Occasionally, people come to me when they spot a problem they want to solve and think it might be possible with the application of mathematics. This is really fun, because it lets me exercise that part of my brain and at least try to do some algebra from time to time. Continue reading Solving the Circles
Tag Archives: Math
My Alma Mater
I recently got the chance to go to Colorado Mesa University and sit on a panel of other graduates to talk about our current position and educational trajectory. This was a lot of fun for me for a few reasons, the least of which was not that, for me, talking to students and talking about my job are both a ton of fun. Continue reading My Alma Mater
A Solution for the Mathematically Inclined
The answer to my post last week is yes. Here’s the quick (intuitive) proof:
First, note that and is the surface of two spheres in three dimensions, and their intersection is either a circle or a point (we know they are not the same sphere since a and b are distinct and that they must intersect because we know p exists). If it is a point, then p is that point (and since we have not used gamma we have proved the hypothesis).
If the intersection is a circle, it intersects the plane containing a, b, and c at two points, but only one is inside the triangular prism, and that must be the point p. We know it cannot be a point not on the plane, since if it was, two points would satisfy , and not satisfy the uniqueness condition.
I personally prefer algebraic proofs though, so let’s crank some algebra! Continue reading A Solution for the Mathematically Inclined
For the Mathematically Inclined
I’ve been thinking about the following math problem lately (I occasionally get distracted by such things):
Suppose you have four points in 3D space, a, b, c, and p, where a, b, and c are distinct and non-colinear and their positions are known, and p is the unique point defined by the following:
- p lies in the interior of the triangular prism defined by a, b, and c that is perpendicular to the plane containing a, b, and c.
As an image:
If there is only one point satisfying the above criteria, can it be found without knowing γ? I plan on posting my proof next week Thursday, 2016-02-25.