given the two diagonals

One diagonal of a cyclic quadrilateral coincides with a diameter of a circle whose area is 36$\pi$ $cm^2$. If the other diagonal which measures 8 $cm$ meets the first diagonal at right angles, find ...
0
votes
1answer
14 views

Finding ellips equation by focuses and tangent line

The Ellips which has focuses in $(±3,0)$ and a tangent line $x+y-5=0$. I need to find ellips equation. I've founded these equations $\frac{x_{0}}{a^2} = \frac{1}{5}, \frac{y_{0}}{b^2} = \frac{1}{5}$ ...
0
votes
5answers
42 views

Obtain coefficients of a line from 2 points

I wish to use two points say $(x_1$,$y_1)$ and $(x_2$,$y_2)$ and obtain the coefficients of the line in the following form: $$ Ax + By + C = 0$$ Is there any direct formula to compute.
3
votes
3answers
43 views

Cutting proportionally

Given any convex quadrilateral $ABCD$ and an inner point $z$ is it possible to draw/construct a line $EF$ passing through $z$ s.t. $$\frac{AE}{EB}=\frac{DF}{FC}$$
3
votes
3answers
60 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
0
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0answers
17 views

Find max cone inscribed parallelepiped volume

There is a right cone with H = 20 and R = 12. How to find the best inscribed parallelepiped parameters which would provide its ...
-5
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3answers
36 views

Extend length of the vector [on hold]

I have a vector $AB$ defined by the points $A$ and $B$ in $x,y$ coordinates. I need to find the coordinates of the point $C$ on the the line defined by $A$ and $B$ for any value of $L$ length I set, ...
1
vote
2answers
37 views

Maximising the Area of a Cyclic Quadrilateral

In cyclic quadrilateral $ABCD$, $AB = AD$. If $AC = 6$ and $AB/BD = 3/5$, find the maximum possible value of $[ABCD]$. (Source: SMT 2014) If we let $AB=AD = 3x$ and $BD=5x$, from Ptolemy, we have ...
0
votes
2answers
45 views

Circle with center point and tangential to lines

I have defined Points all points (3 blue, and one green). All points have the same distance to A point. Yellow lines are bisectors. I have equations of AB and ...
3
votes
0answers
20 views

How many spherical caps of height $h$ and base circle radius $a$ can cover a sphere of radius $R$?

Question How many spherical caps of height $h$ and base circle radius $a$ can cover a sphere $\mathbb S $ of radius $R \quad (R \gg a)$? What I have thought so far Since the area of the ...
1
vote
2answers
28 views

Find point on line withv given start point, distance, and line equation

I have line equation $$ Ax +By + C = 0.$$ I have start point (on this line): $ P_0 = (X_0, Y_0)$. I have distance $d$ too. I need find point $P_2$ with distance $d$ from $P_0$ and placed on ...
0
votes
1answer
31 views

Euclidean metric formula

Is this the correct formula for the euclidean metric (in $R^4$ )? $g_E = dr^2 + r^2(d\theta^2 + d\phi^2 + d\tau^2 + \cos \theta d\tau d\phi).$ I have been doing some calculations that are wrong and ...
0
votes
1answer
29 views

Is there a formula for finding the centers of the faces of a platonic solid?

Is there a formula for finding the centers of the faces of a platonic solid given the center of the first (origin) face to be $P_0(x_0,y_0,z_0)$?
3
votes
1answer
58 views

Area of a circumcenter triangle equals area of medial triangle

Let $X$, $Y$, $Z$ be the midpoints of sides $BC$, $AC$, $AB$ respectively in triangle $ABC$. Let $O_{A}$, $O_{B}$, and $O_{C}$ be the circumcenters of triangles $AZX$, $BXY$, and $CYZ$ respectively. ...
4
votes
1answer
89 views

Geometry construction problem

Given two circles $S_1$ and $S_2$, a line $l_1$, and a length $a$ that is less than the sum of the diameters of the circles, construct a line $l$, parallel to $l_1$, so that the sum of the chords that ...
6
votes
2answers
89 views

What is the geometric interpretation of a vector squared?

I'm working through Introduction to Space Dynamics by William Tyrrell Thomson. I am having to do a lot of research to make it through even small parts, but I am unable to find information to make me ...
0
votes
2answers
16 views

different formulae to find aspect ratio

I am working on a software 2D model where we need to work with aspect ratios. My boss gave us a formula which defines it as: ...
0
votes
1answer
37 views

Easy question about line up points ?

Well, there is a demonstration to prove that 1+1=2 so is there a demonstration to prove if you take two points on the space, they are line up ? Thank's
0
votes
0answers
38 views

Geometric proof of BD/BE = CD/CE ; methods for congruent triangles

It seems to me that if BAC = DEA this would be straightforward, but I lost myself in the variety of congruencies here.
3
votes
1answer
50 views

General form for the rotation of a function.

When rotating linear functions, I would approach the task geometrically (find invariant point etc.), yet I tried using a matrix which worked nicely. This was what I did to rotate $y=2x+1$ by ...
2
votes
0answers
57 views

Which convex $2n$-gons have symmetry group $D_n$ instead of $D_{2n}$?

The equilateral octagon $M$ in the first image has the same symmetry group as the small embedded square - namely the dihedral group $D_4$ - with $8$ elements and generators ${x,y}$ with $x^4 = e, y^2 ...
3
votes
3answers
59 views

Distance between the nail and the center of the disk

Suppose you have a disk with radius $r$ and a string of length $2 \pi r+l$, i.e. longer than the perimeter of the disk. Hang the disk (of center $O$) from the nail at $A$ using the string as shown ...
0
votes
1answer
25 views

Geometry - Volume of a distorted tent

How would one calculate the volume of a tent shaped object with the upper edge not parallel with the base plane of the tent? edit: The tent has a rectangular base with two poles at different heights ...
1
vote
1answer
31 views

How can you prove that perimeter of right triangle equal to diameter of incircle and twice the diameter of circumcircle? [on hold]

How can you prove that perimeter of right triangle equal to diameter of incircle and twice the diameter of circumcircle?
2
votes
1answer
26 views

Are the principal congruence subgroups of SL(2,Z) normally generated by a single element?

Let $N\ge 3$, then would I be correct in saying that the principal congruence subgroup $\Gamma(N)$ (defined to be the 2x2 matrices in $SL(2,\mathbb{Z}$) congruent to the identity mod $N$) is the ...
3
votes
3answers
438 views

How did the Ancient Greeks know that the circle method of finding square roots was mathematically valid? How do we know that?

The Ancients used this method. (or at least James Grime said in a numberphile video) To construct the square root of a number, draw an interval of length $a+1$, and then draw a semi-circle with the ...
1
vote
2answers
32 views

Space formed by dot products of three vectors

Suppose I have 3 3D unit vectors $\mathbf{v}_1$, $\mathbf{v}_2$, and $\mathbf{V}$. I define the three corresponding scalars $u_1=\mathbf{v}_1 \cdot \mathbf{V}$, $u_2=\mathbf{v}_2 \cdot \mathbf{V}$, ...
3
votes
3answers
59 views

How to solve for $\theta$ in an expression involving linear and $\sin$ terms

While trying to solve a spatial geometry problem, I came across the expression: $$156θ-36\sin\theta=554.8$$ And I have no idea where to even begin.
0
votes
4answers
41 views

Ellipse focal proof

In the ellipse with equation: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ How to proof the production of distances between focal and a random tangent is $b^2$ $F1A * F2B = b^2$
2
votes
0answers
31 views

Partial Integral of an ellipse

this is my first question on stack exchange so please bear with me. I am trying to generate a synthetic image of an ellipse in Matlab where each pixel is shaded according to how much of that pixel ...
0
votes
0answers
28 views

Isoceles Triangles on a Grid Proof

Given: A Finite Set of Unit Squares on a Large Grid. If we were to choose one of those sets of unit squares, we see that the squares of the set are tiled with isoceles right triangles, each with a ...
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votes
0answers
21 views

Convex basis and conical basis (how to draw?)

There is a question, I'm struggling with: Find vertices of the following described polyhedron, $P:=P(A,b)=conv(V)+cone(E)$ where $V$ is the set of all vertices of $P$ and $E$ is the set of all ...
0
votes
1answer
19 views

Calculating my location based on known location

This question is linked to Can known object be used to back-calculate my location? (been almost a month, figured it would be best to start a new question.) I have a map, and I know which way true ...
1
vote
0answers
51 views

Physical or geometric meaning of the trace of a matrix

The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too. Is there ...
2
votes
1answer
26 views

Does there exist a 4D torus with a spherical cross-section, analogous to a circle for the 3D case?

I don't mean to be a bother. It seems as though the answer may be obvious, but then, seemingly simple math questions can have surprising answers. I should also like any pointers re: the general ...
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0answers
33 views

Show that the Axioms are satisfied [on hold]

A real number x is called dyadic, if it can be written as $x = a/2^n$, for some integers $a,n \in \Bbb Z$. In particular, all the dyadic numbers are rational numbers. Let $\Pi = \{(a/2^m, b/2^n)|a, b, ...
0
votes
1answer
23 views

Polygonal sides when interior angle relationship is given

The difference between any two consecutive interior angles of a polygon is 5°. The smallest angle is 120°. Find the number of sides. I know that the sum of interior angles of a polygon is ...
-5
votes
1answer
72 views

Can anyone tell me how to factor this expression? [on hold]

...$\dfrac{2x^2-4x}{x+10}$ this is in response to a side splitting theorem question where these values are part of the proportions. Here is the complete question: We have 2 similar right triangles. ...
-2
votes
1answer
33 views

Proof involving circumradius of triangle and Law of Sines

Show that in any triangle, we have $ \frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right), $ where $R$ is the circumradius of the triangle. I'm not quite ...
2
votes
1answer
19 views

What is the solid angle of the intersection loop between a cone and an off-axis sphere?

An upright (green) cone with opening angle $2a < \pi/10$ has its vertex at point O with cartesian xyz coordinates $(0,0,0)$. The cone axis (dotted line) lies in the plane $y=0$ and is parallel to ...
-1
votes
1answer
27 views

Show that the midpoint of $AB$, $AC$, and $DE$ are aligned.

Let $ABC$ be a rod, $D$ and $E$ two points such as: $\vec{EC} = k \cdot \vec{EA} / \vec{DA} = k \cdot\vec{DB}$. How can I show that the midpoint of $AB$, $AC$, and $DE$ are aligned?