Hints and Solutions: Patty Paper Trisection

Posted on by Denise Gaskins

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.

Continue reading Hints and Solutions: Patty Paper Trisection

Puzzle: Patty Paper Trisection

Posted on by Denise Gaskins

[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.

Continue reading Puzzle: Patty Paper Trisection

Geometry: Can You Find the Center of a Circle?

Posted on by Denise Gaskins

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

Posted on by Denise Gaskins

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

Posted on by Denise Gaskins

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.

Continue reading 2007 Mathematics Game