Pyramid Definition and 106 Threads

A pyramid (from Greek: πυραμίς pyramís) is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilateral, or of any polygon shape. As such, a pyramid has at least three outer triangular surfaces (at least four faces including the base). The square pyramid, with a square base and four triangular outer surfaces, is a common version.
A pyramid's design, with the majority of the weight closer to the ground, and with the pyramidion at the apex, means that less material higher up on the pyramid will be pushing down from above. This distribution of weight allowed early civilizations to create stable monumental structures.
Civilizations in many parts of the world have built pyramids. The largest pyramid by volume is the Great Pyramid of Cholula, in the Mexican state of Puebla. For thousands of years, the largest structures on Earth were pyramids—first the Red Pyramid in the Dashur Necropolis and then the Great Pyramid of Khufu, both in Egypt—the latter is the only one of the Seven Wonders of the Ancient World still remaining.

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  1. shivajikobardan

    How to print this pyramid pattern?

    How to print this pyramid pattern? I've built a matrix like this in order to generate logic. The "0" means spaces. At i=1, j=5 should be printed as star, rest as white spaces At i=2, j=4,6… At i=3, j=3,5,7…. At i=4,j=2,4,6,8… At i=5, j=1,3,5,7,9… How do I convert this into logic?
  2. I

    Physics of Water in the Closed System of the Great Pyramid

    Hello, I am working on a theory for a Great Pyramid power plant and I need some help understanding if my current hypothesis is even possible and how to calculate how much water will fill the upper structure. I believe the water system to work as follows: An aqueduct delivers a steady flow of...
  3. T

    Eating based on the food pyramid vs Mediterranean and no meat

    Hello all again. You might have heard or remember the food pyramid they would teach about in grade school, there is a Wikipedia article on it. I would prefer the latest updated version of that if its healthier then the Mediterranean food. I thought about switching to eating healthy using the...
  4. S

    Volume of pyramid formed by center of 5 spheres inside a hemisphere

    Let the radius of the small sphere = r 3r = 1 → r = 1/3 ##x=\sqrt{4r^2-r^2}=r\sqrt{3}## Volume of pyramid: $$=\frac{1}{3} \times (2r\sqrt{3})^2 \times r$$ $$=\frac{4}{27}$$ So m + n = 31, but the answer is 29. I guess my mistake is assuming line AB is tangent to the top sphere. How to do...
  5. neilparker62

    B Cross section (?) of Great Pyramid from drone footage

    Following is a frame carefully chosen from this drone footage. At about 0:29 into the video the drone is directly in front of one of the four faces (if you know Cairo, you will know which one) and moving from left to right. At that point I have paused and 'frame-stepped' till the moment before...
  6. M

    Area of interior triangle of pyramid normal to a side length

    This isn't homework, but I figured it's fine if I make it a HW problem and post here (if not, please let me know). Let ##z^*=0## be the vertex of the pyramid, and let ##z^*## run the altitude. It's easy to show the area of the base normal to the altitude is ##A = 4 \left.z^*\right.^2...
  7. A

    News The height of the pyramid of Cheops

    On the site https://www.wisfaq.nl/show3archive.asp?id=2537&j=2002 it is said that the ratio of the height of the Cheops pyramid (##a##) to the length of one side of the base (##a + b##) is equal to $$ \frac{2 \, (a + b) / Pi}{ a + b}= 2 / Pi = 0.6366197722$$ But if you use the golden ratio as a...
  8. E

    Volume Of Intersection Between Square Pyramid And Sphere

    I'm assuming the way to go about it is to integrate in spherical coordinates, but I have no idea what the bounds would be since the bottom edges of the square pyramid are some function of r, theta, and phi.
  9. L

    A pyramid of three cylinders (statics problem)

    Firstly the normal reaction force of the bottom cylinder is ##R## and because all three cylinders are identical ##2R=3mg##, and so the frictional force is going to be ##F_r={(3mg)/(2}{\mu})##. I don't use this, though. If the normal reaction force between the top cylinder and one of the bottoms...
  10. jaychay

    MHB Find Point D on Plane for 4 Unit Cube Pyramid

    Find point d on the line of r(t)=(0,0,0)+(−1,1,1)t which make the triangular pyramid abcd has the volume of 4 unit cube when a(0,0,0),b(1,0,1),c(0,1,0) are the points on the plane of −x+z=0.
  11. Amitkumarr

    To find induced charges on the edges of a right pyramid

    Due to symmetry of the system,when the frame is rotated to make the electric field point from corner A to corner C,the magnitude of charges induced on these-(AB,BC,CD,DA),(OA,OC),(OB,OD) will be equal(different for each group but same for elements in these groups). For the sign of induced...
  12. Z

    What happens if you put a sphere (ball) on the top of a pyramid?

    I was wondering what happens if you put a perfect sphere (a ball) on the top of a perfect pyramid. To which side will the ball fall and why? It is random? An if it is, does a pattern emerge after many attempts?
  13. A

    What is the formula for calculating torque in a rotating pyramid?

    torque=Force*radius*sin(theta) center of mass x direction = ( 0(6 x 10^9 kg)+ (118m)(6 x 10^9 kg)+ (236m)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 118m center of mass y direction = ( 0(6 x 10^9 kg)+ (140m)(6 x 10^9 kg)+ (0)(6 x 10^9 kg) )/(3(6 x 10^9 kg)) = 46.7 m radius = (118^2 + 46.7^2)^(1/2) =...
  14. Monoxdifly

    MHB [ASK] Find the volume of Pyramid in a Cube

    Given a cube ABCD.EFGH whose side length is 4 cm. If the point I, K, and J is dividing EF, FG, and BG to two equal lengths respectively, determine the volume of pyramid D.IJK! I think I can work out the pyramid's base area by deriving for the formula of equilateral triangle area. What I can't...
  15. J

    MHB Simpsons formula and the volume of a pyramid frustum

    Simpsons formula and the volume of a pyramid frustum Normally I consider myself quite adept in mathematics, but I simply lack the right idea and/or the mathematical creativity to solve this assignmenent: "Prove that the Simpsons formula V = 1/6 * h * (Ab + 4Am + At) can be used to calculate...
  16. P

    Force to lift a pyramid that is sitting in a water tank

    Homework Statement A pyramid weighing 4000 lb has a base 6ft square and an altitude of 4ft. The base covers an opening in the floor of a tank in which there is water 4 ft deep. Underneath the floor of the tank and on the water surface there is air at atmospheric pressure. What vertical force is...
  17. D

    What is the basis for beach erosion control methods?

    https://www.msn.com/en-ph/news/technology/egypts-most-famous-pyramid-has-a-mystery-power/ar-BBLlYJ5?ocid=spartanntp How true is this?
  18. S

    Centre of mass of a hollow pyramid

    Question: Calculate the centre of mass of a uniform, square-based pyramid of height H and base length B (taking the centre of the base as the origin). Hence, or otherwise, derive an expression for the centre of mass of such a pyramid with a pyramid-shaped hollow cavity (of height h and base...
  19. R

    Volume of smaller pyramid is less than the volume of the whole.

    I have a test coming up next week and while doing some practice questions I found one I can't wrap my head around. The question is: A pyramid (assume uniform density) is divided in two parts by a horizontal plane through its center of mass. How do the masses of the two parts compare ? There are...
  20. M

    MHB What is the application of Gauss theorem on a pyramid?

    Hey! :o Using Gauss theorem I want to calculate $\iint_{\Sigma}f\cdot NdA$, where $\Sigma$ is the closed boundary surface of the pyramid with vertices $(0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0)$ and $f(x,y,z)=(x^2y, 3y^2z, 9xz^2)$ and the perpendicular vectors $N$ to the inside of the...
  21. L

    MHB Is the Plane MKPN Possible Inside Pyramid ABCD?

    Good morning (or evening), I have a geometrical tricky question, which I need your assistance with. Look at the following sketch: In the sketch you see a pyramid ABCD. Inside the space of ABCD, you see a plane MKPN, where M, K, P and N are points on the pyramid sides. Using the axioms of...
  22. Kirito123

    Finding volume of Square pyramid

    Homework Statement Homework Equations V= a21/3 h The Attempt at a Solution I may be wrong or right I don't know. I'm pretty sure I did it right.
  23. G

    B Calculating Volume of an Arbitrary Pyramid

    I am trying to gain some understanding from this article regarding deriving the volume of an arbitrary pyramid. "An arbitrary pyramid has a single cross-sectional shape whose lengths scale linearly with height. Therefore, the area of a cross section scales quadratically with height, decreasing...
  24. F

    How many ping pong balls would fit into the Great Pyramid?

    The ancient Great Pyramid of Giza had a base of 230.4 meters, and a height of 146.5 meters. A ping pong ball has a diameter of 40 millimeters. The volume of the Great Pyramid = (b^2 x h)/3 = (230.4^2 x 146.5)/3 = 2,592,276 cubic meters. The diameter of a ping pong ball is 40 millimeters =...
  25. Dotini

    News A New Anomaly is Discovered in the Great Pyramid

    CREDIT: HIP INSTITUTE/PHILIPPE BOURSEILLER "We have several hypothesis but no conclusion for the moment," said Tayoubi. http://www.huffingtonpost.com/entry/pyramid-scan-anomaly_56417a19e4b0b24aee4ba9ad?ncid=txtlnkusaolp00000592&ref=yfp
  26. K

    Is there any pyramid like that?

    I had geometry quite a while ago and I wonder if anyone has any idea how to tackle this problem: Is there any ABCDS pyramid (where ABCD is a rectangle) in which each 2 edges have different lengths and |AS|+|CS|=|BS|+|DS| Thanks
  27. D

    Angle Elevation of King's Chamber in Pyramid: Get Answer Here

    I have posted this question in other forums and received nothing for an answer, So it's worth a shot here :-) What is the angle elevation of the king's chamber in reference to the base of the X,Y,Z center of the pyramid? Or should I ask the question this way? Measuring from the center of the...
  28. P

    Find the average height of a pyramid

    Homework Statement Homework Equations V = (1/3) * A * H [Volume of Pyramid] The Attempt at a Solution The first thing I did was to calculate the height of pyramid from the volume formula. I got a perpendicular height of 15. I'm not sure where to go from there. I'm under the impression...
  29. Y

    Constructing a 5-Sided Pyramid Die for Equal Probability

    I want to construct 5 sided dice in the shape of a square-based pyramid. When rolled, I want the die to have equal probability to fall on all sides. That is, I want the odds that the die would fall base down to be 0.2. I insist on a pyramid shaped die (not tetrahedron). Other solutions are not...
  30. B

    MHB Help with Geometry: Volume, Area and Perimeter of Pyramid

    Hello . I am in the end of my exams and i have to do a geometry figure like a pyramid ( view image ) below Now i should find the Perimeter, Volume and Surface of this figure . Lengths are all 5 cm, Can somebody find and write the Permiter,volume and surface for this figure please it's urgent...
  31. MarkFL

    MHB Calculus: Related Rates - Inverted Pyramid Filling w/ Water | Yahoo Answers

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  32. MarkFL

    MHB Radius of Sphere Inscribed in Square Pyramid: Michelle's Q&A

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  33. D

    MHB Volume of a Pyramid: Find A(z) to Calculate V

    I am trying to find the volume of a pyramid where the base has length \(L\) and width \(W\), and the pyramid has height \(h\). Let \(L\) be on the x-axis and \(W\) be on the y axis. In the x-z plane, we have the line \(z = -\frac{h}{L/2}x + h\), and in the y-z plane, we have the line \(z =...
  34. 0

    Center (in y direction) of Mass of 3D pyramid

    Homework Statement A monument is made from stone blocks of density 3800kg/m^3. The monument is 15.7m high, 64.8m wide at the base, and 3.6m thick from front th back. How much work was required to build the monument? (Hint: find ycm). Homework Equations ycm = (1/M) * ∫ydm, M = mass total...
  35. O

    What is the flux through each face of the pyramid?

    Homework Statement base of pyramid is a 6m x 6m square height of pyramid is 4meters. a 52 N/C E field orthogonal to the base of the pyramid Homework Equations EA cos theta The Attempt at a Solution if flux through base = EAcos theta = 52 (36m^2) cos(0) = 1872 N m^2 / C Area...
  36. K

    MHB Sustainability of pyramid scheme

    I’m about to get involved with a new affiliate program, before I market this I want to know that it is going to work. Pyramid (yes, it is legal; there is a product, merchant accounts used, taxes will have to be paid). 2x2 Forced Rotator Matrix with an Automatic Re-Entry at each level. 7...
  37. O

    Calculate the packing fraction of an FCC pyramid

    Homework Statement Solids consist of a crystalline lattice of atoms-a unit cell that has a certain configuration of atoms that is repeated over and over. The picture that I can't post here, shows a pyramidal structure of metal spheres. The base is 8 spheres by 8 spheres with a height of 8...
  38. MarkFL

    MHB Calculate Volume of Truncated Square Pyramid | Yahoo Answers

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  39. E

    Using calculus to derive the volume of a pyramid

    Homework Statement Use calculus to derive the volume of a pyramid The Attempt at a Solution There's probably a simpler way to go about this, but I wanted a challenge. I decided to calculate 1/4 of the pyramid in the first octant and then multiply my final answer by 4. First we have...
  40. Greg Bernhardt

    Mayan pyramid demolished for road fill

    Sad sad sad http://www.cnn.com/2013/05/14/world/americas/belize-mayan-pyramid-destroyed
  41. N

    Trigonometry 3d pyramid question

    Homework Statement http://imgur.com/x8D2wqO I need to solve for theta and I keep getting the angle 65, using cosine law and pythagorean theorem but the answer key says that the angle is 93. The diagram is not to scale. Is my answer wrong or is the answer key incorrect?
  42. D

    Integral of a triangular pyramid

    Homework Statement Find the volume of a pyramid with height 24 and with base an equilateral triangle with side 11. Homework EquationsThe Attempt at a Solution So I know the relationship h/x=b/l where h is my height 24 x is simply x or height above base b is my base 11 l is the length of the...
  43. D

    Alvarez's x-raying of the Gizeh pyramid

    I had a fascinating read about Alvarez "x-raying" the great pyramid in Gizeh in the 1960ies using cosmic muons: www2.lns.mit.edu/fisherp/AlvarezPyramids.pdf The technique has been refined and used even to make tomographies of a volcano in Japan. What I wonder: To obtain the direction of...
  44. M

    Medical Is intermittent fasting a healthy option for students with busy schedules?

    I am wondering if the old saying of having your pyramid of food is valid? Recently I have been discussing with people in the lab whilst waiting around for reactions to occur about nutrition and one guy said the old pyramid thing was a scam. Is he correct in his statement? I have not paid much...
  45. R

    What Are the Realistic Chances of Becoming a Professor with a PhD in Physics?

    I read this article in my latest physicsworld (a publication of the institute of physics), thought it's quite relevant to many of the discussions here. If you're a IOP member you can read it here: http://physicsworld.com/cws/article/indepth/2012/oct/04/the-academic-pyramid Here's what the rest...
  46. B

    Net Electrostatic Force of 4 Charges at a Regular Triangle Pyramid

    Homework Statement 4 identical charges each equal to Q are placed at the 4 vertices of a regular triangular pyramid of each side equal to 'a'. Find the net electrostatic force on anyone charge. Homework Equations F = kQ^2/a^2 The Attempt at a Solution find the force due to each...
  47. veronica1999

    MHB Find the Special Point of a Triangular Pyramid: Proof Explained

    Suppose that the lateral faces VAB, VBC, and V CA of triangular pyramid VABC all have the same height drawn from V . Let F be the point in plane ABC that is closest to V , so that VF is the altitude of the pyramid. Show that F is one of the special points of triangle ABC. I made the triangular...
  48. X

    What is the potential energy of a pyramid?

    Homework Statement The potential energy of a mass element dm at a height a above the Earth's surface is dV = (dM)gz. Compute the potential energy in a pyramid of height h, square base b x b, and mass density p. Homework Equations dV = (dM)gz V = 1/3 Bh - pyramid volume The...
  49. S

    Maximizing volume of a Square-Based Pyramid?

    Homework Statement I am given an 8in x 8 in piece of paper and I need to build a pyramid with a square base with the greatest volume. Homework Equations V = 1/3 * x^2 * h b = base length h = height length I'm trying to get everything in terms of x, which is the length of the base of the...
  50. A

    Maximizing the volume of a square Pyramid?

    Homework Statement I am given an 8cm by 8cm piece of paper. I have to cut out a square-based pyramid out of that that gives me the greatest volume. Homework Equations I know that the volume is V = 1/3 * b^2 * h b = base h = height I know that the surface area is A = b^2 + 2bh...
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