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 TOPICS This page:   higher-dimensional   geometry    Search   Dr. Math See also the Dr. Math FAQ:   geometric formulas Internet Library:   higher-dimensional   geometry HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Higher-Dimensional Geometry Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Do cones or cylinders have edges?     Latitude and longitude.     MaximizIng the volume of a cylinder. Names of Parts of a Cone [8/2/1996] Are the components of a net of a cone called faces in all cases, or only for polyhedra? Nearest Point on a Great Circle [05/27/2002] Given points A, B, and C on the surface of a unit sphere, find the point P on the great circle defined by A and B that is nearest to C. Number of Equations Needed in a Simultaneous Linear System [10/29/2003] Could you tell me why we need the same number of equations as variables in order to get a unique solution to a system of simultaneous linear equations? Number of Faces of a Cylinder and a Cone [1/29/1995] If you have a cylinder, how many faces does it have? What about a cone? Numerically Equal Volumes and Surface Areas [06/04/2001] Find all rectangular solids with integral dimensions, the volumes and surface areas of which are numerically equal. Obtaining Bearing from a Velocity Vector [08/01/2001] I have the x, y, and z components of a velocity vector of an airplane, and must use this vector to calculate the bearing of the plane. Oil Can Dimensions [12/11/2001] What are the dimensions of an oil can with a one-liter capacity that uses the least amount of tin? One Degree Latitude, Longitude: How Many Miles? [04/02/2002] Approximately how many miles are there in one degree of longitude and one degree of latitude in the states of Kansas and Oklahoma? Optimization [11/26/1996] To make a funnel, we take a circular piece of metal, cut out a sector, and connect the two radial edges together to make an open cone. What should the angle of the sector be to maximize the volume of the cone? Order of a 3D Triangle [08/29/2001] If I visit the vertices of a 3D triangle in order going from a to b to c, am I going clockwise or anticlockwise? Packing 4 Spheres Into a Tetrahedron [09/03/99] How can I find the dimensions of the smallest tetrahedron that can serve as a container for 4 spheres packed as snugly as possible? Packing Pennies in a Jar [06/08/1999] If a jar has a height of 11" and a radius of 7" and is full of pennies evenly to the top, how many pennies can fit in it? Packing Spheres [08/16/1999] How many 1.68-inch-diameter spheres fit into a 96.3-cubic-foot space? How many 1.68-inch-diameter spheres would fit into a 96.3-foot- diameter sphere? Painting a Column [07/13/1997] If I have a column 9.5' long and 8'' in diameter, how do I figure out how much paint I need to cover the outside area? Painting Bell Towers [6/3/1996] I need to know the total surface area of three domes with assorted radii. Paper Patterns for Building Cones [11/03/2003] How do you create a paper pattern which can be rolled up into a cone that is 72 inches long and 26 inches in diameter at the open end? Pappus' Centroid Theorem [06/05/2003] What is the formula for the volume of a circular torus? Parallel Lines [12/31/1998] What are some ways of proving lines parallel - geometrically and algebraically? Parallel Lines, Concentric Circles [04/24/2003] If parallel means that two lines never intersect, would the lines that form a circle drawn inside another circle be considered parallel? Parametrics [12/18/1996] You're in 3-D space at point A, you want to get to point B, and you know the coordinates to point B from point C (but B is moving). What heading do you need to set in order to meet point B? Parts of a Cone [04/18/2001] Does a solid cone have any edges? Passing a Larger Cube Through a Smaller One [09/25/2003] How is it possible to cut a hole through a solid cube so that a cube, larger than the original, can be passed in one end and out the other? Pattern for Lampshade [02/17/2001] I would like to know the formula for computing the surface area of a lamp shade so that I can make a pattern from it. Planar Approximation: Latitude and Longitude [04/18/2003] I am trying to calculate the midpoint between cases of legionella and their nearest neighbor. How can I calculate the distance between two points below which they can be treated as if they were in a plane rather than on a sphere? Planes between Planes [04/02/2001] How can I find if a plane lies between two other planes? Planes Intersecting Space [11/24/2001] Can we say that n planes divide space into at most 2^n regions? Polyhedron inside Sphere [5/24/1996] How long do the sides of a dodecahedron have to be to fit into a sphere of diameter 2.9 m? Proof for Volume of a Segment of a Sphere [11/19/2001] I am in need of assistance in proving the volume of a truncated spherical cap (or a segment of a sphere I think it is also called). Proportions of Exact Enlargements [03/18/1998] How are two objects related if one is an "exact enlargement of the other"? Pyramid Construction [05/24/1997] How do you figure out the angles necessary to construct a pyramid out of plywood? A 'Pyramiddle' Tent Problem [07/12/1999] Figure out an equation that yields d when values for h and r are inserted. A Pyramid of Layered Marbles [06/02/1999] How can I find the number of layers, the number of marbles, and the size of a container containing a pyramid of layered marbles? Pyramids and Triangular Prisms [05/09/2000] What's the difference between a pyramid and a triangular prism? Radius of a Sphere [01/29/1998] What is the ratio of the areas and volumes of two spheres, one with radius 3 times the other? What possible theorems are suggested? Radius of a Tennis Ball [04/03/2001] How can we find the radius of a tennis ball without cutting it open? Radius of the Earth as an Ellipsoid [06/26/2000] I have been given two equations to determine the radius of the earth for a given latitude, based on ellipsoid model WGS84. I get different answers... Ratio of Volume to Surface Area in Humans [12/09/1999] What is the healthy ratio of volume to surface area for humans? Ratios and Geometry [10/29/1998] An airplane flying at 33,000 feet has a visibility of 100 miles. What percent of the total land area to the horizon is visible? Rectangle Needed To Make Cone [9/5/1996] I want to make a lampshade by rolling a piece of paper into a non-closed cone shape... Rectangles Inscribed in a Dodecahedron [06/19/1999] What is the equation for determining the size of the rectangles inscribed within a regular dodecahedron? Page: []

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