Introduction In my previous post, I included this image, which I’d made in GeoGebra. The image satisfies the conditions of the problem: \(AD\) is tangent to \(\odot P\) and \(\overline{BC} \cong \overline{AD}\). In order to create this image, I created a dynamic GeoGebra image where A, B, P and the radius of P can be…
Month: June 2014
The Golden Ratio and the Power of a Point Theorem
The Golden Ratio By definition, the Golden Ratio is a ratio involving overlapping line segments. Given collinear points A, B, and C, such that B is between A and C, if the ratio between the two subsegments is the same as the ratio between the entire segment and the longer segment, then that ratio is…
Schrödinger’s Brat and 3-Door Monte
The Monty Hall problem persists in Internet mathematics discussions, as if its results are somehow spectacularly unique or mystifying. Here is the problem: You are on a game show and are presented with three doors. Behind one door is some wonderful prize, and behind the other two is a goat (or something else of negligible…
Proof of the Power of a Point Theorem
I had to dig for a bit to find a complete proof for each part of the Power of a Point Theorem, so I thought it would be useful to compile my own proof. The Power of a Point Theorem states: Given a point P and a circle C, any line through P that intersects…
Math Needs Better PR
I was recently reading a book on Greenfoot, a Java-based GUI intended for teaching programming to high schoolers and college underclassman. In the “Newton’s Lab” project, the writer assuaged the reader who might be leery of the mathematics in that particular project. Remember, the reader was told: Programming can do a variety of things, including…
10 vs Ten
What does “ten” mean? Here are some dictionary definitions: The number 10. (MacMillan) The cardinal number equal to 9 + 1. (American Heritage) Equivalent to the product of five and two; one more than nine; 10. (Oxford) Superficially, these seem like comparably valid definitions: Ten is the number that comes after nine, that is, 10….
Intersecting Secants
In this entry, I’m going to be discussing how mathematicians tend to approach the world, and why we need better PR. I’m currently teaching High School Geometry. Here is what the book has to say about the “Segment of Chords Theorem”: “If two chords intersect in a circle, then the products of the lengths of…