The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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1answer
122 views

Give a geometric description of the following set of points

Give a geometric description of the following set of points: $x^2 +y^2 + z^2-8x+14y-18z>/= 65 $ So I completed the square and got the set to read: $(x-4)^2+(y+7)^2+(z-9)^2>/= 211 $ However ...
0
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0answers
52 views

can every object be represented mathematically?

I was just wondering if all 2D/3D objects/images/shapes could be represented by equations. For example, SpongeBob 2D curve and many more. How should I approach, as in, some theories that already exist?...
3
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2answers
72 views

Pizza Delivery along the shortest path

You are the Captain of the USS Gauss and you have been flying in the direction $2 i + j + k$ for quite awhile. You are currently at the point $(6, 3, 3)$. Your helper monkey Mojo just discovered ...
2
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1answer
39 views

rotation to quaternion matrix handeness

I've understand that quaternions do not have handness but rotation matricies derived from unit quaternions does. The following formula is given by wikipedia for quaternion to rotation matrix ...
4
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1answer
85 views

Complement of a knot that *isn't* rationally null-homologous

Let $K$ be a knot in a closed, oriented 3-manifold $Y$. It is a standard fact that if $K$ is (at least rationally) null-homologous, then $H_1(Y-K;\mathbb{Z})$ is isomorphic to $H_1(Y;\mathbb{Z})\oplus ...
0
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1answer
33 views

Trouble understanding solution to exercise

Given: Right tetrahedron, find $\angle \alpha$, between surrounding edge(not sure if this is the right term in English, but those edges is AD, BD and CD). and the plane of the base, and $\angle \beta$...
2
votes
4answers
154 views

Plane of intersection of two spheres

What is the plane of intersection of spheres $$x^2+y^2+z^2+2x+2y+2z+2=0$$ and $$x^2+y^2+z^2+x+y+z-\frac{1}{4}=0$$ I am not sure of how to do this, i just subtracted the two equations and i got a ...
0
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1answer
25 views

Calculating rotations required to

I have a situation similar to a question asked on StackOverflow with the following image: I have an object that rests at the tip of the green arrow (point XYZ), and I'm using the following formulas ...
0
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1answer
29 views

Geometry problem with rectangular parallelepiped

Given right angled parallelepiped $ABCDA1B1C1D1$, with bases $ABCD$ and $A1B1C1D1$, which are squares with side $1$. if $\angle (B1C;D1A) = 60^\circ$ find the length of the surrounding edge (I'm not ...
0
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0answers
30 views

Project 4 cones onto a sphere

I have four cones. The angle of each cones is 140 degree. I need to project it onto a sphere(place it ) such that, the cones cover the maximum area with minimum overlap. I initially thought that ...
0
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1answer
35 views

Trouble with understanding a solution to an exercise

Given right triangular prism $ABCA_1B_1C_1$, the surrounding edge(not sure if this is the right term in English, but the surrounding edge are $AA_1, BB_1, CC_1$) are equal to $\frac{\sqrt{5}}{5}$ and ...
1
vote
1answer
43 views

What is the initial velocity height of a projectile with destination vector D and gravity G?

I am doing a modification of Unreal Tournament 1999. Normally the game's jump pads' velocity applied to pawns that reach it's radius is defined by a velocity vector, which is a true pain to change and ...
1
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0answers
60 views

Given square pyramid, find all skew lines with line AB

Given square pyramid $ABCDE$, find all skew lines with line AB. Here is drawing: It's kind of obvious for me that those lines are $DE$ and $CE$, however I don't know how to prove it. Note: I can't ...
0
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1answer
37 views

Locus of a point on a variable plane

A variable plane passes through a fixed point $(a,b,c)$ and meets the coordinate axes in A,B,C.The locus of the point common to the planes through $A,B,C$ parallel to coordinate planes is? Ok I ...
2
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2answers
21 views

What does the homogeneous system of equations represent under certain conditions?

Consider the following linear equations $ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0$ 1) $a+b+c \neq o$ and $a^2+b^2+c^2=ab+bc+ca$ 2) $a+b+c \neq o$ and $a^2+b^2+c^2 \neq ab+bc+ca$ 3) $a+b+c =...
0
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1answer
20 views

For the points A,B,C,D is given that C belongs to AB, M belongs to AD and D doesn't belong to AB, prove that the plane (ABD) is the same as (CDM)

For the points $A,B,C,D$ is given that $C$ belongs to $AB$, $M$ belongs to $AD$ and $D$ doesn't belong to $AB$, prove that the plane $(ABD)$ is the same as $(CDM)$. Here is drawing: I tried to prove ...
0
votes
2answers
62 views

Coordinates of circumcentre of an isosceles triangle in 3D

I have an isosceles triangle in 3D and I need to find the coordinates of the circumcentre of this triangle. I know the coordinates of the three vertices. One method I thought of is to solve equation ...
0
votes
1answer
41 views

How to extract an equation from transformation matrix multiplication?

I am trying to rotate a point in a 3D space in the 3 axis together around a specific origin point. Unfortunately I can't use matrices in my application,All I can do is just the basic math operations (...
0
votes
2answers
57 views

Prove that if through three given points two planes can be drawn, then infinitely many planes throught these points can be drawn.

Prove that if through three given points two planes can be drawn, then infinitely many planes through these points can be drawn. I don't get how this is possible, since there is unique plane passing ...
0
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1answer
95 views

Text book on solid geometry/stereometry, without involving analytic geometry

As the title says I'm searching for a textbook, about solid geometry, without involving analytic geometry. The material which the book should cover is the stereometry learned in the eastern bloc. An ...
1
vote
1answer
63 views

Obtain plane equation from the rotating angles that generated it

Consider an $(x, y, z)$ system where positive $x$ points to the right, positive $y$ points upwards, and positive $z$ points outside of the screen. I create a new system $(x', y', z')$ by applying two ...
0
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1answer
31 views

Check Vector3 points on one line using a Matrix

I know that for 3 Vector2 points (say points a, b, c) the determinant of the following ...
0
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1answer
56 views

How to visualize a 3D region plot of an inequality easily?

I can't find the right way to think about the region plot of an inequality. Considering $A=\big\{ (x,y) \in \mathbb{R^2} \mid y<x+1 \big \}$, almost automatically I say: the points "under" the ...
2
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1answer
35 views

Prove that through every point in space, not lying on a given line, there exists a unique line parallel to the given one

Prove that through every point in space, not lying on a given line, there exists a unique line parallel to the given one. let's name the point $A$, the given line $a$, and the searched line $b$. I ...
0
votes
0answers
17 views

Creating 3D program, view becomes warped if turned

I'm creating a 3D program from scratch in Java, but have become stuck and need help with the math. The way the program works is essentially, there are a 'view from' and a 'view to' point. I use these ...
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2answers
102 views

How to proof that two lines in cube are perpendicular, without use of vectors

Given: Cube $ABCDA_1B_1C_1D_1$ Prove that $BD$ is perpendicular to $AC_1$ I don't have any idea how to proof this. Also I can't use vectors(we didn't study them in school). I can use all theorems ...
0
votes
1answer
54 views

What is lower limit condition of a surface of a tetrahedron?

$S_1$, $S_2$, $S_3$, and $S_4$ are the areas of the four faces. We know that a triangle has a condition for their edges $a$, $b$, $c$, so all edge length must satify $$|a-b|<c<a+b$$ or $$|a-...
0
votes
1answer
86 views

How to determine general form of line equation in 3D from 2 points without using vectors, matrices, etc

For a 2D line equation in General Form ($ax + by + c = 0$) it is possible to calculate all coefficients from two given points as follows: $a = y_1-y_2$ $b = x_2-x_1$ $c = (x_1-x_2) y_1 + (y_2-y_1) ...
0
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3answers
33 views

from m$^3$ to length, width, height of cube [closed]

Is it possible to calculate the length, width, height of a cube, based on just the m$^3$. For example if I have a cube with sides of $5$ meters: the m$^3$ is $125$ m$^3$. Is it possible to go back ...
0
votes
2answers
26 views

What is the length of one turn along the axis in strip winding?

In strip winding of a cylindrical surface like this What is the length of one turn along the axis? Or what is the distance between two similar points on consecutive turns along the axis of ...
0
votes
1answer
52 views

How to minimize the surface area taken by a cylinder?

In my math class, we are working on Geometric Optimization problems. We have to create an equation, and then solve for one variable, in terms of another variable. Then, using an expression, we find ...
0
votes
2answers
27 views

How to find if the point lies in which half of the tangent plane to a sphere?

Let $S$ be the sphere $$ x^2 + y^2 + z^2 = 14$$ Equation of tangent plane to $S$ at the point $P(1, 2, 3)$ is $$ \quad \quad x+2y+3z-14=0 $$ This plane divides the whole $3-D$ plane in $2$ halves . ...
2
votes
4answers
102 views

How to find an angle between two sides of cube?

Given $\text{Cube}\ ABCDA_1B_1C_1D_1$ Find the angle between $AB_1$ and $BD_1$ Usually I will find a parallel line which has common point with the other line, however I can't find such line in this ...
0
votes
0answers
25 views

Making a Net from a 2D Image

I'm trying to find the volume of the illustration Fig.1, I've taken a scale reference from the medium diameter of a strawberry and I’ve applied this scale to the remaining sides of the shape. Fig.1 is ...
0
votes
1answer
32 views

If a plane contains one line and intersects another one elsewhere, then the two lines are not coplanar

The straight line $a$ lies in the plane $\alpha$ , the straight line $b$ intersects $\alpha$ in point $M$. If $M$ doesn't belong to the $a$ prove that there isn't plane which contains the two straight ...
1
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0answers
25 views

Points in half space of tangent to a sphere

Given a sphere centered at the origin, with radius R, I want to find a point on the sphere such that the tangent to the sphere at that point divides the plane into 2 half spaces, such that the half-...
0
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1answer
36 views

Calculate position of object rotating around an axis

I have the value θ with range [0, 360] of the object rotating about the y-axis pictured below. Given a certain radius ...
-1
votes
1answer
37 views

Calculating a coordinate of a triangle on a 3D plane.

I've got stuck on quite a simple problem and not sure how to proceed. I have an unknown plane and it contains a point $M(5, 2, 0)$ in it. I also have a point $P(6, 1, -1)$ (distance to the plane is $...
1
vote
1answer
55 views

How to check if a 3 dimensional point lies in a Polygon with 4 vertices

Can anyone provide an equation to this problem? Given that I have a 3 dimensional polygon that consist of 4 vertices, how do I check if pointX lies inside that polygon?
0
votes
0answers
36 views

Producing a 3D Net from a 3d inspired image

Producing a 3D Net from a 2D Image I'm trying to find the volume of the illustration, I've taken reference from the medium size of a strawberry's diameter, I've applied this scale to the remaining ...
1
vote
1answer
80 views

Pove that the angle between planes in which origin lies is acute if $a_1a_2+b_1b_2+c_1c_2<0$

Suppose we have two planes $$a_1x+b_1y+c_1z+d_1=0$$ and $$a_2x+b_2y+c_2z+d_2=0$$ where $d_1,d_2 >0 \ or \ <0$ then prove that the angle between planes in which origin lies is acute if $$a_1a_2+...
2
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1answer
100 views

Finding points along a catenary curve

As I am no mathematician, I have been struggling to find an equation to accurately predict points spaced along a curve separated by distance d. Given two points in 3 dimensional space, assume a string ...
1
vote
1answer
180 views

Center of Arc with Two Points, Radius, and Normal in 3D

I'm struggling to get the math to work out on this. I need to derive an alorithm for a program where I'm representing geometric entities. In this case, it's an arc. I would like to create the arc ...
1
vote
1answer
47 views

The arctangent is a strange floating point number

I have 2 players in a game (Cod 4). I read X, Y, Z and store them in: ...
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0answers
14 views

How to graph polygon rising at an angle in 3D space from the origin of the coordinate axes with shaded region on the $x$-$y$ plane?

I am trying to obtain a graph just like this one that visually shows that an objective function is maximised in z-direction at a certain point and where the “ground” of the graph is the $x$-$y$ ...
0
votes
1answer
72 views

How to tumble a camera about a point

I'm trying to implement camera tumbling as described by this document. I have a camera that defines a view position and orientation. Additionally, there is a center of interest, which is a distance ...
0
votes
1answer
34 views

How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$

How to represent 2D lines (i.e. on $x$ and $y-axis$) on a 3D graph using either Cartesian ($z=f(x,y)$) or Parametric $(x,y,z)=f(u,v)$ Hi, I've been working on a Simplex problem and would like to ...
0
votes
1answer
28 views

Transform matrix to scale away from/towards an arbitrary plane in 3D space

I'm not entirely sure if this belongs in Mathematics or GameDev. I'm trying Mathematics first, so please let me know if it's in the wrong place. In 3D space, I have a plane ...
2
votes
2answers
74 views

How to prove that there can be infinite lines intersecting 3 skewed lines?

Few days back,I learnt somewhere in Mathematics Stack Exchange (don't exactly remember the question) that there can be infinite lines intersecting 3 skewed lines.But I'm not able to visualize or prove ...
1
vote
1answer
34 views

Reflection of a plane on a plane

How to find the reflection of the plane $ax+by+cz+d=0$ in the plane $a'x+b'y+c'z+d'=0$? I can't really think of a method of for doing so. I do know how to reflect a line on a plane though.That ...