In geometry, the truncated octahedron is an Archimedean solid. It has 14 faces (8 regular hexagonal and 6 square), 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a zonohedron. It is also the Goldberg polyhedron GIV(1,1), containing square and hexagonal faces. Like the cube, it can tessellate (or "pack") 3-dimensional space, as a permutohedron.
The truncated octahedron was called the "mecon" by Buckminster Fuller.Its dual polyhedron is the tetrakis hexahedron.
If the original truncated octahedron has unit edge length, its dual tetrakis cube has edge lengths 9/8√2 and 3/2√2.
Hi,
Suppose you have a truncated cone filled water with the lower radius being R, and upper r (R>r), and the height is H.
R, r and H is known so the volume, V, can be calculated using V=1/3*pi*H*(R^2+R*r+r^2). Now suppose you remove some water so that you end up with a lower volume, V1.
The...
I'm trying to find the local truncation error of the autonomous ODE: fx/ft = f(x).
I know that the error is |x(t1) − x1|, but I can't successfully figure out the Taylor expansion to get to the answer, which I believe is O(h^3).
Any help would be greatly appreciated!
This problem seems best treated in cylindrical coordinates. There is azimuthal symmetry, and there is no heat loss or generation within the cone, so our thermal conductivity equation reads:
$$\vec{q} = -k(\frac{\partial T}{\partial \rho} \hat{\rho} + \frac{\partial T}{\partial z} \hat{z})$$
We...
1.Data: We have an truncated cone with a volumentric charge density ρ, and it's uniform. The image show the truncated cone and show some info of the radios.
2. Question. We need to calculate the potential on the vertical axis.
note: adding an image of the problem but it's in spanish, hope...
Hello,
I am trying to find an expression for the signal-to-noise ratio of an oscillating signal on top some white noise. In particular I would like to know how the SNR scales with the integration time. It is well known that during some integration time ##T##, the SNR increases as ##T^{1/2}##...
Homework Statement
Consider the truncated cone tank submerged in water: inside the truncated cone tank there is air. Evaluate the forces acting on the truncated cone tank.
Homework EquationsThe Attempt at a Solution
The forces are the following
Boyuant force : $$F_b= \rho_w g V_{tank}$$...
Homework Statement
Homogeneous body with the shape of a truncated rotating cone has a base shaped like a
circle. The radius of the lower base is R2 = 8 cm and radius of the upper base is R1 =
4 cm. The height h = 8 cm (see figure). Calculate the total electric
resistance between the base...
Suppose that a given population is endowed with a pair of characteristics T and K. Let's think of these characteristics as random variables
(T,K)∼BiNormal((μT,μS),(σT,σS),ρ)
I observe the realisations of T for a sample consisting of those individuals with K<a, where the selection threshold a...
So say I have a truncated normal. That is, N(mu,sigma) that is from 0 to infinity only.
I need to find a Gamma such that a constant C*Gamma(A,B) is always above N(mu, sigma). How would I go about finding such a A, B that would work given fixed mu and sigma?
What is the mathematical formula to calculate "a" for a given "b" in the picture below of a tetrahedron with sides "b" inside of a truncated tetrahedron with sides "a". I think that this is a more challenging problem that what it appears to be.
I am trying to numerically calculate the electric potential inside a truncated cone using the finite element method (FEM). The cone is embedded in cylindrical coordinates (r,phi,z). I am assuming phi-independence on the potential, therefore the problem is essentially 2D; I am working only with...
Does anyone know how to find the area of an intersection between a cylinder of height 8 and radius 6 and a plane that passes through the cylinder, forming a chord of 10 units at the top and bottom faces of the cylinder? The area of intersection curves with the cylinder, forming a truncated...
So I'm currently trying to review a manuscript for my labmate, who I have good working dynamics with, and I've been slowly combing through the rough draft and find that many of the bar graphs he has in the manuscript have truncated Y axes. He claims to have statistical significance between...
Hello.
My friend said a truncated cone that is the upside down (the hole is open downwards) may be held in the air by a stream of water... How? It is really true?
Ok, consider a constant mass flow of water. How can I create a formula, which tell how high I have to place the cone? - (I want to...
Homework Statement
Consider a truncated cone as shown in the figure. the material of the cone is a dielectric with top and bottom electrodes of different radii. Now a potential difference is applied across the capacitor - by connecting it to a battery - let's say. This creates an electric...
The taylor series can obviously be truncated, because the coeffecient of each series gets smaller and smaller due to the factorial.
However this is not the case with the fouriers series, there is no obvious reason why the coeffecients should get smaller and smaller.
So my question is, what kind...
I don't have a ton of experience in numerical methods, so I'm hoping someone can help me out. Suppose I have a sequence of position data points for a car, but they've been truncated to integer values. I want to find the speed (derivative), but for speeds which are low relative to the time...
Hi,
In griffith's "Introduction to Electrodynamics" he indicates that a specific infinite series has a truncated form (the series and truncated form are given below)
And he says the reader can try to show that it indeed has that form...
Hi,
I have a question about basic statics.
I have heard from someone that the forces acting on a truncated cone in a hole of corresponding geometry is different from an ordinary block sliding down a wedge, since the normal force on one side of the cone will be affected by the normal force on...
Suppose that X is a random variable distributed in the interval [a;b] with pdf f(x) and cdf F(x). Clearly, F(b)=1. I only observe X for values that are bigger than y.
I know that E(X|X>y)=\frac{\int_y^b xf(x)dx}{1-F(y)}.
Moreover, \frac{∂E(X|X>y)}{∂y}=\frac{f(y)}{1-F(y)}[E(X|X>y)-y]
I...
This is something I remember as a standard problem given to college math and physics students ... I've been hunting for a model answer online but no luck: everyone is happy to do the cylinder on it's side or a truncated cone or the intersection of two objects with a lot of symmetry in common but...
I am very much confused and frustrated at this point and would just like to understand what I'm doing wrong... This program is supposed to calculate a truncated value of sine using it's series expansion beginning at i = 1. At values under 20 degrees it compares almost exactly with the intrinsic...
Homework Statement
I have an assignment to write a program for calculating the sine (and various other functions) using the method of truncated infinite series using DO statements. The DO statement is supposed to run until the difference between the current and last iterations are less than...
What data do you need to calculate the failure point of a truncated cone when it is under uniaxial stress acting downward on the cone? The cone will be under stresses of roughly 30 tonnes and probably constructed of plastic.
Thanks,
What data do you need to calculate the failure point of a truncated cone when it is under uniaxial stress acting downward on the cone? The cone will be under stresses of roughly 30 tonnes and probably constructed of plastic.
Thanks,
1. The problem statement
A truncated cone 30cm high is made of Aluminum. The dia at the top is 7.5cm, and 12.5cm at the bottom. The lower surface is maintained at 93 deg C, the upper surface at 540 deg C. the other surface is insulated. Assuming 1 dimensional heat flow, calculate the rate of...
Hi,
I'm a biology PhD student looking for some help on how to calculate (or estimate) the surface area of an ellipsoid truncated parallel to the long axis. Any help would be greatly appreciated.
Thanks,
Murphy24
Hi, all,
I am having a problem in calculating a randomly truncated pdf. Let x be a random variable, it's pdf f(x) is known. Let t1 and t2 be anther two random variables, their pdf f(t1) and f(t2) are known as well. Now, how do I compute the pdf f(x|t1<x<t2)?
Thks a lot.
Homework Statement
Let G be the group of rotational symmetries of the octahedron and consider the action of G on the edges of the truncated octahedron.
Describe the orbits of this action.
Choose one representative element in each orbit. Describe the stabilizers of these representative...
Homework Statement
derivation of the centre of mass of the truncated sphere
Homework Equations
The Attempt at a Solution
i tried to solve it with triple integrals but i failed to figure ut the integral limits
a) Write a Matlab function, which accepts the following inputs
-a finite set of Fourier series coefficients
-the fundamental period T of the signal to be reconstructed
-a vector t representing the times for which the signal will be reconstructed.
This function should produce an...
In quantum optics and bose-einstein condensates, this is a well known technique
however, i still cannot grasp its essense.
in bec, what is its advantage over the gross-pitaevskii equation?
Homework Statement
So there's about 4 problems that iI just don't understand. The first one is called H20 in the S-K-Y.
Theres a drawing and it kind of looks like a graduated cylinder with a circle on top. It says the spherical top holds a little over 54,000 gallons of water, the base of...
Please I need a respectable proof how to get the volume of the truncated cone. I need it really quick. So please could you help me. No numbers just "the method" how to get that formula. Thanks.
Ok i need to calculate the work done by gravity , while filling a truncated cone of bottom radius R and upper radius r (R>r) and height H , with sand of density 'd' , if we start filling the cone from bottom..
What i did was , I considered a disc of radius 'x' as a part of the cone and with...
I have been presented with this problem. I somewhat know what I need, I just don't know how to get it :blushing:
The problem:
A truncated cone, top diameter of 1m bottom diameter of 1.5m and a height of 10m. With a given density(I do not have it with me at this moment, I do not remember...
Alright... I've been struggling with this derivation for QUITE some time, and I can't get a hold of my TA... so...
I'm trying to derive the centre of mass of a truncated sphere. The final answer is cm= -(3h^2*(R-h/2)^2)/(4R^3-3Rh^2+h^3) Where R is the radius of the full sphere, and h is the...
Hi, I'm having trouble doing this problem:
A truncated conical cylinder of graphite (bulk resistivity \rho = 1/\sigma ). The top of the cylinder has radius r = a, the bottom has r = b (b>a). Find the effective resistance between top and bottom of the cylinder. Show that the expression reduces...
Not sure if this is the proper place fir this but here goes:
I'm trying to figure out a way to computationally construct a lattice such that each lattice point is the center of the faces of a truncated octahedron which is tesselated through out space. The main problem is that I need to be...