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Browse College Coordinate Plane Geometry

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Card Stacking Problem, Redux [01/31/2017]
A teen seeks clarity on the induction steps that underpin the gravity-defying conundrum of objects balanced over an edge. By switching from torques to centers of mass, Doctor Rick works up an explicit treatment of the recursion often left as an exercise to the reader.

Barycentric Calculus [01/06/1999]
How does barycentric calculus compare with trilinear or cartesian calculus?

Coordinate/Analytic Geometry and the Pythagorean Theorem [6/8/1996]
Is it possible to use the methods of coordinate geometry for proving Pythagoras' theorem?

Degrees of Freedom [12/17/2002]
What is meant by 'degrees of freedom'?

Finding Area Using a Determinant [05/25/2007]
Given two vectors defining a parallelogram, the area can be found using the determinant of the 2x2 matrix representing those vectors. I can't figure out why that works. Can you explain it?

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?

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.

The Jumping Frog of Coordinate County [11/03/2009]
A frog starts at (0,0) and always jumps a distance of exactly 1 unit to a point with rational coordinates. Show that it is possible for the frog to reach the point (1/5,1/17) and not to reach (0,1/4).

Overlapping Polygons [06/10/2003]
Given all the coordinates for two different polygons in an x,y plane, how can I determine whether the polygons overlap?

Points within a Given Distance on a Sphere [07/25/2004]
I have a table of US cities with the latitude and longitude of each. I need to be able to find all cities that are within a given distance of a given city. I can have the computer compare each city to the given city individually, but that's tedious. Is there a faster way to do it?

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