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Puzzle I found this puzzle in the G+ Mathematics community, courtesy of Paul Cooper. Solve the final addition: 50 + 60 + 90 = 380 30 + 40 + 60 = 330 90 + 60 + 70 = 350 50 + 90 + 30 = 10 70 + 30 + 20 = 370 40 +…
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[mathjax]I’ve recently come upon two probability problems with counterintuitive solutions. One I’d seen before and dismissed because I didn’t understand the write-up (mea culpa); the other is new to me. Born on a Sunday Puzzle: You are introduced to a randomly selected family that happens to have two children. If one is a girl that…
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A standard high school geometry textbook talks about congruence in terms of three types of objects: Line segments, angles, and polygons. Congruence is then defined in terms of measurable parameters: “Two figures are congruent if they have the same size and the same shape” (Carnegie’s Bridge to Algebra Student Text, 2008, p. G-9). Math Open Reference…
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Introduction [mathjax]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…
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The Golden Ratio [mathjax]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…
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[mathjax]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…
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[mathjax]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…
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[mathjax]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…
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[mathjax]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.…
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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…