In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space. (Ref: http://en.m.wikipedia.org/wiki/Solid_geometry)

learn more… | top users | synonyms

5
votes
1answer
53 views

Find equation of plane given plane point

So I am given one plane point $M(5,2,0)$, also two points which are not plane points: $P(6,1,-1)$ distance to plane $1$, also point $Q(0,5,4)$ distance to plane $3$. How find equation of plane with ...
0
votes
0answers
13 views

Quasi-planar bifurcations - What constraints are required when generating the 3 angles?

I have a physical bifurcation where the parent vessel (V$_{12}$) is in the same plane as one of the daughter vessels (V$_{23}$). The other daughter vessel (V$_{24}$) is out of plane to both. $(x_1, ...
0
votes
1answer
57 views

In the tetrahedron what is $XY$?

In tetrahedron $ABCD$, $AB = 4$, $CD = 7$, and $AC = AD = BC = BD = 5$. Let $I_A, I_B, I_C,$ and $I_D$ denote the incenters of the faces opposite vertices $A, B, C,$ and $D,$ respecitvely. It is ...
0
votes
1answer
26 views

Solid Geometry. Finding an angle

$\mathrm{AB}=10$ and it intersects plane a. $\mathrm{A}$ and $\mathrm {B}$ are $2\mathrm{m}$ and $3\mathrm{m}$ far from the plane and the question is to find angle formed by plane a and $\mathrm{AB}$. ...
2
votes
3answers
62 views

To find the volume of a certain solid cone

A solid cone is obtained by connecting (with a line segment in $3$ dimensional Euclidean space ) every point of a plane region $S$ with a vertex not in the plane $S$ . Let $A$ denote the area of $S$ ...
1
vote
1answer
75 views

Volume of an octagonal dome

I need a way to find the volume of an octagonal dome. Can someone help me with the formula for that? Here's an example of the object I am trying to analyze
-1
votes
1answer
11 views

what are the symmetries and flags of tetrahedron?

I know that |rot(tetrahedron) | = 12 ( i know how we came up with this number ) my question what is the number of symmetries in tetrahedron ? is it 12 or 24? if is it 24 can anyone explain to me how ...
1
vote
3answers
55 views

Visualizing $180^\circ$ rotational symmetries of a tetrahedron

I am trying to learn about the symmetries of a regular tetrahedron. I understand the identity and all eight $120^\circ$ rotations that keep one vertex fixed, ...
0
votes
0answers
34 views

Is equal curved surface areas a coincidence

If we take a cylinder of height $2x$ and radius $x$, as well as a sphere of radius $x$, we notice that they have the same curved surface area. Also, if we take the frustum of a cone such that it has ...
0
votes
0answers
31 views

Problem regarding generators through principal elliptic section of $\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2} = 1$

The question is the following: Show that the generators through any one of the ends of an equiconjugate diameter of the prinicpal elliptic section of the hyperboloid $$\frac{x^2}{a^2} + ...
1
vote
1answer
34 views

point inclusion in a half-plane 3D

I have a 3D half-plane defined using a line segment an a point (as shown in picture taken from here). I am wondering how I can detect if a point belongs to the half-plane. Is there any way to ...
0
votes
2answers
60 views

Solid of Revolution Problem (semi-circular Groove turned into a Cylinder)

A groove, semi-circular in section and 1cm deep, is turned in a solid cylindrical shaft of diameter 6cm. Find the volume of material removed and the surface area of the groove. The problem is ...
0
votes
0answers
34 views

Arithmetic: mensuration

Image of problem In part three, the question asked for the surface area of the trough, which the formula should be the area of two segments with the addition of the area of the curved side of the ...
0
votes
0answers
27 views

The planes $\lambda x+y+z=\lambda-1,x+\lambda y+z=\lambda-1,x+y+\lambda z=\lambda-1$ form a triangular prism.

The planes $\lambda x+y+z=\lambda-1,x+\lambda y+z=\lambda-1,x+y+\lambda z=\lambda-1$ form a triangular prism.Then find the value of $\lambda $.And find the distance of the origin from an edge of the ...
0
votes
1answer
34 views

Let $OABC$ be a tetrahedron with edges and lateral edges given

Let $OABC$ be a tetrahedron with edges $BC=\sqrt2,CA=\sqrt3,AB=2,OA=\sqrt5,OB=\sqrt6$ and $OC=\sqrt7$.Let $G$ be the centroid of triangle $ABC$ and $M$ and $N$ be the midpoints of $OB$ and $CA$.Find ...
3
votes
2answers
569 views

What is the maximum volume of an equilateral triangular prism inscribed in a sphere of radius 2?

What is the maximum volume of an equilateral triangular prism inscribed in a sphere of radius 2? Since the volume of an equilateral triangular prism is $\frac{\sqrt3}{4}a^2h$,where $a$ is the side ...
1
vote
2answers
68 views

A cone with diameter $12$cm and height $8$cm. Find the volume of the inscribed Sphere.

A cone with diameter $12\ cm$ and height $8\ cm$. Find the volume of the inscribed Sphere. Can someone help me solve this maths problem?
3
votes
3answers
44 views

uncertain point in textbook's solution of a “distance from point to line” problem

We have a cube with each side equaling $1$ unit of length. We need to determine the distance from $B$ to the line $A_1C_1$ In my calculation, each side of the yellowish-shaded triangle equals ...
1
vote
0answers
89 views

Lateral area of oblique cylinder and cone

As following picture : I can find the lateral Area of right cylinder and cone. There spread forms are a rectangles and a circular sector. That's very easy. But in the oblique cases ? Are there same ...
1
vote
1answer
56 views

What is the intersective curve between sphere and a right cone?

I am confused this picture : What the curve is? I think that the curve is not circle and not the ellipse too, What is the intersective curve?
3
votes
1answer
286 views

Construct the intersection of a cube by a plane through $3$ points on its edges, no pair of which is on the same face

So this is a rather old problem, but I still cannot find a pure constructive solution to it. Please, do not offer me to write a plane equation, etc. I would be grateful, if you offer a solution by ...
2
votes
1answer
141 views

Given a solid angle, how do I calculate the surface area subtended by the angle on the surface of a sphere?

I am interested in calculating the elemental surfaces $dS$ (AF) and d$S'$ (EG), given that the solid angle of the very tiny cones' apex, $H$ are both dΩ. Knowing this will help me prove Newton's ...
0
votes
1answer
45 views

Finding the volume of oil in a cylinder which is lying parallel to the ground.

A cylinder of height 2 m and radius 2 m is partially filled with oil. When the cylinder is lying parallel to the ground the height of oil level is 1.5 m from ground. What is the volume of oil? How ...
2
votes
2answers
46 views

Dihedral angle Finding

I meet a wall while some problem solving. The wall is following question. There is a triangle ABC, The vertice A touch bottom plane and the distance from B, C to the bottom : BE = b, CD = c . When ...
6
votes
2answers
52 views

Integer Tetrahedra

The points $\{(0, 0, 0), (12, 27, 44), (48, 0, 20), (48, 0, -64)\}$ have the property that All vertices are on the integer grid, All edge lengths are integers and different $\{51, 52, 53, ...
0
votes
0answers
39 views

Tangent Sphere centers

For circles of Descartes, the "curvatures" or "bends" (1/radius) of four mutually tangent circles have the property that $$2 (c_1^2 + c_2^2+ c_3^2+ c_4^2) = (c_1 + c_2 + c_3+ c_4)^2$$ With the ...
2
votes
1answer
37 views

Coordinates of a rhombohedron

I have found this question (Coordinates for vertices of the "silver" rhombohedron.) which asks: "The "silver" rhombohedron (a.k.a the trigonal trapezohedron) is a three-dimensional object ...
3
votes
0answers
37 views

Ratio between subsegments of space diagonal of a cube

Let $ABCDEFGH$ be a cube where $ABCD$ is the ground face and $E$ is about $A$, $F$ above $B$, and so on. Consider the space diagonal $AG$, and call $P$ the orthogonal projection of $B$ on $AG$. The ...
1
vote
0answers
39 views

Pyramid with unit sides inside a cube

Let $ABCDEFGH$ be a unit cube with base $ABCD$. Let $P$ be the top of the pyramid with base $ABCD$ and all edges of length $1$. One has a standard 2-dimensional projection of this cube on the back ...
0
votes
0answers
960 views

Finding the base radius of the cone.

A solid cone has a lateral surface area of $100\pi$ square centimeters and a total surface area of $269\pi$ square centimeters. Find the base radius of the cone. I would need to find the radius or ...
3
votes
1answer
88 views

The Rhombohedron

I am trying to model a rhombohedron (using Blender) as a first pass to building Dürer's solid so I am trying to calculate the (x,y,z) values for a given side length 'a' and angle 'theta' (starting ...
3
votes
0answers
57 views

Stellating the Octahedron

I have a few related questions and I'd be happy to get some help with any one of them. Is the stellation of a polyhedron generally a 'messy' affair that involves trimming away portions of the ...
1
vote
0answers
60 views

Calculate the area of a solid of revolution

So the subject title is self-descriptive. My question is how can I calculate the area of a solid of revolution with the information below: ...
0
votes
1answer
169 views

Prove synthetically: projection of a circle onto a plane is an ellipse

I am wondering how I can prove synthetically that the projection of a circle onto a plane is an ellipse.
0
votes
1answer
33 views

Measure the slope of a triangle relative to a plane

Suppose I have a list of vertices that form triangles floating in space. How do I measure the slope of each triangle relative to a flat ground plane?
2
votes
0answers
17 views

Best hinged solids to enclose unit volume, if hinges are expensive

In three-dimnesional space, you are asked to construct a polytope (a geometric object with flat sides) enclosing a volume of $1$. The cost of the model is the sum of the areas of the faces, plus some ...
5
votes
0answers
75 views

Keplerian orbits and closest approaches to Earth.

This question arose out of a discussion on Space.SE, but I think it will appeal to mathematicians more than astronomers: Let's consider a small astronomical object following an ideal elliptic ...
7
votes
1answer
149 views

Smallest cylinder into which a regular tetrahedron can fit?

Given a regular tetrahedron (as shown) of edge length $b$, determine the diameter $d$ of the smallest right circular cylinder (pipe) of infinite length along which the tetrahedron can slide.
1
vote
1answer
101 views

Small Stellated Dodecahedron, generating triangle vertices

I have been trying to draw a small stellated dodecahedron (would post an image if I had enough rep) using OpenGL, and would like to generate the vertices programmatically. I'm looking for a way to map ...
1
vote
1answer
74 views

How to generate the icosahedral groups $I$ and $I_h$?

The icosahedral groups $I$ with 60 elements and $I_h = I \times Z_2$ are also three dimensional point groups. However, ever unlike other point groups, it seems there is rarely reference to give their ...
2
votes
1answer
43 views

Solve multiple tangencies in solid geometry

Given three spherical balls of known diameter D resting in contact on a plane, a cylindrical rod is lain across them and the height, h, from the plane to the top of the rod is measured. I want to ...
1
vote
1answer
58 views

logarithmic spiral around cone stump

Based on the answer on my previous question I managed to come up with the following equations: $$\begin{eqnarray} k &=& 1 \\ r_\Delta &=& r_b - r_t \\ r(\theta) &=& r_t * ...
3
votes
1answer
76 views

spirals around cone

I have multiple spirals running around a cone. The spirals are $$r_\Delta = r_b - r_t$$ $$x(z) = r_b \cos(z) - r_\Delta z \cos(z)$$ $$y(z) = r_b \sin(z) - r_\Delta z \sin(z)$$ $$d(z) = ...
3
votes
1answer
175 views

How to make an icosahedron from 20 tetrahedra?

To make an icosahedron out of Sierpinsky tetrahedrons is difficult because regular tetrahedra can't tile in space. The dihedral angle of a tetrahedron is ~70.53. So the first step would be to make ...
0
votes
1answer
29 views

Calculating the volume of a solid of revolution about a line.

A figure is formed by revolving the region bounded by $f(x) = \cos{(x)}$ and $g(x) = \sin{(x)}$ from $0$ to $\dfrac{\pi}{4}$ about the line $y=-1$. This figure is formed by integration of two ...
-3
votes
1answer
57 views

A problem about prism with triangular bases

Consider a prism with triangular base . The total area of the three faces containing a particular given vertex is $k$ . Then is the maximum possible volume of the prism $\sqrt {\dfrac {k^3} {54} } $ ? ...
1
vote
1answer
189 views

Find corners of a square in a plane in 3d space

I am given two angles (similar to theta and phi in spherical coordinates) from which I can calculate a normal vector to a plane in 3d space. I am also given the center point of the square and the area ...
0
votes
2answers
206 views

Questions on the relation of the axis of a cone to its conic sections

(1) Does the axis of a cone pass through the foci of any its conic sections? Consider the image below: Is the intersection of the axis of cone and the ellipse the same as the focus of the ellipse? ...
4
votes
0answers
62 views

Volume of intersection between two horn tori

While playing around in Blender, I recently stumbled across a certain shape. The shape is found by taking the volume shared between two identical horn tori rotated at right angles to each other: The ...
1
vote
1answer
35 views

Mathematical designation of a cuboid that has one or two edges with infinite length

Is there a mathematical designation for a cuboid that has one or two of its edges with infinite length (in essence, forming an infinite subset of the 3-D space)? This would be some kind of 3-D strip ...