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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.

A Rectangular Prism [11/26/1995]
Is it possible to have a rectangular prism that has a volume greater than its surface area?

Relative Motion on Face of Earth [05/06/2007]
If I am traveling along the earth's surface at the same rate of speed that the earth is rotating in the opposite direction then would I appear to not be moving if you watched me from space?

Resolving Pitch and Yaw [02/10/2003]
Is there an equation to find the resultant of pitch and yaw?

Resources on 3D Surface Plots [9/12/1995]
I would appreciate it if you would let me know of any databases or handbooks on the Internet for 3D surface plots of equations z=f(x,y,...).

Rhumb Lines and Great Circle Routes [09/24/1998]
Can you explain great circles and rhumb lines and how they relate to shortest distances in geometry?

The Role of Postulates [03/29/2003]
Who decided what were postulates and what were theorems? Why is it okay that postulates aren't proven?

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?

Same Surface Area and Volume [03/28/2001]
How can I find two objects of the same type of shape with the same surface area but different volumes? For example, two rectangular prisms or two cylinders?

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.

Segment of an Ellipse [09/06/2001]
We often use horizontal oval tanks for storing drinking water and fuel, and we would like to be able to calculate the contents.

Setting Sun [5/19/1995]
A fellow Naval retiree and I have been discussing whether the sun appears to set faster at the horizon near the equator than it does in the northern latitudes...

Shared Points on Concentric Circles [03/11/2004]
Can two concentric circles share only a few points? If they are concentric and they have the same radius, they would share all of their points, and if they don't have the same radius they will share no points. It seems like it's all or none.

Shortest Distance between Points [01/17/1998]
I am doing a project on the shortest distance between two points via another plane. I need help with my theorems.

Similar Pyramids and Measurement Ratios [08/10/2002]
The volumes of two similar pyramids are 27 and 64. If the smaller has lateral surface area of 18, how would I find the lateral surface area of the larger one?

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 geometrically?

Skew Axis? Cue Pappus [07/19/2015]
How do you calculate the volume of a solid of revolution generated around a skew axis? Doctor Anthony leans on Pappus' Theorem.

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 spherical coordinates.

Spaces Formed by Intersecting Planes [07/19/1998]
Do you know of a proof that would be used to show how many spaces can be formed by the intersecting of five planes in space? n spaces?

Sphere Equation Variables [08/21/2001]
In the standard equation: r^2 = (x-h)^2 + (y-K0^2 + (z-l)^2 ...what do the points h, k, and l represent?

Sphere Eversion [8/11/1996]
How do you mathematically turn a sphere inside out?

Sphere Formulas [03/26/1997]
What are the formulas for area and volume of a sphere?

A Sphere in a Cube [3/23/1996]
I have a cube of 200x200x200 and a sphere with a radius of 100 is inside it. I want to be able to put in x and y and using a formula get z.

A Sphere's Surface Area and Volume [12/17/1998]
What is the relation between a sphere's surface area and its volume? How does their ratio change?

Sphere Surface Area Precision [04/22/2003]
How can the formula 4*pi*r^2 for the surface area of a sphere be precise?

Spherical Triangles [10/26/1996]
Why can't you use the Pythagorean formula to measure the distance between two points on Earth?

Surface Area and Volume: Cubes and Prisms [05/27/1998]
What is the definition of surface area and volume? What are the differences and similarities between surface area and volume?

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 to differentiate?

Surface Area and Volume of a Sphere [08/30/1999]
Besides using integration, is there an intuitive way of seeing why the surface area of a sphere = 4(pi)r^2 and the volume = (4/3)(pi)r^3?

Surface Area and Volume of a Sphere [05/16/2000]
Without using calculus, how can I show why the coefficient in the formula for the surface area of a sphere is 4, and why 4/3 is the coefficient in the formula for the volume of a sphere?

Surface Area and Volume of Cylinders [05/25/2001]
How do you find the surface area and volume of a cylinder?

Surface Area of a Cone [06/18/1998]
What is the formula for the surface area of a cone?

Surface Area of a Cylinder [9/25/1995]
What is the formula to calculate the surface of a cylinder with 25cm diameter and 20cm height?

Surface Area of an Egg [02/28/2001]
How do you find the surface area of an egg?

Surface Area of an Egg [07/20/2002]
How do I find the surface area of an egg?

Surface Area of an n-dimensional Sphere [07/28/1997]
I was wondering how to calculate the surface area of a sphere in n dimensions.

Surface Area of a Rectangular Solid [09/21/1999]
Can you find the surface area of a cube or other 3D rectangular object by calculating the area of the sides you can see and multiplying by 2?

Surface Area of a Right Circular Cone [9/5/1995]
Could you please tell me the formula for finding the surface area of a right circular cone?

Surface Area of a Right Cylinder [08/21/2001]
The problem in my book asked me to find the surface area of a right cylinder in centimeters with the dimensions given in meters.

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?

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