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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.
- Knot Theory [10/24/1996]
What does Knot Theory actually describe and mean, what does it state
about knots, and what is its usefulness in real life?
- Lateral Area of Oblique Cones [05/27/1998]
Can you find a formula for the lateral/surface areas of oblique cones?
- Lateral Areas of Right and Oblique Circular Cylinders [06/03/2002]
Can you explain to me why the formulas for the lateral surface areas
of right and oblique cylinders appear to be the same?
- Lateral Surface of a Cone [02/10/1999]
How do you find the formula for the lateral surface of a right cone?
- Latitude and Longitude and Daylight Hours [09/21/1998]
Is there a formula for calculating the number of hours of daylight, given
the latitude and longitude of a point on the globe?
- Latitude and Longitude, GPS Conversion [12/07/2001]
What is the equation to convert latitude/longitude/altitude (LLA) data
into earth-centered/earth-fixed (ECEF) data?
- Latitude and Longitude of a Point Halfway between Two Points [10/10/2001]
I would like to know how to determine the latitude and longitude of a
point halfway between New York and Los Angeles.
- Length of a Nautical Mile at a Given Latitude [11/06/2002]
I am trying to work out a formula for accurately predicting the exact
length of a nautical mile at any given latitude, in metres.
- Length of Cable on a Reel [05/07/2003]
What is the formula used to determine the length of cable on a reel?
- Length of Coiled Belt [04/11/2003]
Working with conveyor belts we use a formula that gives a very close
approximation of the length of a coil of belt, but I would like to
- Length of Material on a Cylindrical Roll [6/21/1996]
Is there a formula for calculating the length of material on a roll
knowing the roll diameter, the core diameter, and the material thickness?
- Line of Sight Distances between Two Objects [01/27/2005]
An offshore drilling rig is being towed out to sea. What is the
maximum distance that the navigation lights can still be seen by an
observer standing at the shoreline?
- Liquid in an Elliptical Tank [02/28/1999]
Given any height of liquid, say 3 ft., how can I calculate the volume?
- Location of Plane Flying on Great Circle [11/20/2003]
An aircraft flies from 60°N 030°W to 60°N 030°W following a great
circle. When 025°W is passed, what will the plane's latitude be?
- Longitude and Latitude to Determine Distance [5/21/1996]
Using longitude and latitude to determine distance in rectangular
- Longitude Degrees at the Equator [09/09/1997]
What is the distance in miles between degrees of longitude at the
- Longitude-Latitude Product and Distance [02/14/2001]
Is the difference between the product of the longitude and latitude of
one point and that of another point related to the distance between them?
- Making Hemispheres out of Paper [07/28/1999]
How would you make a hemisphere from a piece of paper? Using triangular
wedges of 30 degrees?
- Making Labels for Cones [06/26/1997]
How do you make a label that will fit on a yogurt container without
- Mapping a Sphere to a Plane [11/28/2001]
Maps of the world are always distorted in some way when put on a flat map
instead of a globe. Why?
- Map Projections [04/26/1999]
Demonstrate the mathematics of creating a flat map of a curved object.
- Math in soccer [05/21/1999]
How is math involved in soccer?
- Maximum Difference, Longitude and Latitude [04/10/2001]
Find the maximum longitude and latitude difference between two points on
Earth 1000 kilometers apart.
- The Meaning of Space [07/23/1997]
Is the term 'Space' a mathematical object? I have seen it in "Vector
Space," "Banach Space," and "Hilbert Space," but are they the same thing?
- Mean Latitude/Longitude [07/10/2003]
Given three points on the earth measured in latitude/longitude, what
is the formula to calculate a mean latitude/longitude for this group
- Measuring 3D Curvatures and Angles [10/21/2001]
What are solid angles and how are they measured? How and in what units
can we determine the curvature of a sphere? What is the relation between
solid angles and the spherical curves they create when they intersect a
sphere whose center is the same as the vertex?
- Measuring Angles Using Steradians [2/8/1996]
How do you measure a solid angle by using steradians?
- Measuring the Area of a Region of Sky [05/30/2003]
When I look through my telescope, what percentage of the sky am I
- Medicine Cup Frustum [04/25/2002]
I have a frustum (medicine cup) and am required to give measurements
of 5ml, 10ml, 15ml, 20ml, 25ml, and 30ml.
- Minimizing the Surface Area of a Can [05/22/2000]
What coke can dimensions would use the least amount of aluminum while
still holding 375 ml?
- Miter Angle of a Pipe [02/10/1999]
Find the miter angle of a pipe of certain shape.
- Miter for a Pyramid [07/31/1997]
I want to construct a 4-sided pyramid out of glass for a garden fountain.
I need to know the degree of miter to put on the edges of the uprights of
- Moebius Strip [8/14/1995]
Dr. Math, I know what a Moebius strip is, but I forget how to define its
unique physical property. Could you please help?
- Moebius Strip [5/24/1996]
What would happen if you cut a moebius strip in half lengthwise?
- Moebius Strips: How Many Sides and Surfaces? [10/18/2001]
What is the difference between a side and a surface?
- Moment of Inertia of a Solid Cone [02/03/1999]
Find the Moment of Inertia of a solid cone in terms of its height and
- More on the Intersection of Two Lines in Three Dimensions [02/17/2009]
How to isolate for "a" in the vector equation a(V1 x V2) = (P2 - P1) x
V2, with a suggestion for computer coding.
- Movement on a Sphere, Charted on a Spreadsheet [11/20/2010]
A student seeks help coding a spherical navigation spreadsheet program. Doctor Vogler helps him
develop an algorithm that accounts for the trigonometry involved, with each drawing
on archived conversations.
- Multidimensional Calculus and Vector Geometry [02/09/1999]
The depth of iron ore can be approximated by a plane...
- 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!