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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.

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 know why.

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 60N 030W to 60N 030W following a great circle. When 025W 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 coordinates.

Longitude Degrees at the Equator [09/09/1997]
What is the distance in miles between degrees of longitude at the equator?

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 puckering?

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 of 3?

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 looking at?

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 the triangles...

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 base.

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!

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