# Questions tagged [geometry]

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

42,143 questions
Filter by
Sorted by
Tagged with
1answer
13 views

### Angles of an incircle

In triangle $ABC$, $\angle BAC = 72^\circ$. The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find $\angle EDF$, in degrees. I am currently taking ...
0answers
7 views

### Geometry vectorial

Hello i have a question, what's is the vector of this equation? Find the vectorial equation of this exercise. Contain the point (7, 3, 1) and intersect perpendicular to the rect (x, y, z) = (1, 2, 0)+ ...
0answers
19 views

### Integrating over a hypersphere surface

I have an $n$ dimensional hypersphere $S$ with radius $D$. Along one axis, I cut off the caps of the sphere at a position of $-a$ and $a$. I wish to find the remaining surface area of the hypersphere. ...
0answers
23 views

### Regarding an isometric drawing of a circle, how does this align perfectly?

In the above image, the circle is drawn as an isometric view. Why does it align well when we draw a six-pointed star? The radius of the larger arc is thrice the radius of the smaller arc. My question ...
1answer
37 views

### How can curves approximate curves, but lines cannot approximate lines?

This is my first question on StackExchange, and i have very little knowledge of mathematics to tell if it is a physics issue or a math issue, so any info will be useful. Main question Let's say i want ...
0answers
11 views

### How to rotate a vector to find its location in the image that has been rolled

I have a camera with the center of elevation/pitch:87.3837 roll:-0.5763 yaw/azimuth:-35.8876 and object with ...
0answers
36 views

### Circle problem intersecting

Two circles $C_1$ and $C_2$ pass through the centres of each other and intersect at $X$ and $Y$. Chord $YA$ of $C_1$ intersects $C_2$ again at $B$. If $AB= a$, radii $C_1$ and $C_2$ are $r_1$ and $r_2$...
0answers
21 views

### Conic sections appendix [duplicate]

My questions concerns a chapter in Michael Spivak's math book Calculus. On page 81, Spivak talks about finding a coordinate axes for a plane P that intersects a cone. What I don't understand is the ...
2answers
60 views

### Is this line uniquely determined?

Let $\alpha: x-y+2z-2=0$ and $\beta: x-2y-2z+3=0$ be two planes in $\mathbb{R}^3$. I am asked to find a line $d_1\subset \alpha$ such that $d_1$ is perpendicular on the line $\alpha \cap \beta$ and ...
2answers
36 views

### Conditions for existence of $k$ vectors In $\mathbb R^k$ with given pairwise angles $\theta_{ij}$

Given angles $0<\theta_{ij}<\pi$ for $1\leq i<j\leq k,$ what conditions are there on the angles to ensure that there exists $k$ unit vector $v_i\in \mathbb R^k$ so that the angle between $v_i$...
0answers
15 views

### Get a rotation matrix with euler angles without rotation matrix per axis

From this question, I managed to rotate vectors without euler angle rotation matrix. But I'm still struggling with the case which needs euler angles. I'm already aware of the rotation matrix something ...
2answers
98 views

### Geometric reason why this determinant can be factored to (x-y)(y-z)(z-x)?

The determinant $\begin{vmatrix} 1 & 1 &1 \\ x & y & z \\ x^2 & y^2 &z^2 \\ \end{vmatrix}$ can be factored to the form $(x-y)(y-z)(z-x)$ Proof: Subtracting ...
2answers
75 views

### Proof of equation resembling power of a point in triangle

I've tried this problem for a while now, and I'm stuck on it. Let $D$ be the foot of altitude $AD$ on side $BC$ of triangle $ABC$. Denote a point $N$ on altitude $AD$. Prove that this point $N$ is the ...
1answer
91 views

### Circle under tangents meets incircle at same point on BC

Inside $\triangle ABC$, let a circle $\omega$ be tangent to sides AB and AC, not touching BC. Tangents from B and from C to $\omega$ (different from the triangle sides) intersect at point X. Show that ...
1answer
38 views

### Find the area of rhombus $ABCD$

This is a problem for homework that I'm stuck on. [![enter image description here]] So far, I've only drawn the line $GA$ and found that it was $12$ but I haven't been able to find anything else....
1answer
21 views

### How to generate random velocity vectors that can only move an object forward within a valid arc?

I have an object with known coordinates in in 3D but on the ground (z=0). The object has a direction vector. My goal is to move this object on the ground (so ...
0answers
28 views

1answer
35 views

### Some questions involving two lines and two planes in $\mathbb{R}^3$

Let $d_1:\begin{cases} 2x+y-z=1 \\ x-z=2\end{cases}$ and $d_2:\begin{cases} x-y+2z=1 \\ x-y=2\end{cases}$ be two lines in $\mathbb{R}^3$. I have to find the plane $\pi_1$ that contains $d_1$ and is ...
1answer
27 views

### Proving that a square is made by connecting point-opposite midpoint in larger square

Below is a diagram of a square, where $E, H, F,$ and $G$ are the midpoints of the square. I want to prove that the smaller square formed by the intersections of $EC, FD, BH,$ and $AG$ is a square. So ...
0answers
12 views

### Surface area and volume for Minkowski sum

Let $K_1$ and $K_2$ two convex bodies in the euclideand space $\mathbb{E}^3$ (of dimesion 3): Let's denote the $V$ as the volume and $S$ the surface area I am looking for two thing(with reference): 1-...
1answer
50 views

### Construction of angle bisector of a given angle

Steps of Construction : Taking B as centre and any radius, draw an arc to intersect the rays BA and BC, say at E and D respectively [see Fig.11.1(i)]. Next, taking D and E as centres and with the ...
1answer
22 views

### Euclid's fourth postulate and cone points

In the following answer answer , Euclid's right-angle postulate excludes the existence of cone points: right angles at the vertex of a cone are smaller than right angles elsewhere on the cone. So ...
0answers
42 views

### If you know three angles in a triangle are equal (meaning each measure 60 degrees), does that mean the triangle is equilateral?

If you know three angles in a triangle are equal (meaning each measure 60 degrees), does that mean the triangle is equilateral? Meaning, if we know the three angles are equal, does that mean the sides ...
0answers
18 views

### Minimum cost required to cover a line with line segments.

We are given a line segment $[1, n]$ with $m$ smaller line segments $[l_{i}, r_{i}]$. An example being $[1, 4]$ and line segments ${[1,2], [2,3], [3,4]}$. We can cover this using first and third ...
0answers
67 views

### Determinant not equal to volume error (closed)

The determinant of a $3\times 3$ matrix $\begin{vmatrix} 1 & 1 &1 \\ x & y & z \\ x^2 & y^2 &z^2 \\ \end{vmatrix}$ is the volume of a parallelopiped with its three sides as ...
1answer
102 views

2answers
42 views

1answer
68 views

### Geometry Question about a triangle

I was sent this by a friend who could not solve it and I did the problem, and got the answer of 3/8 using similar triangles and then using areas perpendicular heights and bases. Can someone please ...
1answer
39 views

### Trying to create a 3D model of Kelvin’s Tetradecahedron / Tetrakaidecahedron polyhedra

How can I go about creating a 3D model / 3D image of a Kelvin’s Tetrakaidecahedron Cell / Tetrakaidecahedron. I planned on using Octave to 3D model an image it mathematically then convert that into a ...
0answers
68 views

### Minimum area binding box for set of points [closed]

I am writing some paper and stuck at proving that in min area binding box there needs to be 2 points on the edge of min rectangle. Every single time I make a new case I got that. By getting extreme ...
0answers
76 views

### Show that $\sin^2c = \sin^2a + \sin^2b$. True?? [closed]

The vertex $B$ of the triangle $ABC$ lies in the plane $P$. The plane of the triangle meets the plane in a line $L$. The angle between $L$ and $AB$ is a, and the angle between $L$ and $BC$ is $b$. The ...
1answer
51 views

1answer
31 views

### Triangle of least perimeter for a given area is the equilateral. [duplicate]

I want the opposite of this question, i.e., a proof that the equilateral triangle has the least perimeter of all the triangles with a given area. If possible I'd prefer an answer without Lagrange ...