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Browse College Higher-Dimensional Geometry

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Finding the Center of Three Latitude/Longitude Points [07/27/2005]
If I have three known points (lat/long), how do I get the center point in latitude/longitude coordinates?

Finding the Circumcenter of a Sphere [09/24/2003]
How can I find the circumcenter of a sphere given 3 points on the sphere, along with the radius?

Finding the Equation of a Globe [6/29/1996]
There is a globe that has 2 points given, P(-14/3/8) , Q(2/3/-16); the center of the globe C is on the line g...what is the equation of the globe?

Finding the Surface Area of Rocks [10/5/1995]
I am attempting to determine the surface area of rocks (8-12 mm diameter) I'm using in a bacterial incubation experiment. The closest reference I have found is to calculate the surface area of a sphere and use correction factor to estimate the surface area. Are there any citations I can look up?

Find the Bearing [01/17/2003]
Is there a formula to find the bearing of one point from another on a 2D map (or graph) just using normal co-ordinate systems?

Find the Cities [06/19/2001]
Given the latitudes and longitudes of Detroit, MI, and Miami, FL, find every city within 10 miles of a straight line between them.

Formula for Radial Latitudes and Longitudes [10/15/2002]
I want to make a radius search tool that returns all places based on latitude/longitude within a certain radius of a given place.

Formula for the Curvative of a Curve [10/10/2002]
Is there a formula or theorem I can use to convince someone who believes a wall has only side that there is another side to it?

Formulas for N-Dimensional Spheres [10/26/2000]
What is the next term in the sequence pi*r^2, (4/3)pi*r^3, ...? Would it be the formula for the volume of a 4-dimensional sphere?

Frustum of a Pyramid with a Rectangular Base [02/20/2002]
I am an engineer with a water treatment agency and need to figure the amount of water per foot of elevation in our reservoirs...

GPS Formula [11/27/2002]
How can I calculate the position from 3 points (or more) in latitude longitude format?

Great Circle Parametric Equation [05/25/1998]
How can you calculate specific points of a great circle on a sphere? Can you help me find the parametric equation?

How Far Do the Birds Fly? [08/12/2002]
I am a racing pigeon enthusiast, and one problem I wanted to solve for myself and others in the sport is how to calculate the survey distance our birds fly from point A to point B, where A is the release point and B is the home loft of a returning bird.

How Much Material on a Spool? [05/02/2007]
A reel of flat blade has an outer diameter of 1016 mm and an inner diameter of 508 mm. The blade thickness is 20 mm. Could you tell me the length of the blade and show me the formula for working it out?

Ice Cream Cone Problem [02/27/2000]
What radius of a sphere of ice cream placed in a cone of height h and base angle of 30 degrees will give the most volume of ice cream inside the cone, as opposed to above the cone?

Inclination of an Ellipse's Major Axis ... in Three Dimensions? [01/09/2011]
An astronomer seeks the least number of points required to uniquely determine an ellipse, given one focus at the origin, in order to subsequently calculate the inclination of its major axis. Doctor George outlines the method, simplifies it, reviews the astronomer's resulting JavaScript code -- then addresses an extension into three dimensions.

Information About Topology [11/12/1996]
Where can I learn more about topology?

Intersecting Circles in 3 Space [04/19/2006]
I have two circles defined by P1 = C1 + R1cos(t)U + R1sin(t)V and P2 = C2 + R2cos(s)U + R2sin(s)V. How can I find where they intersect?

Intersection Between Circle and Plane in 3D [05/03/2006]
I am trying to find the intersection point(s) between a circle and a plane in 3D space.

Intersection of a Hyperplane and an Ellipsoid [07/02/2007]
Is the intersection of an ellipsoid in R^p with a plane in R^{p-1} also an ellipsoid in R^{p-1}?

Intersection of Ellipsoid and Plane [05/04/2007]
I need to find the general equation of the ellipse resulting from the intersection of an ellipsoid and a plane. When I solve the system of two equations, I wind up with an xy term and need to know how to eliminate that from the final equation of the ellipse.

Intersection of Line and Triangle in 3-D Space [11/30/2003]
For a 3-D game, I need to determine if a given ray does or does not intersect (or pass through) a given three-sided polygon in space.

Intersection of Three Spheres [06/05/2003]
How do you find the intersection of three spheres?

Intersection of Two Spheres [10/13/2003]
How can I find the equation of the circle that results from intersecting two spheres?

Klein Bottle Intersection [11/04/2002]
I would like a detailed description of the intersection domain in a Klein bottle.

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 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?

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.

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?

Mathematics of Soap Bubbles [2/22/1995]
Do you know anything or can you direct me to someone who does know something about the mathematics of soap bubbles?

Maximum Difference, Longitude and Latitude [04/10/2001]
Find the maximum longitude and latitude difference between two points on Earth 1000 kilometers apart.

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 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?

Minimize Distance between 3D Point Sets with Rotation and Translation [07/15/2007]
I need to fit two sets of 3D points (a, b, c... n) and (a', b', c'...n') in such a way that the Euclidean distances between the point pairs (a,a'), (b,b') ...(n,n') is minimum. I can apply only rotations and translations but no scale changes.

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?

Monstrous Moonshine Conjecture [11/12/1998]
I've been reading about the monstrous moonshine conjecture. Can you explain more on the j function and the Monster Group?

Multidimensional Calculus and Vector Geometry [02/09/1999]
The depth of iron ore can be approximated by a plane...

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