The Mysterious Temporal Freeze

Pyramids clip artAlexandria Jones stepped into the huge tent that protected her father’s excavation site from the desert winds. She laughed to herself. It was like walking into a circus.

She knelt down to whisper in the ear of her faithful dog Ramus. “In this ring, grad students carefully brush away another layer of sand. In the next ring, the artist sketches every piece as it is found.” She waved her arm. “And over there, our flashiest attraction — drum roll, please — the photographers shoot each shard of pottery from every possible angle. But where is the Master of Ceremonies?”

Alex and Rammy found Professor Jones near the back of the tent, talking to another student. While she waited for her dad, she looked through an assortment of numbered artifacts that were ready to be packed and sent to the museum.

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Hints and Solutions: Patty Paper Trisection

No peeking! This post is for those of you who have given the trisection proof a good workout on your own. If you have a question about the proof or a solution you would like to share, please post a comment here.

But if you haven’t yet worked at the puzzle, go back and give it a try. When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.

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Puzzle: Patty Paper Trisection

[Feature photo above by Michael Cory via Flickr (CC BY 2.0).]

trisection

One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.

One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why.

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Geometry: Can You Find the Center of a Circle?

Is it possible that AB is a chord but NOT a diameter? That is, could circle ABC have a center that is NOT point O?

For the last couple of days, I have been playing around with this geometry puzzle. If you have a student in geometry or higher math, I recommend you print out the original post (but not the comments — it’s no fun when someone gives you the answer!) and see what he or she can do with it.

[MathNotations offers many other puzzles for 7-12th grade math students. While you are at his blog, take some time to browse past articles.]

Confession: I Am Not Good at Math

I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers. People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.

Apply logic to that statement. The conclusion simply isn’t valid. …

Update: This post has moved.

Click here to read the new, expanded version

2007 Mathematics Game

Are your students ready for a challenge?
The Math Forum: 2007 Mathematics Game will be a tricky one:

Use the digits in the year 2007 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial), along with grouping symbols, to write expressions for the counting numbers 1 through 100.

  • All four digits must be used in the expression.
  • Only the digits 2, 0, 0, 7 may be used.
  • Multi-digit numbers such as 20, 207, or .02 MAY be used this year.
  • The square function may NOT be used.
  • The integer function may NOT be used.

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