Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [solid-geometry]

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)

In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space. Reference: Wikipedia.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, cylinders, cones, truncated cones, spheres, and prisms.

924 questions
2
votes
1 answer

Inscribed spheres in irregular tetrahedra

Let $ABCD$ be an irregular tetrahedron, and let $K$ be the center of its inscribed sphere. Let $M$ be the center of the inscribed sphere of $KBCD$. Are $A$, $M$, $K$ necessarily collinear? I have trouble finding a simple counterexample. (Having a…
hmakholm left over Monica
  • 286,031
2
votes
2 answers

Use cylinder's formula for frustum (conical frustum)

I know that frustum(conical) has a formula for its volume,i.e. $\frac1 3\pi h(r^2+R^2+rR)$, but why can't we place the average of two radii into cylinder's formula: $\pi(\frac{r+R}2)^2(h)$? I need the reason why I get wrong answer on doing this.
Harshal Gajjar
  • 1,664
2
votes
3 answers

what will be the angle at the centre?

Taken a tetrahedron of same edges, a point is taken inside it which is equidistant from all $4$ vertices, i.e if a sphere is made taking it as a centre, all the vertices will be on the sphere, now taking any two vertex and that centre (on the plane…
Myshkin
  • 35,974
  • 27
  • 154
  • 332
2
votes
0 answers

Proof of number of regular polyhedra

A polyhedron is a solid bounded by F plane faces, which meet in E edges and V vertices. You may assume Euler’s formula, that $V − E + F = 2$. In a regular polyhedron the faces are equal regular m-sided polygons, n of which meet at each vertex. Show…
Jake Stone
  • 209
2
votes
1 answer

minutes to fill a fountain

In a public square, there is a fountain that is formed by two cylinders, one with radius $r$ and height $h_1$, and the other with radius $R$ and height $h_2$. The middle cylinder fills and, after overflowing, starts to fill the other one. If $R= r…
Lambert macuse
  • 4,266
2
votes
2 answers

I need an algorithm that calculates the surface area of an unpredictably irregular object.

I'm developing a game that allows players to design their own star ships. The design system uses a cube grid for the player to lay out internal systems and decks, creating a wide variety of shapes that the program then skins with a variety of…
H. A. Harvey
  • 21
2
votes
1 answer

Geometry of a d10

A d10, in roleplayers' lingo, is a 10-sided dice. Several different shapes for this item exist, but the most common is that of two 5-sided pyramids with their equilateral bases lying on the same plane and offset by 36° (1/10, or half a side of a…
Zachiel
  • 129
2
votes
2 answers

Irregular tetrahedron problem.

If you are given all side lengths of an irregular tetrahedron (ie, for ABCD we know the lenght of AB and AC and AD and so on), and given the positions of three of it's vertexes - how do you find the position(s) of the fourth vertex.
Martin Welsh
  • 41
2
votes
1 answer

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 with six faces composed of congruent rhombi. You can see it…
Gary
  • 61
2
votes
0 answers

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 non-negative cost $\alpha$ for each edge (for…
Mark Fischler
  • 41,743
2
votes
2 answers

Uniform Polyhedron with 500 congruent right kite faces!

The diagram above shows a uniform polyhedron having 502 vertices exactly lying on a spherical surface, 1000 edges & 500 congruent right kite faces each having two unequal edges $a$ & $b$ given $b>a$. How to find out the ratio $\frac{b}{a}$ of…
Harish Chandra Rajpoot
  • 37,450
1
vote
1 answer

Compare light volume of two light bulbs with different degree spreads

I got two light bulbs, they are the same, but one spreads the light with an angle of 45 degrees, while the other 60 degrees. I have measured their lux from a height of 1 meter, starting right below the light bulb an, then measured again, walking 20…
gulbaek
  • 143
1
vote
2 answers

Point of tangency between plane and sphere

How can one find the point of tangency between a plane and a sphere in $\mathbb{R}^3$? The equations of the plane and the sphere are $x + y + z - 5 = 0$ and $(x-1)^2 + (y-2)^2 + (z+1)^2 = 3$ respectively. I realized that the distance between the…
user122677
  • 13
1
vote
1 answer

Icosahedron and dual dodecahedron coordinates and rotations

I'm trying to build a 20 sided die in Actionscript 3, like one in the picture. I figure the best way would be to make it out of 20 equilateral triangles rotated in 3D space. The vertices of the icosahedron's dual dodecahedron would be the centroids…
BladePoint
  • 137
1
vote
2 answers

finding the height of a prismoid

Imagine a prismoid container like the one pictured. I have poured water into it and I know all values of the resulting water prismoid - I know its volume, it's height, the areas of its bases, the area of the midsection and the angles of its…
morkfromork
  • 11
1
2
3 4 5 6