Tetrahedron Definition and 77 Threads

I'm working through Advanced Calculus: A Differential Forms Approach at my leisure. In going over two-forms the notions of "flow across an area" and "oriented area" are introduced I hit a brick wall with grasping orientations, though, when asked to find the total flow into a tetrahedron. So...

Homework Statement Let points P1: (1, 3, -1), P2: (2, 1, 4), P3: (1, 3, 7), P4: (5, 0, 2)...form the vertices of a tetrahedron. Find the volume of the tetrahedron. Homework Equations V = 1/3 ah A = area of base h = height of tetrahedron The Attempt at a Solution I wanted to...

There is a big list of possible ways to tessellate space. But why just those 2 for 3 and 4 dimensions? http://en.wikipedia.org/wiki/List_of_regular_polytopes

Homework Statement Find the volume of the tetrahedron with vertices at (0,0,0),(1,0,0),(0,1,0),(0,0,1) The Attempt at a Solution I worked out the triple integral and found out that the volume is \frac{1}{6} ? Is this correct? I know there is probably a much quicker way working the volume...

Volume of Tetrahedron[Solved] My textbook opts to integrate with respect to y before x(dydx vs dxdy), so I assumed that it would not affect the outcome. I set the upper and lower bounds of y, respectively, as y = 24 - 7x/4 (from 7x+4y=96) to y = x/4 (from x = 4y). For x I set it from...

Homework Statement Imagine a planet in the shape of a regular tetrahedron (its surface consists of 4 equilateral triangles). Suppose that on each face there is a car traveling at a constant speed in clockwise direction along the edges bounding the face. Can they travel without crashing...

Find the volume of a tetrahedron under a plane with equation 3x + 2y + z = 6 and in the first octant. Use spherical coordinates only. The answer is six. x=psin(phi)cos(theta) y=psin(phi)sin(theta) z=pcos(phi) I've been trying to figure out the boundaries of this particular...

Homework Statement Four vectors are erected perpendicular to the four faces of a general tetrahedron. Each vector is pointing outwards and has a length equal to the area of the face. Show that the sum of these four vectors is zero. Homework Equations The Attempt at a Solution Let A, B and C...

Consider the tetrahedron which is bounded on three sides by the coordinate planes and on the fourth by the plane x+(y/2)+(z/3)=1 Now the question asks to find the area of the tetrahedron which is neither vertical nor horizontal using integral calculus (a double integral)? I think they mean...

Homework Statement what is the outward flux through one of the 4 triangular faces of a tetrahedron centered at the origin if the charge density is q*(delta)^3(r) Homework Equations The Attempt at a Solution So, I figured that all I had to do was find the point charge q that the...

i strongly thought that if we know every side of the tetrahedron,we can confirm its volume. but i just puzzled about how to find out the expression. please help me!

Commandino’s Theorem states that The four medians of a tetrahedron concur in a point that divides each of them in the ratio 1:3, the longer segment being on the side of the vertex of the tetrahedron. can someone put links below where about proof of this theorem thx so much

is silicon-oxygen tetrahedron(SiO4) stable or unstable? is there covalent or ionic bonding? Im not sure but i think it is stable and there's ionic boding. Silicon gives away one electron to every oxygen molecule making silicon a +4 ion and making each oxygen molecule have a charge of -1. b/c...

Homework Statement I have to find volume of tetrahedron that is bounded between 4 planes. Planes are x+y+z-1=0 x-y-1=0 x-z-1=0 z-2=0Homework Equations \vec{a}=\vec{AB}=(X2-X1)\vec{i}+(y2-y1)\vec{j}+(z2-z1)\vec{k} \vec{b}=\vec{AC}=(X2-X1)\vec{i}+(y2-y1)\vec{j}+(z2-z1)\vec{k}...

Homework Statement "ASSIGNMENT 1 The Methane Molecule Introduction: The methane molecule CH4, composed of four hydrogen atoms and one carbon atom, is shaped liked a regular tetrahedron. The four hydrogen atoms are on the vertices and the carbon atom is at the center. What is the angle...

Homework Statement [FONT="Courier New"] Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1,0,0), (0,2,0) and (0,0,3) Homework Equations [FONT="Courier New"]V=∫∫∫dV [FONT="Courier New"]...D The Attempt at a...

I wish to drill four evenly-spaced holes in a ball. How do I form my construction lines so that my marks are accurate? Obviously, if I could circumscribe a tetrahedron inside (or outside) the ball its vertices (or face-centres) would mark my holes. But I can't do that. I need to scribe my...

Question Statement: Each surface of a tetrahedron ABCD is an equilateral triangle with each side 2 units long. The midpoint of AB and CD are L and M respectively. Calculate, by giving your answers correct to 3 s.f. or to the nearest 0.1 degree, a) The length of the perpendicular from A to...

Here's the problem: A regular tetrahedron is a three-dimensional object that has four faces, each of which is an equilateral triangle. Each of the edges of such an object has a length L. The height H of a regular tetrahedron is the perpendicular distance from one corner to the center of the...

Find the volume of "A tetrahedron with three mutually perpendicular faces and three mutually perpendicular edges with lengths 3 cm, 4 cm, and 5cm." This is how I visualized it: http://img282.imageshack.us/img282/9466/calculus31re.th.jpg The area of a triangle along the x-axis is: A(x) =...

i have the point P(x0,y0,z0) i need to find the minimal volume of a tetrahedron which is constructed by a plane which crosses over point P, and by the axis planes. i got that the side of the tetrahedron is sqrt[(x-x0)^2+(y-y0)^2+(z-z0)^2], but I am not sure it's correct because then the...

There is ABCD tetrahedron with inscribed sphere. S is a center of the sphere, radius of the sphere equates 1 and SA>=SB>=SC. Prove that SA>(5)^(0,5). I can't solve it. Could anybody help me?

why NH3 is arranged as a tetrahedron rather than arranged like the earth(N) is surrounded by 3 satellite(H)? O=C=O If is +ve, then it is repelled at its position but it will be attracted if it is at the position of . Why CO2 is still considered as a non-polar molecule? is exactly...

Check the Stokes' theorem for the function \vec v = y\hat z Here it is over a tetrahedron. Stokes' theorem suggests: \int_s {(\nabla\times \vec v).d\vec a = \oint_p\vec v.d\vec r For the right hand side I computed the line integral from (a,0,0)--->(0,2a,0)--->(0,0,a)--->(a,0,0); which...

Determine whether the points A = (1, 2, 3), B = (1, 1, 1), C = (1, 0, 2), and D = (2,-2, 0) are coplanar and find the volume of the tetrahedron with vertices ABCD. My professor did this problem in class as a review for an upcoming test and he didn't get the answer that was on the key. He...

Archived thread "Volumes of Regular Icosahedron and Regular Tetrahedron" Hi, The above-referenced thread is at this url address: https://www.physicsforums.com/archive/t-3876 I have something to add, having worked with this structure, in a bit of a different way, however, than is spoken...

Please teach me. Is one Regular Icosahedron equal to twenty Regular Tetrahedrons ? If the edgelength of both Regular Polyhedras is 1, What would be their volumes ? Can we prove (or disprove) the equation below ? volume of Regular Icosahedron = 20 * volume of Regular Tetrahedron...