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- Name of Truncated Circle [12/29/2003]
What is the name of a rectangle with two rounded ends, like a circle
with top and bottom evenly truncated? For example, an 'oval' racetrack
with two straightaways on opposite sides, parallel to each other and
both of the same length. I know that's not really an oval, but I'm
not sure what else to call it!
- n-Dimensional Cubes [09/06/2002]
Define #(n,A) to be the number of corners of an n-dimensional cube
whose distance to 0 is greater than A. The limit (as n goes to
infinity) #(n,A)/(2^n) = 1. How would I verify the limit statement?
- 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.
- 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.
- 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?
- Pappus' Centroid Theorem [06/05/2003]
What is the formula for the volume of a circular torus?
- Parametric Form of Circle Equation [08/04/2003]
If I know the center and radius of a circle, and three points on the
circle, can I find the parametric form of the circle equation in 3D
- Parametric Sphere Formula [7/7/1996]
What is the parametric form of a circle in 3 space that passes through a
particular 3 points?
- 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 Intersecting Space [11/24/2001]
Can we say that n planes divide space into at most 2^n regions?
- 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).
- 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
- The Reflection of a Line [04/21/1998]
How can I find a vector equation of the reflection of a line in three-
- Resolving Pitch and Yaw [02/10/2003]
Is there an equation to find the resultant of pitch and yaw?
- Roll of Paper [06/15/2003]
I am getting a paper rewinder that runs 6,000 ft a minute, and the
roll is 50' high above the floor. How many miles and feet are there in
this roll of paper and how long will it take to run?
- The Second Octant [04/03/2002]
Where is the second octant? No one seems to know how to count the next
octants after the first.
- Sketching a Plane in Three Dimensional Space [11/15/2005]
I know that an equation like 2x + y + z = 3 represents a plane in
three dimensions. How can I sketch that plane on the xyz axes? Also,
how can I sketch a system of such equations to find the solution
- Small Section of a Sphere [01/10/2002]
Find the volume and the areas of each of the surfaces/faces of a small
section of a sphere with "dimensions" delta r, delta theta, delta phi, in
- Sphere Eversion [8/11/1996]
How do you mathematically turn a sphere inside out?
- Spherical Geometry [02/10/2003]
How do I calculate whether two lines that lie on the surface of a
sphere intersect, and if they do intersect, the point of that
- Spherical Polygon Area [08/09/1999]
Could you please explain the formula for the area of a spherical polygon,
and show how to determine the values of the thetas in it?
- Spherical 'Rectangles' [05/13/2002]
How can I find the 'spherical rectangle' defined by a pair of corner
- Steinmetz Solid [06/08/2003]
Two pipes (radius = r) cross each other normally. What is the common
- Surface Area and Volume Derivative [10/30/2000]
For what 3D figures is the derivative of the volume formula equal to the
formula for surface area? With respect to which variable would you need
- Surface Area of an Ellipsoid [02/11/1997]
How do you calculate the surface area of an ellipsoid?
- Surface Area of an n-dimensional Sphere [07/28/1997]
I was wondering how to calculate the surface area of a sphere in n
- Surface Area of a Sphere [10/03/1997]
How is the surface area of a sphere calculated, and why?
- Surface Area of a Sphere [04/10/1998]
Can you derive the formula for the surface area of a sphere?
- Surface Area of Cones and Pyramids [09/27/2003]
Can the method for finding the surface area of a pyramid be used as
well to find the surface area of a cone?
- Surface Area of Solid of Revolution [05/21/2001]
I tried to derive the formula for the surface area of a cone by taking
the integral the circumference of the solid of revolution, but it didn't
work. What did I do wrong? Can the formula be derived using this method?
- Tesseract [04/25/2001]
Why does a tesseract contain eight cubes?
- Tetrahedron Projected on a Plane [10/29/1996]
How do you project a regular tetrahedron perpendicularly onto a plane to
get the maximum area shadow?
- Tipped and Partially Filled Frustum [12/14/2003]
A vessel in a plant where I work is the frustum of a cone on its side.
A liquid is contained in this section and pours out the end of the
cone section, therefore the liquid only takes up a certain portion of
the cone's volume. How can I compute the volume of the liquid?
- Transformation between (x,y) and (longitude, latitude) [01/02/2002]
I have two questions on the transformation between (x,y) and (longitude,
- Two Polygons in 3D Space [01/31/2003]
How do you find the shortest distance between two polygons in 3D
- Understanding Fourth Dimension Figures [07/05/1998]
Can you help me figure out the equations for fourth dimension figures
such as the tesseract and the hypertetrahedron?
- Uniform Distribution of Random Points on a Sphere [07/14/2005]
Is there a method to pick random points on a sphere so that the points
wind up uniformly distributed on the sphere? I keep getting a higher
density of points near the poles.
- Using Longitude and Latitude to Determine Distance [4/17/1995]
I've been looking for the equation for finding the distance between two
cities, given the latitude and longitude of both cities.
- Variable Volumes in an Oblate Spheroid [12/21/2002]
We need to know how much water is in the tank at any given time.
- Vectors and the Volume of Parallelepipeds [03/08/2003]
Explain the derivation of the formula V = |a.(b x c)| (the volume of a
parallelepiped is equal to the magnitude of the scalar triple product
of the vectors that determine the parallelepiped; where a, b, and c
are those vectors).