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Browse High School Higher-Dimensional Geometry
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Selected answers to common questions:
Do cones or cylinders have edges?
Latitude and longitude.
MaximizIng the volume of a cylinder.
- 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
- 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
- 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
- Pyramid Construction [05/24/1997]
How do you figure out the angles necessary to construct a pyramid out of
- A 'Pyramiddle' Tent Problem [07/12/1999]
Figure out an equation that yields d when values for h and r are
- 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
- 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
- Rectangles Inscribed in a Dodecahedron [06/19/1999]
What is the equation for determining the size of the rectangles inscribed
within a regular dodecahedron?
- A Rectangular Prism [11/26/1995]
Is it possible to have a rectangular prism that has a volume greater than
its surface area?